Manual — unbundled WorkShop_5.0

Section (4)

Workspace command and file-change log

1. Commands (intro)

CC	Sun WorkShop C++ Compiler 5.0
CCadmin	clean the templates database; provide information from and updates to the database.
acc	C compiler
adjust_flexlm_owner	changes the owner of the license server daemon
analyzer	Motif interface for analyzing an experiment that is generated by using the Sampling Collector from the Sun WorkShop Debugging window.
bcheck	batch utility for Runtime Checking (RTC)
bil2xd	Converts BIL source to WorkShop Visual save files
bringover	copy files from a parent workspace to a child workspace
c++filt	c++ name demangler
c89	compile standard C programs
cb	C program beautifier
cc	C compiler
cflow	generate C flowgraph
codemgr	The TeamWare "umbrella" command.
codemgrtool	teamware is a graphical user interface (GUI) tool for CodeManager commands.	[ teamware, twconfig, codemgrtool ]
cscope	interactively examine a C program
ctrace	C program debugger
cxref	generate C program cross-reference
dbx	source-level debugging tool
def.dir.flp	default directory file list program
dem	demangle a C++ name
dmake	DistributedMake
dumpstabs	utility for dumping out debug information
er_export	export experiment data to a file.
er_mapgen	generates a mapfile using an experiment that has been generated by the Sampling Collector in the Sun WorkShop Debugging window.
er_mv	move experiment
er_print	print an ASCII version of the various displays supported by the Sampling Analyzer
er_rm	remove (unlink) experiments.
etags	generate tag file for Emacs, vi	[ etags, ctags ]
f77	FORTRAN 77 compiler
f90	FORTRAN 90 compiler
fbe	assembler
filemerge	twmerge is a window-based file comparison and merging program	[ twmerge, filemerge ]
fpp	the Fortran language preprocessor for FORTRAN 77 and Fortran 90.
fpr	convert FORTRAN carriage-control output to printable form
fpversion	print information about the system CPU and FPU
freezept	generate or translate SCCS Mergeable delta IDs for lists of files
freezepttool	generate or translate SCCS Mergeable delta IDs for lists of files	[ twfreeze, freezepttool ]
fsplit	split a multi-routine FORTRAN 90 or FORTRAN 77 source file into individual files.
gcmonitor	web interface to Sun WorkShop Memory Monitor
gil2xd	Converts GIL source to WorkShop Visual save files
gnuattach	Server and Clients for XEmacs	[ gnuserv, gnuclient ]
gnuclient	Server and Clients for XEmacs	[ gnuserv, gnuclient ]
gnudoit	Server and Clients for XEmacs	[ gnuserv, gnuclient ]
gnuserv	Server and Clients for XEmacs	[ gnuserv, gnuclient ]
ild	incremental link editor (ild) for object files
indent	indent and format a C program source file
inline	in-line procedure call expander
intro	introduction to FORTRAN manual pages
lint	a C program checker
lmdiag	diagnostic license checkout tool
lmdown	graceful shutdown of all license daemons
lmgrd.ste	flexible license manager daemon
lmhostid	report the hostid of a system
lmremove	remove specific licenses and return them to license pool
lmreread	tells the license daemon to reread the license file and start any new vendor daemons that have been added
lmstat	monitor the status of all network licensing activities
lmver	reports the FLEXlm software version of a library or binary file
lock_lint	verify use of locks in multi-threaded programs
loopreport	print loop timing data to stdout
looptool	graphically display loop timing data
maketool	twbuild is a graphical user interface (GUI) tool for Sun WorkShop TeamWare Building commands.	[ twbuild, maketool ]
memdb	Memory Debugger. Run Workshop Memory Monitor on an Executable
ptclean	clean up the parameterized types database
putback	copy files from a child workspace to its parent workspace
ratfor	rational FORTRAN dialect
rcs2ws	produce a TeamWare workspace from an RCS source hiearchy
resolve	merge files in conflict using interactive commands and/or Filemerge
rtc_patch_area	patch area utility for Runtime Checking (SPARC only)
sbcleanup	deletes old Source Browsing database files
sbenter	generate SourceBrowser database with more general information
sbfocus	generate SourceBrowser data file for focus units
sbquery	command-line interface to the Source Browsing mode of WorkShop
sbtags	create database files for the Source Browsing mode of WorkShop
tcov	source code test coverage analysis and statement-by-statement profile
teamware	teamware is a graphical user interface (GUI) tool for CodeManager commands.	[ teamware, twconfig, codemgrtool ]
twbuild	twbuild is a graphical user interface (GUI) tool for Sun WorkShop TeamWare Building commands.	[ twbuild, maketool ]
twconfig	teamware is a graphical user interface (GUI) tool for CodeManager commands.	[ teamware, twconfig, codemgrtool ]
twfreeze	generate or translate SCCS Mergeable delta IDs for lists of files	[ twfreeze, freezepttool ]
twmerge	twmerge is a window-based file comparison and merging program	[ twmerge, filemerge ]
twversion	twversion is a graphical user interface (GUI) tool for the Source Code Control System (SCCS). twversion is available as part of the Sun WorkShop TeamWare product.	[ twversion, vertool ]
uil2xd	Converts UIL source to WorkShop Visual save files
version	display version identification of object file or binary
vertool	twversion is a graphical user interface (GUI) tool for the Source Code Control System (SCCS). twversion is available as part of the Sun WorkShop TeamWare product.	[ twversion, vertool ]
visu	OSF/Motif user interface builder
visu_capture	captures user interface design from a running Motif/Xt application
visu_record	record user actions from a Motif/Xt program
visu_replay	simulate user input for Motif/Xt program
visutosj	convert visu MFC code before transfer to PC
workshop	An Integrated Programming Environment
workspace	manipulate TeamWare workspaces
ws_undo	undo the effects of the last bringover or putback command
xemacs-ctags	generate tag file for Emacs, vi	[ etags, ctags ]
xemacs	Emacs: The Next Generation

3. Functions and Libraries

demangle	decode a C++ encoded symbol name	[ demangle, cplus_demangle ]
gcFixPrematureFrees	enable and disable fixing of premature frees by the Sun WorkShop Memory Monitor	[ gcFixPrematureFrees, gcStopFixingPrematureFrees ]
gcInitialize	configure Sun WorkShop Memory Monitor at startup
license_errors	Explanations of the error text and numbers printed with FLEXlm licensing errors	[ license_errors ]

Section 3C++

Algorithms	Generic algorithms for performing various operations on containers and sequences.	[ Algorithms ]
Associative_Containers	Associative containers are ordered containers. These containers include member functions that allow key insertion, retrieval, and manipulation. The standard library has the map, multimap, set, and multiset associative containers. map and multimap associate values with the keys and allow for fast retrieval of the value, based upon fast retrieval of the key. set and multiset store only keys, allowing fast retrieval of the key itself.	[ Associative_Containers ]
Bidirectional_Iterators	An iterator that can both read and write and can traverse a container in both directions	[ Bidirectional_Iterators ]
Containers	A standard template library (STL) collection.	[ Containers ]
Forward_Iterators	A forward-moving iterator that can both read and write.	[ Forward_Iterators ]
Function_Objects	Function objects are objects with an operator() defined. They are used as arguments to templatized algorithms, in place of pointers to functions.	[ Function_Objects ]
Heap_Operations		[ Heap_Operations See the entries for make_heap, pop_heap, push_heap and sort_heap ]
Input_Iterators	A read-only, forward moving iterator.	[ Input_Iterators ]
Insert_Iterators	An iterator adaptor that allows an iterator to insert into a container rather than overwrite elements in the container.	[ Insert_Iterators ]
Iterators	Pointer generalizations for traversal and modification of collections.	[ Iterators ]
Negators	Function adaptors and function objects used to reverse the sense of predicate function objects.	[ Negators ]
Operators	Operators for the C++ Standard Template Library.	[ Operators ]
Output_Iterators	A write-only, forward moving iterator.	[ Output_Iterators ]
Predicates	A function or a function object that returns a boolean (true/false) value or an integer value.	[ Predicates ]
Random_Access_Iterators	An iterator that reads, writes, and allows random access to a container.	[ Random_Access_Iterators ]
Sequences	A sequence is a container that organizes a set of objects of the same type into a linear arrangement. vector, list, deque, and string fall into this category. Sequences offer different complexity trade-offs. vector offers fast inserts and deletes from the end of the container. deque is useful when insertions and deletions take place at the beginning or end of the sequence. Use list when there are frequent insertions and deletions from the middle of the sequence.	[ Sequences ]
Stream_Iterators	Stream iterators include iterator capabilities for ostreams and istreams. They allow generic algorithms to be used directly on streams. See the sections istream_iterator and ostream_iterator for a description of these iterators.	[ Stream_Iterators ]
__distance_type	Determines the type of distance used by an iterator. This function is now obsolete. It is retained in order to include backward compatibility and support compilers that do not include partial specialization.	[ __distance_type ]
__iterator_category	Determines the category to which an iterator belongs. This function is now obsolete. It is included for backward compatibility and to support compilers that do not include partial specialization.	[ __iterator_category ]
__reverse_bi_iterator	An iterator that traverses a collection backwards. __reverse_bi_iterator is included for those compilers that do not support partial specialization. The template signature for reverse_iterator matches that of __reverse_bi_iterator when partial specialization is not available (in other words, it has six template parameters rather than one).	[ __reverse_bi_iterator, reverse_iterator ]
accumulate	Accumulates all elements within a range into a single value.	[ accumulate ]
adjacent_difference	Outputs a sequence of the differences between each adjacent pair of elements in a range.	[ adjacent_difference ]
adjacent_find	Find the first adjacent pair of elements in a sequence that are equivalent.	[ adjacent_find ]
advance	Moves an iterator forward or backward (if available) by a certain distance.	[ advance ]
allocator	The default allocator object for storage management in Standard Library containers.	[ allocator ]
auto_ptr	A simple, smart pointer class.	[ auto_ptr ]
back_insert_iterator	An insert iterator used to insert items at the end of a collection.	[ back_insert_iterator, back_inserter ]
back_inserter	An insert iterator used to insert items at the end of a collection.	[ back_insert_iterator, back_inserter ]
basic_filebuf	Class that associates the input or output sequence with a file.	[ basic_filebuf ]
basic_fstream	Supports reading and writing of named files or devices associated with a file descriptor.	[ basic_fstream ]
basic_ifstream	Supports reading from named files or other devices associated with a file descriptor.	[ basic_ifstream ]
basic_ios	A base class that includes the common functions required by all streams.	[ basic_ios ]
basic_iostream	Assists in formatting and interpreting sequences of characters controlled by a stream buffer.	[ basic_iostream ]
basic_istream	Assists in reading and interpreting input from sequences controlled by a stream buffer.	[ basic_istream ]
basic_istringstream	Supports reading objects of class basic_string from an array in memory.	[ basic_istringstream ]
basic_ofstream	Supports writing into named files or other devices associated with a file descriptor.	[ basic_ofstream ]
basic_ostream	Assists in formatting and writing output to sequences controlled by a stream buffer.	[ basic_ostream ]
basic_ostringstream	Supports writing objects of class basic_string	[ basic_ostringstream ]
basic_streambuf	Abstract base class for deriving various stream buffers to facilitate control of character sequences.	[ basic_streambuf ]
basic_string	A templatized class for handling sequences of character-like entities. string and wstring are specialized versions of basic_string for char’s and wchar_t’s, respectively. typedef basic_string string; typedef basic_string wstring;	[ basic_string ]
basic_stringbuf	Associates the input or output sequence with a sequence of arbitrary characters.	[ basic_stringbuf ]
basic_stringstream	Supports writing and reading objects of class basic_string to/from an array in memory.	[ basic_stringstream ]
binary_function	Base class for creating binary function objects.	[ binary_function ]
binary_negate	A function object that returns the complement of the result of its binary predicate.	[ binary_negate ]
binary_search	Performs a binary search for a value on a container.	[ binary_search ]
bind1st	Templatized utilities to bind values to function objects.	[ bind1st, bind2nd, binder1st, binder2nd ]
bind2nd	Templatized utilities to bind values to function objects.	[ bind1st, bind2nd, binder1st, binder2nd ]
binder1st	Templatized utilities to bind values to function objects.	[ bind1st, bind2nd, binder1st, binder2nd ]
binder2nd	Templatized utilities to bind values to function objects.	[ bind1st, bind2nd, binder1st, binder2nd ]
bitset	A template class and related functions for storing and manipulating fixed-size sequences of bits.	[ bitset ]
cartpol	cartesian/polar functions in the C++ complex number math library
cerr	Controls output to an unbuffered stream buffer associated with the object stderr declared in .	[ cerr ]
char_traits	A traits class with types and operations for the basic_string container and iostream classes.	[ char_traits ]
cin	Controls input from a stream buffer associated with the object stdin declared in .	[ cin ]
clog	Controls output to a stream buffer associated with the object stderr declared in .	[ clog ]
codecvt	A code conversion facet.	[ codecvt ]
codecvt_byname	A facet that includes code set conversion classification facilities based on the named locales.	[ codecvt_byname ]
collate	A string collation, comparison, and hashing facet.	[ collate, collate_byname ]
collate_byname	A string collation, comparison, and hashing facet.	[ collate, collate_byname ]
compare	A binary function or a function object that returns true or false. compare objects are typically passed as template parameters, and used for ordering elements within a container.	[ compare ]
complex	C++ complex number library	[ complex ]
copy	Copies a range of elements.	[ copy, copy_backward ]
copy_backward	Copies a range of elements.	[ copy, copy_backward ]
count	Count the number of elements in a container that satisfy a given condition.	[ count, count_if ]
count_if	Count the number of elements in a container that satisfy a given condition.	[ count, count_if ]
cout	Controls output to a stream buffer associated with the object stdout declared in .	[ cout ]
cplx.intro	introduction to C++ complex number math library	[ cplx.intro complex ]
cplxerr	error-handling functions in the C++ complex number math library	[ cplxerr complex error ]
cplxexp	functions in the C++ complex number math library	[ cplxexp, exp, log, log10, pow, sqrt ]
cplxops	arithmetic operator functions in the C++ complex number math library
cplxtrig	trigonometric functions in the C++ complex number math library
ctype	A facet that includes character classification facilities.	[ ctype ]
ctype_byname	A facet that includes character classification facilities based on the named locales.	[ ctype_byname ]
deque	A sequence that supports random access iterators and efficient insertion/deletion at both beginning and end.	[ deque ]
distance	Computes the distance between two iterators.	[ distance ]
divides	Returns the result of dividing its first argument by its second.	[ divides ]
equal	Compares two ranges for equality.	[ equal ]
equal_range	Find the largest subrange in a collection into which a given value can be inserted without violating the ordering of the collection.	[ equal_range ]
equal_to	A binary function object that returns true if its first argument equals its second.	[ equal_to ]
exception	A class that supports logic and runtime errors.	[ exception ]
facets	A family of classes used to encapsulate categories of locale functionality.	[ facets ]
filebuf	buffer class for file I/O
fill	Initializes a range with a given value.	[ fill, fill_n ]
fill_n	Initializes a range with a given value.	[ fill, fill_n ]
find	Finds an occurrence of value in a sequence.	[ find ]
find_end	Finds the last occurrence of a sub-sequence in a sequence.	[ find_end ]
find_first_of	Finds the first occurrence of any value from one sequence in another sequence.	[ find_first_of ]
find_if	Finds an occurrence of a value in a sequence that satisfies a specified predicate.	[ find_if ]
for_each	Applies a function to each element in a range.	[ for_each ]
fpos	Maintains position information fort he iostream classes.	[ fpos ]
front_insert_iterator	An insert iterator used to insert items at the beginning of a collection.	[ front_insert_iterator, front_inserter ]
front_inserter	An insert iterator used to insert items at the beginning of a collection.	[ front_insert_iterator, front_inserter ]
fstream	stream class for file I/O
generate	Initialize a container with values produced by a value-generator class.	[ generate, generate_n ]
generate_n	Initialize a container with values produced by a value-generator class.	[ generate, generate_n ]
get_temporary_buffer	Pointer based primitive for handling memory	[ get_temporary_buffer ]
greater	A binary function object that returns true if its first argument is greater than its second.	[ greater ]
greater_equal	A binary function object that returns true if its first argument is greater than or equal to its second	[ greater_equal ]
gslice	A numeric array class used to represent a generalized slice from an array.	[ gslice ]
gslice_array	A numeric array class used to represent a BLAS-like slice from a valarray.	[ gslice_array ]
has_facet	A function template used to determine if a locale has a given facet.	[ has_facet ]
ifstream	Supports reading from named files or other devices associated with a file descriptor.	[ basic_ifstream ]
includes	A basic set of operation for sorted sequences.	[ includes ]
indirect_array	A numeric array class used to represent elements selected from a valarray.	[ indirect_array ]
inner_product	Computes the inner product A X B of two ranges A and B.	[ inner_product ]
inplace_merge	Merges two sorted sequences into one.	[ inplace_merge ]
insert_iterator	An insert iterator used to insert items into a collection rather than overwrite the collection.	[ insert_iterator, inserter ]
inserter	An insert iterator used to insert items into a collection rather than overwrite the collection.	[ insert_iterator, inserter ]
interrupt	signal handling for the task library	[ interrupt Interrupt_handler ]
ios	basic iostreams formatting
ios.intro	introduction to iostreams and the man pages
ios_base	Defines member types and maintains data for classes that inherit from it.	[ ios_base ]
iosfwd	The header iosfwd forward declares the input/output library template classes and specializes them for wide and tiny characters. It also defines the positional types used in class char_traits instantiated on tiny and wide characters.	[ iosfwd ]
isalnum	Determines if a character is alphabetic or numeric.	[ isalnum ]
isalpha	Determines if a character is alphabetic.	[ isalpha ]
iscntrl	Determines if a character is a control character.	[ iscntrl ]
isdigit	Determines if a character is a decimal digit.	[ isdigit ]
isgraph	Determines if a character is a graphic character.	[ isgraph ]
islower	Determines whether a character is lower case.	[ islower ]
isprint	Determines if a character is printable.	[ isprint ]
ispunct	Determines if a character is punctuation.	[ ispunct ]
isspace	Determines if a character is a space.	[ isspace ]
istream	formatted and unformatted input
istream_iterator	A stream iterator that has iterator capabilities for istreams. This iterator allows generic algorithms to be used directly on streams.	[ istream_iterator ]
istreambuf_iterator	Reads successive characters from the stream buffer for which it was constructed.	[ istreambuf_iterator ]
istringstream	Supports reading objects of class basic_string from an array in memory.	[ basic_istringstream ]
istrstream	Reads characters from an array in memory.	[ istrstream ]
isupper	Determines whether a character is upper case.	[ isupper ]
isxdigit	Determines whether a character is a hexadecimal digit.	[ isxdigit ]
iter_swap	Exchanges values in two locations.	[ iter_swap ]
iterator	A base iterator class.	[ iterator ]
iterator_traits	Returns basic information about an iterator.	[ iterator_traits ]
less	A binary function object that returns true if its first argument is less than its second.	[ less ]
less_equal	A binary function object that returns true if its first argument is less than or equal to its second.	[ less_equal ]
lexicographical_compare	Compares two ranges lexicographically.	[ lexicographical_compare ]
limits		[ limits Refer to the numeric_limits section of this reference guide. ]
list	A sequence that supports bidirectional iterators.	[ list ]
locale	A localization class containing a polymorphic set of facets.	[ locale ]
logical_and	A binary function object that returns true if both of its arguments are true.	[ logical_and ]
logical_not	A unary function object that returns true if its argument is false.	[ logical_not ]
logical_or	A binary function object that returns true if either of its arguments are true.	[ logical_or ]
lower_bound	Determine the first valid position for an element in a sorted container.	[ lower_bound ]
make_heap	Creates a heap.	[ make_heap ]
manip	iostream manipulators
map	An associative container with access to non-key values using unique keys. A map supports bidirectional iterators.	[ map ]
mask_array	A numeric array class that gives a masked view of a valarray.	[ mask_array ]
max	Finds and returns the maximum of a pair of values.	[ max ]
max_element	Finds the maximum value in a range.	[ max_element ]
mem_fun	Function objects that adapt a pointer to a member function, to take the place of a global function.	[ mem_fun, mem_fun1, mem_fun_ref, mem_fun_ref1 ]
mem_fun1	Function objects that adapt a pointer to a member function, to take the place of a global function.	[ mem_fun, mem_fun1, mem_fun_ref, mem_fun_ref1 ]
mem_fun_ref	Function objects that adapt a pointer to a member function, to take the place of a global function.	[ mem_fun, mem_fun1, mem_fun_ref, mem_fun_ref1 ]
mem_fun_ref1	Function objects that adapt a pointer to a member function, to take the place of a global function.	[ mem_fun, mem_fun1, mem_fun_ref, mem_fun_ref1 ]
merge	Merges two sorted sequences into a third sequence.	[ merge ]
messages	Messaging facets.	[ messages, messages_byname ]
messages_byname	Messaging facets.	[ messages, messages_byname ]
min	Finds and returns the minimum of a pair of values.	[ min ]
min_element	Finds the minimum value in a range.	[ min_element ]
minus	Returns the result of subtracting its second argument from its first.	[ minus ]
mismatch	Compares elements from two sequences and returns the first two elements that don’t match each other.	[ mismatch ]
modulus	Returns the remainder obtained by dividing the first argument by the second argument.	[ modulus ]
money_get	Monetary formatting facet for input.	[ money_get ]
money_put	Monetary formatting facet for output.	[ money_put ]
moneypunct	Monetary punctuation facets.	[ moneypunct, moneypunct_byname ]
moneypunct_byname	Monetary punctuation facets.	[ moneypunct, moneypunct_byname ]
multimap	An associative container that gives access to non-key values using keys. multimap keys are not required to be unique. A multimap supports bidirectional iterators.	[ multimap ]
multiplies	A binary function object that returns the result of multiplying its first and second arguments.	[ multiplies ]
multiset	An associative container that allows fast access to stored key values. Storage of duplicate keys is allowed. A multiset supports bidirectional iterators.	[ multiset ]
negate	Unary function object that returns the negation of its argument.	[ negate ]
next_permutation	Generates successive permutations of a sequence based on an ordering function.	[ next_permutation ]
not1	A function adaptor used to reverse the sense of a unary predicate function object.	[ not1 ]
not2	A function adaptor used to reverse the sense of a binary predicate function object.	[ not2 ]
not_equal_to	A binary function object that returns true if its first argument is not equal to its second.	[ not_equal_to ]
nth_element	Rearranges a collection so that all elements lower in sorted order than the nth element come before it and all elements higher in sorter order than the nth element come after it.	[ nth_element ]
num_get	A numeric formatting facet for input.	[ num_get ]
num_put	A numeric formatting facet for output.	[ num_put ]
numeric_limits	A class for representing information about scalar types.	[ numeric_limits ]
numpunct	A numeric punctuation facet.	[ numpunct, numpunct_byname ]
numpunct_byname	A numeric punctuation facet.	[ numpunct, numpunct_byname ]
ofstream	Supports writing into named files or other devices associated with a file descriptor.	[ basic_ofstream ]
ostream	formatted and unformatted output
ostream_iterator	Stream iterators allow for use of iterators with ostreams and istreams. They allow generic algorithms to be used directly on streams.	[ ostream_iterator ]
ostreambuf_iterator	Writes successive characters onto the stream buffer object from which it was constructed.	[ ostreambuf_iterator ]
ostringstream	Supports writing objects of class basic_string	[ basic_ostringstream ]
ostrstream	Writes to an array in memory.	[ ostrstream ]
pair	A template for heterogeneous pairs of values.	[ pair ]
partial_sort	Templatized algorithm for sorting collections of entities.	[ partial_sort ]
partial_sort_copy	Templatized algorithm for sorting collections of entities.	[ partial_sort_copy ]
partial_sum	Calculates successive partial sums of a range of values.	[ partial_sum ]
partition	Places all of the entities that satisfy the given predicate before all of the entities that do not.	[ partition ]
permutation	Generates successive permutations of a sequence based on an ordering function. See the entries for next_permutation and prev-_permutation.	[ permutation ]
plus	A binary function object that returns the result of adding its first and second arguments.	[ plus ]
pointer_to_binary_function	A function object that adapts a pointer to a binary function, to take the place of a binary_function.	[ pointer_to_binary_function ]
pointer_to_unary_function	A function object class that adapts a pointer to a function, to take the place of a unary_function.	[ pointer_to_unary_function ]
pop_heap	Moves the largest element off the heap.	[ pop_heap ]
prev_permutation	Generates successive permutations of a sequence based on an ordering function.	[ prev_permutation ]
priority_queue	A container adapter that behaves like a priority queue. Items popped from the queue are in order with respect to a "priority."	[ priority_queue ]
ptr_fun	A function that is overloaded to adapt a pointer to a function, to take the place of a function.	[ ptr_fun ]
push_heap	Places a new element into a heap.	[ push_heap ]
queue	A container adaptor that behaves like a queue (first in, first out).	[ queue ]
random_shuffle	Randomly shuffles elements of a collection.	[ random_shuffle ]
raw_storage_iterator	Enables iterator-based algorithms to store results into uninitialized memory.	[ raw_storage_iterator ]
remove	Moves desired elements to the front of a container, and returns an iterator that describes where the sequence of desired elements ends.	[ remove ]
remove_copy	Moves desired elements to the front of a container, and returns an iterator that describes where the sequence of desired elements ends.	[ remove_copy ]
remove_copy_if	Moves desired elements to the front of a container, and returns an iterator that describes where the sequence of desired elements ends.	[ remove_copy_if ]
remove_if	Moves desired elements to the front of a container, and returns an iterator that describes where the sequence of desired elements ends.	[ remove_if ]
replace	Substitutes elements in a collection with new values.	[ replace ]
replace_copy	Substitutes elements in a collection with new values, and moves the revised sequence into result.	[ replace_copy ]
replace_copy_if	Substitutes elements in a collection with new values, and moves the revised sequence into result.	[ replace_copy_if ]
replace_if	Substitutes elements in a collection with new values.	[ replace_if ]
return_temporary_buffer	A pointer-based primitive for handling memory.	[ return_temporary_buffer ]
reverse	Reverses the order of elements in a collection.	[ reverse ]
reverse_copy	Reverses the order of elements in a collection while copying them to a new collection.	[ reverse_copy ]
reverse_iterator	An iterator that traverses a collection backwards. __reverse_bi_iterator is included for those compilers that do not support partial specialization. The template signature for reverse_iterator matches that of __reverse_bi_iterator when partial specialization is not available (in other words, it has six template parameters rather than one).	[ __reverse_bi_iterator, reverse_iterator ]
rotate	Swaps the segment that contains elements from first through middle-1 with the segment that contains the elements from middle through last.	[ rotate, rotate_copy ]
rotate_copy	Swaps the segment that contains elements from first through middle-1 with the segment that contains the elements from middle through last.	[ rotate, rotate_copy ]
sbufprot	protected interface of the stream buffer base class
sbufpub	public interface of the stream buffer base class
search	Finds a sub-sequence within a sequence of values that is element-wise equal to the values in an indicated range.	[ search, search_n ]
search_n	Finds a sub-sequence within a sequence of values that is element-wise equal to the values in an indicated range.	[ search, search_n ]
set	An associative container that supports unique keys. A set supports bidirectional iterators.	[ set ]
set_difference	A basic set operation for constructing a sorted difference.	[ set_difference ]
set_intersection	A basic set operation for constructing a sorted intersection.	[ set_intersection ]
set_symmetric_difference	A basic set operation for constructing a sorted symmetric difference.	[ set_symmetric_difference ]
set_union	A basic set operation for constructing a sorted union.	[ set_union ]
slice	A numeric array class for representing a BLAS-like slice from an array.	[ slice ]
slice_array	A numeric array class for representing a BLAS-like slice from a valarray.	[ slice_array ]
smanip	Helper classes used to implement parameterized manipulators.	[ smanip, smanip_fill ]
smanip_fill	Helper classes used to implement parameterized manipulators.	[ smanip, smanip_fill ]
sort	A templatized algorithm for sorting collections of entities.	[ sort ]
sort_heap	Converts a heap into a sorted collection.	[ sort_heap ]
ssbuf	buffer class for for character arrays
stable_partition	Places all of the entities that satisfy the given predicate before all of the entities that do not, while maintaining the relative order of elements in each group.	[ stable_partition ]
stable_sort	A templatized algorithm for sorting collections of entities.	[ stable_sort ]
stack	A container adapter that behaves like a stack (last in, first out).	[ stack ]
stdiobuf	buffer and stream classes for use with C stdio
stream_MT	base class to provide dynamic changing of iostream class objects to and from MT safety.
stream_locker	class used for application level locking of iostream class objects.
streambuf	Abstract base class for deriving various stream buffers to facilitate control of character sequences.	[ basic_streambuf ]
string	A typedef for: basic_string, allocator> For more information about strings, see the entry basic_string.	[ string ]
stringbuf	Associates the input or output sequence with a sequence of arbitrary characters.	[ basic_stringbuf ]
stringstream	Supports writing and reading objects of class basic_string to/from an array in memory.	[ basic_stringstream ]
strstream	Reads and writes to an array in memory.	[ strstream ]
strstreambuf	Associates either the input sequence or the output sequence with a tiny character array whose elements store arbitrary values.	[ strstreambuf ]
swap	Exchanges values.	[ swap ]
swap_ranges	Exchanges a range of values in one location with those in another.	[ swap_ranges ]
task	coroutines in the C++ task library
task.intro	introduction to the coroutine library and man pages
tasksim	histogram and random numbers for the task library
time_get	A time formatting facet for input.	[ time_get ]
time_get_byname	A time formatting facet for input, based on the named locales.	[ time_get_byname ]
time_put	A time formatting facet for output.	[ time_put ]
time_put_byname	A facet that includes formatted time output facilities based on the named locales.	[ time_put_byname ]
tolower	Converts a character to lower case.	[ tolower ]
toupper	Converts a character to upper case.	[ toupper ]
transform	Applies an operation to a range of values in a collection and stores the result.	[ transform ]
unary_function	A base class for creating unary function objects.	[ unary_function ]
unary_negate	A function object that returns the complement of the result of its unary predicate	[ unary_negate ]
uninitialized_copy	An algorithm that uses construct to copy values from one range to another location.	[ uninitialized_copy ]
uninitialized_fill	An algorithm that uses the construct algorithm for setting values in a collection.	[ uninitialized_fill ]
uninitialized_fill_n	An algorithm that uses the construct algorithm for setting values in a collection.	[ uninitialized_fill_n ]
unique	Removes consecutive duplicates from a range of values and places the resulting unique values into the result.	[ unique, unique_copy ]
unique_copy	Removes consecutive duplicates from a range of values and places the resulting unique values into the result.	[ unique, unique_copy ]
upper_bound	Determines the last valid position for a value in a sorted container.	[ upper_bound ]
use_facet	A template function used to obtain a facet.	[ use_facet ]
valarray	An optimized array class for numeric operations.	[ valarray ]
vector	A sequence that supports random access iterators.	[ vector ]
wcerr	Controls output to an unbuffered stream buffer associated with the object stderr declared in .	[ wcerr ]
wcin	Controls input from a stream buffer associated with the object stdin declared in .	[ wcin ]
wclog	Controls output to a stream buffer associated with the object stderr declared in .	[ wclog ]
wcout	Controls output to a stream buffer associated with the object stdout declared in .	[ wcout ]
wfilebuf	Class that associates the input or output sequence with a file.	[ basic_filebuf ]
wfstream	Supports reading and writing of named files or devices associated with a file descriptor.	[ basic_fstream ]
wifstream	Supports reading from named files or other devices associated with a file descriptor.	[ basic_ifstream ]
wios	A base class that includes the common functions required by all streams.	[ basic_ios ]
wistream	Assists in reading and interpreting input from sequences controlled by a stream buffer.	[ basic_istream ]
wistringstream	Supports reading objects of class basic_string from an array in memory.	[ basic_istringstream ]
wofstream	Supports writing into named files or other devices associated with a file descriptor.	[ basic_ofstream ]
wostream	Assists in formatting and writing output to sequences controlled by a stream buffer.	[ basic_ostream ]
wostringstream	Supports writing objects of class basic_string	[ basic_ostringstream ]
wstreambuf	Abstract base class for deriving various stream buffers to facilitate control of character sequences.	[ basic_streambuf ]
wstring	A typedef for: basic_string, allocator > For more information about strings, see the entry basic_string.	[ wstring ]
wstringbuf	Associates the input or output sequence with a sequence of arbitrary characters.	[ basic_stringbuf ]

Section 3F (intro)

abort	terminate abruptly; write memory image to core file
access	return access mode (r,w,x) or existence of a file
alarm	execute a subroutine after a specified time
bit	and, or, xor, not, rshift, lshift, bic, bis, bit, setbit functions
chdir	change default directory
chmod	change mode of a file
ctime	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
ctime64	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
date	return date in character form
date_and_time	Returns date and time in character form
dtime	return elapsed time	[ etime, dtime ]
etime	return elapsed time	[ etime, dtime ]
exit	terminate process with status
f77_floatingpoint	FORTRAN IEEE floating-point definitions
f77_ieee_environment	mode, status, and signal handling for IEEE arithmetic
fdate	return date and time in an ASCII string
fgetc	get a character from a logical unit	[ getc, fgetc ]
flush	flush output to a logical unit
fork	create a copy of this process
fputc	write a character to a FORTRAN logical unit	[ putc, fputc ]
free	deallocate a region of memory allocated by malloc
fseek	reposition a file on a logical unit	[ fseek, fseeko64, ftell, ftello64 ]
fseeko64	reposition a file on a logical unit	[ fseek, fseeko64, ftell, ftello64 ]
fstat	get file status	[ stat, lstat, fstat ]
fstat64	get file status for long files	[ stat64, lstat64, fstat64 ]
ftell	reposition a file on a logical unit	[ fseek, fseeko64, ftell, ftello64 ]
ftello64	reposition a file on a logical unit	[ fseek, fseeko64, ftell, ftello64 ]
gerror	get system error messages	[ perror, gerror, ierrno ]
getarg	get the kth command-line argument	[ getarg, iargc ]
getc	get a character from a logical unit	[ getc, fgetc ]
getcwd	get the path name of the current working directory
getenv	get value of environment variables
getfd	get the file descriptor of an external unit number
getfilep	get the file pointer of an external unit number
getgid	get user or group ID of the caller	[ getuid, getgid ]
getlog	get user’s login name
getpid	get process id
getuid	get user or group ID of the caller	[ getuid, getgid ]
gmtime	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
gmtime64	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
hostnm	get name of current host
iargc	get the kth command-line argument	[ getarg, iargc ]
idate	return date in numerical form
ierrno	get system error messages	[ perror, gerror, ierrno ]
index	get index or length of substring	[ index, rindex, lnblnk, len ]
intro	introduction to FORTRAN library functions and subroutines
ioinit	initialize I/O: carriage control, blanks, append, file names
irand	return random values	[ rand, drand, irand ]
isatty	find name of terminal port; also: is unit a terminal?	[ ttynam, isatty ]
isetjmp	longjmp returns to the location set by isetjmp	[ longjmp, isetjmp ]
itime	return time in numerical form
kill	send a signal to a process
len	get index or length of substring	[ index, rindex, lnblnk, len ]
libm_double	FORTRAN access to double precision libm functions and subroutines
libm_quadruple	FORTRAN access to quadruple-precision functions (SPARC only)
libm_single	FORTRAN access to single-precision libm functions
link	make a link to an existing file	[ link, symlnk ]
lnblnk	get index or length of substring	[ index, rindex, lnblnk, len ]
loc	return the address of an object
long	integer object conversion	[ long, short ]
longjmp	longjmp returns to the location set by isetjmp	[ longjmp, isetjmp ]
lstat	get file status	[ stat, lstat, fstat ]
lstat64	get file status for long files	[ stat64, lstat64, fstat64 ]
ltime	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
ltime64	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
malloc	allocate memory and return the address	[ malloc, malloc64 ]
malloc64	allocate memory and return the address	[ malloc, malloc64 ]
mvbits	move specified bits
perror	get system error messages	[ perror, gerror, ierrno ]
putc	write a character to a FORTRAN logical unit	[ putc, fputc ]
qsort	quick sort	[ qsort, qsort64 ]
qsort64	quick sort	[ qsort, qsort64 ]
ran	return a random number between 0 and 1
rand	return random values	[ rand, drand, irand ]
rename	rename a file
rindex	get index or length of substring	[ index, rindex, lnblnk, len ]
secnds	return system time in seconds since midnight
sh	fast execution of an sh shell command
short	integer object conversion	[ long, short ]
signal	change the action for a signal
sleep	suspend execution for an interval
stat	get file status	[ stat, lstat, fstat ]
stat64	get file status for long files	[ stat64, lstat64, fstat64 ]
symlnk	make a link to an existing file	[ link, symlnk ]
system	execute operating system command
tclose	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
time	return system time	[ time, ctime, ctime64, ltime, ltime64, gmtime, gmtime64 ]
topen	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
tread	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
trewin	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
tskipf	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
tstate	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
ttynam	find name of terminal port; also: is unit a terminal?	[ ttynam, isatty ]
twrite	FORTRAN tape I/O	[ topen, tclose, tread, twrite, trewin, tskipf, tstate ]
unlink	remove a file
wait	wait for a process to terminate

3M. Math Library (intro)

Intro	introduction to mathematical library functions and constants	[ Intro, intro ]
acosd	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
acosp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
acospi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
addrans	additive pseudo-random number generators
aint	round to integral value in floating-point or integer format	[ aint, anint, irint, nint ]
anint	round to integral value in floating-point or integer format	[ aint, anint, irint, nint ]
annuity	exponential, logarithm, financial	[ exp2, exp10, log2, compound, annuity ]
asind	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
asinp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
asinpi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
atan2d	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
atan2pi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
atand	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
atanp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
atanpi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
clibmvec	vector versions of some complex mathematical functions
compound	exponential, logarithm, financial	[ exp2, exp10, log2, compound, annuity ]
convert_external	convert external binary data formats
cosd	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
cosp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
cospi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
exp10	exponential, logarithm, financial	[ exp2, exp10, log2, compound, annuity ]
exp2	exponential, logarithm, financial	[ exp2, exp10, log2, compound, annuity ]
feclearexcept	access floating point exception flags	[ feclearexcept, feraiseexcept, fetestexcept, fegetexceptflag, fesetexceptflag ]
fegetenv	manage the floating point environment	[ fegetenv, fesetenv, feholdexcept, feupdateenv, fex_merge_flags ]
fegetexceptflag	access floating point exception flags	[ feclearexcept, feraiseexcept, fetestexcept, fegetexceptflag, fesetexceptflag ]
fegetprec	control floating point rounding precision modes	[ fesetprec, fegetprec ]
fegetround	control floating point rounding direction modes	[ fesetround, fegetround ]
feholdexcept	manage the floating point environment	[ fegetenv, fesetenv, feholdexcept, feupdateenv, fex_merge_flags ]
feraiseexcept	access floating point exception flags	[ feclearexcept, feraiseexcept, fetestexcept, fegetexceptflag, fesetexceptflag ]
fesetenv	manage the floating point environment	[ fegetenv, fesetenv, feholdexcept, feupdateenv, fex_merge_flags ]
fesetexceptflag	access floating point exception flags	[ feclearexcept, feraiseexcept, fetestexcept, fegetexceptflag, fesetexceptflag ]
fesetprec	control floating point rounding precision modes	[ fesetprec, fegetprec ]
fesetround	control floating point rounding direction modes	[ fesetround, fegetround ]
fetestexcept	access floating point exception flags	[ feclearexcept, feraiseexcept, fetestexcept, fegetexceptflag, fesetexceptflag ]
feupdateenv	manage the floating point environment	[ fegetenv, fesetenv, feholdexcept, feupdateenv, fex_merge_flags ]
fex_get_handling	control floating point exception handling modes	[ fex_set_handling, fex_get_handling, fex_getexcepthandler, fex_setexcepthandler ]
fex_get_log	log retrospective diagnostics for floating point exceptions	[ fex_set_log, fex_get_log, fex_set_log_depth, fex_get_log_depth, fex_log_entry ]
fex_get_log_depth	log retrospective diagnostics for floating point exceptions	[ fex_set_log, fex_get_log, fex_set_log_depth, fex_get_log_depth, fex_log_entry ]
fex_getexcepthandler	control floating point exception handling modes	[ fex_set_handling, fex_get_handling, fex_getexcepthandler, fex_setexcepthandler ]
fex_log_entry	log retrospective diagnostics for floating point exceptions	[ fex_set_log, fex_get_log, fex_set_log_depth, fex_get_log_depth, fex_log_entry ]
fex_merge_flags	manage the floating point environment	[ fegetenv, fesetenv, feholdexcept, feupdateenv, fex_merge_flags ]
fex_set_handling	control floating point exception handling modes	[ fex_set_handling, fex_get_handling, fex_getexcepthandler, fex_setexcepthandler ]
fex_set_log	log retrospective diagnostics for floating point exceptions	[ fex_set_log, fex_get_log, fex_set_log_depth, fex_get_log_depth, fex_log_entry ]
fex_set_log_depth	log retrospective diagnostics for floating point exceptions	[ fex_set_log, fex_get_log, fex_set_log_depth, fex_get_log_depth, fex_log_entry ]
fex_setexcepthandler	control floating point exception handling modes	[ fex_set_handling, fex_get_handling, fex_getexcepthandler, fex_setexcepthandler ]
fp_class	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
ieee_flags	mode and status function for IEEE standard arithmetic
ieee_handler	IEEE exception trap handler function
ieee_retrospective	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
ieee_sun	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
ieee_values	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
infinity	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
intro	introduction to mathematical library functions and constants	[ Intro, intro ]
irint	round to integral value in floating-point or integer format	[ aint, anint, irint, nint ]
isinf	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
isnormal	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
issubnormal	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
iszero	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
lcrans	linear congruential pseudo-random number generators
libmvec	vector versions of some elementary mathematical functions
log2	exponential, logarithm, financial	[ exp2, exp10, log2, compound, annuity ]
max_normal	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
max_subnormal	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
min_normal	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
min_subnormal	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
mwcrans	multiply with carry pseudo-random number generators
nint	round to integral value in floating-point or integer format	[ aint, anint, irint, nint ]
nonstandard_arithmetic	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
quad_precision	Quadruple-precision access to libm and libsunmath functions
quiet_nan	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
shufrans	random number shufflers
signaling_nan	functions that return extreme values of IEEE arithmetic	[ ieee_values, min_subnormal, max_subnormal, min_normal, max_normal, infinity, quiet_nan, signaling_nan ]
signbit	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
sincos	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
sincosd	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
sincosp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
sincospi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
sind	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
single_precision	Single-precision access to libm and libsunmath functions
sinp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
sinpi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
standard_arithmetic	miscellaneous functions for IEEE arithmetic	[ ieee_sun, fp_class, isinf, isnormal, issubnormal, iszero, signbit, nonstandard_arithmetic, standard_arithmetic, ieee_retrospective ]
tand	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
tanp	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
tanpi	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]
trig_sun	more trigonometric functions	[ trig_sun, sincos, sind, cosd, tand, asind, acosd, atand, atan2d, sincosd, sinp, cosp, tanp, asinp, acosp, atanp, sincosp, sinpi, cospi, tanpi, asinpi, acospi, atanpi, atan2pi, sincospi ]

Section 3P

available_threads	returns information about current thread usage
caxpy	Compute y := alpha ∗ x + y
cbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
cchdc	compute the Cholesky decomposition of a symmetric positive definite matrix A.
cchdd	downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
cchex	compute the Cholesky decomposition of a symmetric positive definite matrix A.
cchud	update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
ccnvcor	compute the convolution or correlation of complex vectors
ccnvcor2	compute the convolution or correlation of complex matrices
ccopy	Copy x to y
cdotc	Compute the dot product of two vectors x and conjg(y).
cdotu	Compute the dot product of two vectors x and y.
cfft2b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
cfft2f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
cfft2i	initialize the array xWSAVE, which is used in both xFFT2F and xFFT2B.
cfft3b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
cfft3f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
cfft3i	initialize the array xWSAVE, which is used in both xFFT3F and xFFT3B.
cfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
cfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
cffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
cfftopt	compute the length of the closest fast FFT
cgbbrd	reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
cgbco	compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
cgbcon	estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm.
cgbdi	compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA.
cgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
cgbfa	compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
cgbmv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y
cgbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
cgbsl	solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x.
cgbsv	compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
cgbsvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
cgbtf2	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrf	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
cgbtrs	solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by CGBTRF
cgebak	form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL
cgebal	balance a general complex matrix A
cgebd2	reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
cgebrd	reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
cgeco	compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A.
cgecon	estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF
cgedi	compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA.
cgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
cgees	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeesx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
cgeev	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgeevx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
cgefa	compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A.
cgegs	compute for a pair of N-by-N complex nonsymmetric matrices A,
cgegv	compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,
cgehd2	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
cgehrd	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
cgelq2	compute an LQ factorization of a complex m by n matrix A
cgelqf	compute an LQ factorization of a complex M-by-N matrix A
cgels	solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
cgelss	compute the minimum norm solution to a complex linear least squares problem
cgelsx	compute the minimum-norm solution to a complex linear least squares problem
cgemm	perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C
cgemv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y
cgeql2	compute a QL factorization of a complex m by n matrix A
cgeqlf	compute a QL factorization of a complex M-by-N matrix A
cgeqpf	compute a QR factorization with column pivoting of a complex M-by-N matrix A
cgeqr2	compute a QR factorization of a complex m by n matrix A
cgeqrf	compute a QR factorization of a complex M-by-N matrix A
cgerc	perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A
cgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
cgerq2	compute an RQ factorization of a complex m by n matrix A
cgerqf	compute an RQ factorization of a complex M-by-N matrix A
cgeru	perform the rank 1 operation A := alpha∗x∗y’ + A
cgesl	solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.
cgesv	compute the solution to a complex system of linear equations A ∗ X = B,
cgesvd	compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors
cgesvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B,
cgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
cgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
cgetri	compute the inverse of a matrix using the LU factorization computed by CGETRF
cgetrs	solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF
cggbak	form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL
cggbal	balance a pair of general complex matrices (A,B)
cggglm	solve a general Gauss-Markov linear model (GLM) problem
cgghrd	reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular
cgglse	solve the linear equality-constrained least squares (LSE) problem
cggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
cggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
cggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
cggsvp	compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0
cgtcon	estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF
cgtrfs	improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
cgtsl	solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.
cgtsv	solve the equation A∗X = B,
cgtsvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
cgttrf	compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
cgttrs	solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
chbev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
chbgst	reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,
chbgv	compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x
chbmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
chbtrd	reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
checon	estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF
cheev	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
cheevd	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
cheevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
chegs2	reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegst	reduce a complex Hermitian-definite generalized eigenproblem to standard form
chegv	compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
chemm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
chemv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
cher	perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A
cher2	perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A
cher2k	perform one of the Hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C
cherfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
cherk	perform one of the Hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C
chesv	compute the solution to a complex system of linear equations A ∗ X = B,
chesvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,
chetd2	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
chetf2	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetrd	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
chetrf	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
chetri	compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF
chetrs	solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF
chgeqz	implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
chico	compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.
chidi	compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA.
chifa	compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.
chisl	solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x.
chpco	compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.
chpcon	estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF
chpdi	compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA.
chpev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
chpevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
chpevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
chpfa	compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.
chpgst	reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
chpgv	compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
chpmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
chpr	perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A
chpr2	perform the Hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A
chprfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
chpsl	solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x.
chpsv	compute the solution to a complex system of linear equations A ∗ X = B,
chpsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
chptrd	reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
chptrf	compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
chptri	compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF
chptrs	solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF
chsein	use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
chseqr	compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
clabrd	reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
clacgv	conjugate a complex vector of length N
clacon	estimate the 1-norm of a square, complex matrix A
clacpy	copie all or part of a two-dimensional matrix A to another matrix B
clacrm	perform a very simple matrix-matrix multiplication
clacrt	apply a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex
cladiv	:= X / Y, where X and Y are complex
claed0	the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
claed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
claed8	merge the two sets of eigenvalues together into a single sorted set
claein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
claesy	compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
claev2	compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
clags2	compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
clagtm	perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be zero, one, or minus one
clahef	compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
clahqr	i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
clahrd	reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
claic1	apply one step of incremental condition estimation in its simplest version
clangb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
clange	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
clangt	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
clanhb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
clanhe	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
clanhp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
clanhs	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
clanht	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
clansb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
clansp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
clansy	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
clantb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
clantp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
clantr	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
clapll	two column vectors X and Y, let A = ( X Y )
clapmt	rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
claqgb	equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
claqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
claqhb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqhe	equilibrate a Hermitian matrix A using the scaling factors in the vector S
claqhp	equilibrate a Hermitian matrix A using the scaling factors in the vector S
claqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
claqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S
claqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S
clar2v	apply a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
clarf	apply a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
clarfb	apply a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right
clarfg	generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I
clarft	form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
clarfx	apply a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
clargv	generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
clarnv	return a vector of n random complex numbers from a uniform or normal distribution
clartg	generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
clartv	apply a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
clascl	multiply the M by N complex matrix A by the real scalar CTO/CFROM
claset	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
clasr	perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
classq	return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,
claswp	perform a series of row interchanges on the matrix A
clasyf	compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
clatbs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
clatps	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
clatrd	reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
clatrs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
clatzm	apply a Householder matrix generated by CTZRQF to a matrix
clauu2	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
clauum	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
coptimal_workspace	Get the optimal amount of workspace for the last routine called that supports varying length complex workspace.
cosqb	synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
cosqf	compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
cosqi	initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB.
cost	compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N-1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence.
costi	initialize the array xWSAVE, which is used in xCOST.
cpbco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
cpbcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF
cpbdi	compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA.
cpbequ	compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
cpbfa	compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
cpbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
cpbsl	section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x.
cpbstf	compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbsv	compute the solution to a complex system of linear equations A ∗ X = B,
cpbsvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
cpbtf2	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrf	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
cpbtrs	solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF
cpoco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
cpocon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF
cpodi	compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC.
cpoequ	compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
cpofa	compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
cporfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
cposl	solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x.
cposv	compute the solution to a complex system of linear equations A ∗ X = B,
cposvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
cpotf2	compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A
cpotri	compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF
cpotrs	solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF
cppco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
cppcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF
cppdi	compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA.
cppequ	compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
cppfa	compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
cpprfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
cppsl	solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x.
cppsv	compute the solution to a complex system of linear equations A ∗ X = B,
cppsvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
cpptrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
cpptri	compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF
cpptrs	solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF
cptcon	compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by CPTTRF
cpteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor
cptrfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
cptsl	solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.
cptsv	compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
cptsvx	use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
cpttrf	compute the factorization of a complex Hermitian positive definite tridiagonal matrix A
cpttrs	solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by CPTTRF
cqrdc	compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A.
cqrsl	solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x.
crot	apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex
crotg	Construct a Given’s plane rotation
cscal	Compute y := alpha ∗ y
csico	compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
csidi	compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA.
csifa	compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
csisl	solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x.
cspco	compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
cspcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF
cspdi	compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA.
cspfa	compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
cspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,
cspr	perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A,
csprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
cspsl	solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x.
cspsv	compute the solution to a complex system of linear equations A ∗ X = B,
cspsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
csptrf	compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
csptri	compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF
csptrs	solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF
csrot	Apply a plane rotation
csrscl	multiply an n-element complex vector x by the real scalar 1/a
csscal	Compute y := alpha ∗ y
cstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
cstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
csteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
cstsv	compute the solution to a complex system of linear equations A ∗ X = B where A is a Hermitian tridiagonal matrix
csttrf	compute the factorization of a complex Hermitian tridiagonal matrix A
csttrs	computes the solution to a complex system of linear equations A ∗ X = B
csvdc	compute the singular value decomposition of a general matrix A.
cswap	Exchange vectors x and y.
csycon	estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF
csymm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
csymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,
csyr	perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A,
csyr2k	perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C
csyrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
csyrk	perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C
csysv	compute the solution to a complex system of linear equations A ∗ X = B,
csysvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,
csytf2	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytrf	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
csytri	compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF
csytrs	solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF
ctbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ctbmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ctbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ctbsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ctbtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ctgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
ctgsja	compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
ctpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ctpmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ctprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ctpsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ctptri	compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ctptrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ctrans	transpose and scale source matrix
ctrco	estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
ctrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
ctrdi	compute the determinant and inverse of a triangular matrix A.
ctrevc	compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ctrexc	reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST
ctrmm	perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ )
ctrmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ctrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ctrsen	reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
ctrsl	solve the linear system Ax = b for a triangular matrix A and vectors b and x.
ctrsm	solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B
ctrsna	estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary)
ctrsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ctrsyl	solve the complex Sylvester matrix equation
ctrti2	compute the inverse of a complex upper or lower triangular matrix
ctrtri	compute the inverse of a complex upper or lower triangular matrix A
ctrtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ctzrqf	reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
cung2l	generate an m by n complex matrix Q with orthonormal columns,
cung2r	generate an m by n complex matrix Q with orthonormal columns,
cungbr	generate one of the complex unitary matrices Q or P∗∗H determined by CGEBRD when reducing a complex matrix A to bidiagonal form
cunghr	generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD
cungl2	generate an m-by-n complex matrix Q with orthonormal rows,
cunglq	generate an M-by-N complex matrix Q with orthonormal rows,
cungql	generate an M-by-N complex matrix Q with orthonormal columns,
cungqr	generate an M-by-N complex matrix Q with orthonormal columns,
cungr2	generate an m by n complex matrix Q with orthonormal rows,
cungrq	generate an M-by-N complex matrix Q with orthonormal rows,
cungtr	generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD
cunm2l	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
cunm2r	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
cunmbr	VECT = ’Q’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunmhr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunml2	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
cunmlq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunmql	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunmqr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunmr2	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
cunmrq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cunmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cupgtr	generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage
cupmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
cvmul	compute the scaled product of complex vectors
dasum	Return the sum of the absolute values of a vector x.
daxpy	Compute y := alpha ∗ x + y
dbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
dchdc	compute the Cholesky decomposition of a symmetric positive definite matrix A.
dchdd	downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
dchex	compute the Cholesky decomposition of a symmetric positive definite matrix A.
dchud	update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
dcnvcor	compute the convolution or correlation of double precision vectors
dcnvcor2	compute the convolution or correlation of real matrices
dcopy	Copy x to y
dcosqb	synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
dcosqf	compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
dcosqi	initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB.
dcost	compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N-1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence.
dcosti	initialize the array xWSAVE, which is used in xCOST.
ddisna	compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix
ddot	Compute the dot product of two vectors x and y.
dfft2b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
dfft2f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
dfft2i	initialize the array xWSAVE, which is used in both xFFT2F and xFFT2B.
dfft3b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
dfft3f	compute the Fourier coefficients of a real periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
dfft3i	initialize the array xWSAVE, which is used in both xFFT3F and xFFT3B.
dfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
dfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
dffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
dfftopt	compute the length of the closest fast FFT
dgbbrd	reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
dgbco	compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
dgbcon	estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
dgbdi	compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA.
dgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
dgbfa	compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
dgbmv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y
dgbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
dgbsl	solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x.
dgbsv	compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
dgbsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
dgbtf2	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrf	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
dgbtrs	solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by DGBTRF
dgebak	form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
dgebal	balance a general real matrix A
dgebd2	reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
dgebrd	reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
dgeco	compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A.
dgecon	estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF
dgedi	compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA.
dgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
dgees	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeesx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
dgeev	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgeevx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
dgefa	compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A.
dgegs	compute for a pair of N-by-N real nonsymmetric matrices A, B
dgegv	compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR)
dgehd2	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
dgehrd	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
dgelq2	compute an LQ factorization of a real m by n matrix A
dgelqf	compute an LQ factorization of a real M-by-N matrix A
dgels	solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
dgelss	compute the minimum norm solution to a real linear least squares problem
dgelsx	compute the minimum-norm solution to a real linear least squares problem
dgemm	perform one of the matrix matrix operations C := alpha∗op( A )∗op( B ) + beta∗C
dgemv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y
dgeql2	compute a QL factorization of a real m by n matrix A
dgeqlf	compute a QL factorization of a real M-by-N matrix A
dgeqpf	compute a QR factorization with column pivoting of a real M-by-N matrix A
dgeqr2	compute a QR factorization of a real m by n matrix A
dgeqrf	compute a QR factorization of a real M-by-N matrix A
dger	perform the rank 1 operation A := alpha∗x∗y’ + A
dgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
dgerq2	compute an RQ factorization of a real m by n matrix A
dgerqf	compute an RQ factorization of a real M-by-N matrix A
dgesl	solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.
dgesv	compute the solution to a real system of linear equations A ∗ X = B,
dgesvd	compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
dgesvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B,
dgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
dgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
dgetri	compute the inverse of a matrix using the LU factorization computed by DGETRF
dgetrs	solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF
dggbak	form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL
dggbal	balance a pair of general real matrices (A,B)
dggglm	solve a general Gauss-Markov linear model (GLM) problem
dgghrd	reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular
dgglse	solve the linear equality-constrained least squares (LSE) problem
dggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
dggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
dggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
dggsvp	compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0
dgtcon	estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF
dgtrfs	improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
dgtsl	solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.
dgtsv	solve the equation A∗X = B,
dgtsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B,
dgttrf	compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
dgttrs	solve one of the systems of equations A∗X = B or A’∗X = B,
dhgeqz	implement a single-shift or double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
dhsein	use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
dhseqr	compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
dlabad	take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
dlabrd	reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
dlacon	estimate the 1-norm of a square, real matrix A
dlacpy	copie all or part of a two-dimensional matrix A to another matrix B
dladiv	perform complex division in real arithmetic (p + i∗q) = (a + i∗b) / (c + i∗d) The algorithm is due to Robert L
dlae2	compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
dlaebz	contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
dlaed0	compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
dlaed1	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed2	merge the two sets of eigenvalues together into a single sorted set
dlaed3	find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP
dlaed4	subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
dlaed5	subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
dlaed6	compute the positive or negative root (closest to the origin) of f(x) = rho + (z(1) / (d(1)-x)) + (z(2) / (d(2)-x)) + (z(3) / (d(3)-x)) It is assumed that if ORGATI = .true
dlaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
dlaed8	merge the two sets of eigenvalues together into a single sorted set
dlaed9	find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
dlaeda	compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
dlaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
dlaev2	compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
dlaexc	swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
dlag2	compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A-wB, with scaling as necessary to avoid overflow/underflow
dlags2	compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) (-SNU CSU ) (-SNV CSV ) (-SNQ CSQ ) Z’ denotes the transpose of Z
dlagtf	factorize the matrix (T-lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T-lambda∗I = PLU,
dlagtm	perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be zero, one, or minus one
dlagts	may be used to solve one of the systems of equations (T-lambda∗I)∗x = y or (T-lambda∗I)’∗x = y,
dlahqr	i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
dlahrd	reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
dlaic1	apply one step of incremental condition estimation in its simplest version
dlaln2	solve a system of the form (ca A-wD ) X = s B or (ca A’-wD) X = s B with possible scaling ("s") and perturbation of A
dlamch	determine double precision machine parameters
dlamrg	will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order
dlangb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
dlange	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
dlangt	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
dlanhs	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
dlansb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
dlansp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
dlanst	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
dlansy	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
dlantb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
dlantp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
dlantr	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
dlanv2	compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
dlapll	two column vectors X and Y, let A = ( X Y )
dlapmt	rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
dlapy2	return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow
dlapy3	return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow
dlaqgb	equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
dlaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
dlaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
dlaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S
dlaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S
dlaqtr	solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE
dlar2v	apply a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
dlarf	apply a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlarfb	apply a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right
dlarfg	generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I
dlarft	form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
dlarfx	apply a real elementary reflector H to a real m by n matrix C, from either the left or the right
dlargv	generate a vector of real plane rotations, determined by elements of the real vectors x and y
dlarnv	return a vector of n random real numbers from a uniform or normal distribution
dlartg	generate a plane rotation so that [ CS SN ]
dlartv	apply a vector of real plane rotations to elements of the real vectors x and y
dlaruv	return a vector of n random real numbers from a uniform (0,1)
dlas2	compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
dlascl	multiply the M by N real matrix A by the real scalar CTO/CFROM
dlaset	initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
dlasq1	DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
dlasq2	DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E
dlasq3	DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm
dlasq4	DLASQ4 estimates TAU, the smallest eigenvalue of a matrix
dlasr	perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
dlasrt	the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ )
dlassq	return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,
dlasv2	compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
dlaswp	perform a series of row interchanges on the matrix A
dlasy2	solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B,
dlasyf	compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dlatbs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
dlatps	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
dlatrd	reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
dlatrs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow
dlatzm	apply a Householder matrix generated by DTZRQF to a matrix
dlauu2	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
dlauum	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
dnrm2	Return the Euclidian norm of a vector.
dopgtr	generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage
dopmtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
doptimal_workspace	Get the optimal amount of workspace for the last routine called that supports varying length
dorg2l	generate an m by n real matrix Q with orthonormal columns,
dorg2r	generate an m by n real matrix Q with orthonormal columns,
dorgbr	generate one of the real orthogonal matrices Q or P∗∗T determined by DGEBRD when reducing a real matrix A to bidiagonal form
dorghr	generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD
dorgl2	generate an m by n real matrix Q with orthonormal rows,
dorglq	generate an M-by-N real matrix Q with orthonormal rows,
dorgql	generate an M-by-N real matrix Q with orthonormal columns,
dorgqr	generate an M-by-N real matrix Q with orthonormal columns,
dorgr2	generate an m by n real matrix Q with orthonormal rows,
dorgrq	generate an M-by-N real matrix Q with orthonormal rows,
dorgtr	generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD
dorm2l	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
dorm2r	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
dormbr	VECT = ’Q’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dormhr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dorml2	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
dormlq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dormql	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dormqr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dormr2	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
dormrq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dormtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
dpbco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
dpbcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF
dpbdi	compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA.
dpbequ	compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
dpbfa	compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
dpbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
dpbsl	section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x.
dpbstf	compute a split Cholesky factorization of a real symmetric positive definite band matrix A
dpbsv	compute the solution to a real system of linear equations A ∗ X = B,
dpbsvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
dpbtf2	compute the Cholesky factorization of a real symmetric positive definite band matrix A
dpbtrf	compute the Cholesky factorization of a real symmetric positive definite band matrix A
dpbtrs	solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF
dpoco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
dpocon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF
dpodi	compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC.
dpoequ	compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
dpofa	compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
dporfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
dposl	solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x.
dposv	compute the solution to a real system of linear equations A ∗ X = B,
dposvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
dpotf2	compute the Cholesky factorization of a real symmetric positive definite matrix A
dpotrf	compute the Cholesky factorization of a real symmetric positive definite matrix A
dpotri	compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF
dpotrs	solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF
dppco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
dppcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF
dppdi	compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA.
dppequ	compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
dppfa	compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
dpprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
dppsl	solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x.
dppsv	compute the solution to a real system of linear equations A ∗ X = B,
dppsvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
dpptrf	compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
dpptri	compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF
dpptrs	solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF
dptcon	compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF
dpteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor
dptrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
dptsl	solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.
dptsv	compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
dptsvx	use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
dpttrf	compute the factorization of a real symmetric positive definite tridiagonal matrix A
dpttrs	solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF
dqdota	Compute a double precision constant plus an extended precision constant plus the extended precision dot product of two double precision vectors x and y.
dqdoti	Compute a constant plus the extended precision dot product of two double precision vectors x and y.
dqrdc	compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A.
dqrsl	solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x.
drot	Apply a Given’s rotation constructed by DROTG.
drotg	Construct a Given’s plane rotation
drotm	Apply a Gentleman’s modified Given’s rotation constructed by DROTMG.
drotmg	Construct a Gentleman’s modified Given’s plane rotation
drscl	multiply an n-element real vector x by the real scalar 1/a
dsbev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
dsbgst	reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,
dsbgv	compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x
dsbmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
dsbtrd	reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
dscal	Compute y := alpha ∗ y
dsdot	Compute the double precision dot product of two single precision vectors x and y.
dsecnd	return the user time for a process in seconds.
dsico	compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
dsidi	compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA.
dsifa	compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
dsinqb	synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
dsinqf	compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
dsinqi	initialize the array xWSAVE, which is used in both xSINQF and xSINQB.
dsint	compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence.
dsinti	initialize the array xWSAVE, which is used in subroutine xSINT.
dsisl	solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x.
dspco	compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
dspcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF
dspdi	compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA.
dspev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
dspevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
dspevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
dspfa	compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
dspgst	reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
dspgv	compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
dspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
dspr	perform the symmetric rank 1 operation A := alpha∗x∗x’ + A
dspr2	perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A
dsprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
dspsl	solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x.
dspsv	compute the solution to a real system of linear equations A ∗ X = B,
dspsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
dsptrd	reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
dsptrf	compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
dsptri	compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF
dsptrs	solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF
dstebz	compute the eigenvalues of a symmetric tridiagonal matrix T
dstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
dstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
dsteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
dsterf	compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
dstev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
dstevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
dstevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
dstsv	compute the solution to a system of linear equations A ∗ X = B where A is a symmetric tridiagonal matrix
dsttrf	compute the factorization of a symmetric tridiagonal matrix A
dsttrs	computes the solution to a double precision system of linear equations A ∗ X = B
dsvdc	compute the singular value decomposition of a general matrix A.
dswap	Exchange vectors x and y.
dsycon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF
dsyev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsyevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsyevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
dsygs2	reduce a real symmetric-definite generalized eigenproblem to standard form
dsygst	reduce a real symmetric-definite generalized eigenproblem to standard form
dsygv	compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
dsymm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
dsymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
dsyr	perform the symmetric rank 1 operation A := alpha∗x∗x’ + A
dsyr2	perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A
dsyr2k	perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C
dsyrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
dsyrk	perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C
dsysv	compute the solution to a real system of linear equations A ∗ X = B,
dsysvx	use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B,
dsytd2	reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
dsytf2	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytrd	reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
dsytrf	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
dsytri	compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF
dsytrs	solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF
dtbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
dtbmv	perform one of the matrix-vector operations x := A∗x or x := A’∗x
dtbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
dtbsv	solve one of the systems of equations A∗x = b or A’∗x = b
dtbtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
dtgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
dtgsja	compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
dtpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
dtpmv	perform one of the matrix-vector operations x := A∗x or x := A’∗x
dtprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
dtpsv	solve one of the systems of equations A∗x = b or A’∗x = b
dtptri	compute the inverse of a real upper or lower triangular matrix A stored in packed format
dtptrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
dtrans	transpose and scale source matrix
dtrco	estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
dtrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
dtrdi	compute the determinant and inverse of a triangular matrix A.
dtrevc	compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
dtrexc	reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST
dtrmm	perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A )
dtrmv	perform one of the matrix-vector operations x := A∗x or x := A’∗x
dtrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
dtrsen	reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
dtrsl	solve the linear system Ax = b for a triangular matrix A and vectors b and x.
dtrsm	solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B
dtrsna	estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal)
dtrsv	solve one of the systems of equations A∗x = b or A’∗x = b
dtrsyl	solve the real Sylvester matrix equation
dtrti2	compute the inverse of a real upper or lower triangular matrix
dtrtri	compute the inverse of a real upper or lower triangular matrix A
dtrtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
dtzrqf	reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
dwiener	perform Wiener deconvolution of two signals
dzasum	Return the sum of the absolute values of a vector x.
dznrm2	Return the Euclidian norm of a vector.
dzsum1	take the sum of the absolute values of a complex vector and returns a double precision result
ezfftb	computes a periodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB.
ezfftf	computes the Fourier coefficients of a periodic sequence. EZFFTF is a simplified but slower version of RFFTF.
ezffti	initializes the array WSAVE, which is used in both EZFFTF and EZFFTB.
icamax	Return the index of the element with largest absolute value.
icmax1	find the index of the element whose real part has maximum absolute value
idamax	Return the index of the element with largest absolute value.
ilaenv	choose problem-dependent parameters
isamax	Return the index of the element with largest absolute value.
izamax	Return the index of the element with largest absolute value.
izmax1	find the index of the element whose real part has maximum absolute value
lapack	introduction to LAPACK
lsame	case-insensitive comparison of two characters
lsamen	test if the first N letters of CA are the same as the first N letters of CB, regardless of case
rfft2b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
rfft2f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
rfft2i	initialize the array xWSAVE, which is used in both xFFT2F and xFFT2B.
rfft3b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
rfft3f	compute the Fourier coefficients of a real periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
rfft3i	initialize the array xWSAVE, which is used in both xFFT3F and xFFT3B.
rfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
rfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
rffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
rfftopt	compute the length of the closest fast FFT
sasum	Return the sum of the absolute values of a vector x.
saxpy	Compute y := alpha ∗ x + y
sbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
scasum	Return the sum of the absolute values of a vector x.
schdc	compute the Cholesky decomposition of a symmetric positive definite matrix A.
schdd	downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
schex	compute the Cholesky decomposition of a symmetric positive definite matrix A.
schud	update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
scnrm2	Return the Euclidian norm of a vector.
scnvcor	compute the convolution or correlation of real vectors
scnvcor2	compute the convolution or correlation of real matrices
scopy	Copy x to y
scsum1	take the sum of the absolute values of a complex vector and returns a single precision result
sdisna	compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix
sdot	Compute the dot product of two vectors x and y.
sdsdot	Compute a constant plus the double precision dot product of two single precision vectors x and y.
second	return the user time for a process in seconds.
sgbbrd	reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
sgbco	compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
sgbcon	estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
sgbdi	compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA.
sgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
sgbfa	compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
sgbmv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y
sgbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
sgbsl	solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x.
sgbsv	compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
sgbsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
sgbtf2	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrf	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
sgbtrs	solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by SGBTRF
sgebak	form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL
sgebal	balance a general real matrix A
sgebd2	reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
sgebrd	reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
sgeco	compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A.
sgecon	estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF
sgedi	compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA.
sgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
sgees	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeesx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
sgeev	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgeevx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
sgefa	compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A.
sgegs	compute for a pair of N-by-N real nonsymmetric matrices A, B
sgegv	compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR)
sgehd2	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
sgehrd	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
sgelq2	compute an LQ factorization of a real m by n matrix A
sgelqf	compute an LQ factorization of a real M-by-N matrix A
sgels	solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
sgelss	compute the minimum norm solution to a real linear least squares problem
sgelsx	compute the minimum-norm solution to a real linear least squares problem
sgemm	perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C
sgemv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y
sgeql2	compute a QL factorization of a real m by n matrix A
sgeqlf	compute a QL factorization of a real M-by-N matrix A
sgeqpf	compute a QR factorization with column pivoting of a real M-by-N matrix A
sgeqr2	compute a QR factorization of a real m by n matrix A
sgeqrf	compute a QR factorization of a real M-by-N matrix A
sger	perform the rank 1 operation A := alpha∗x∗y’ + A
sgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
sgerq2	compute an RQ factorization of a real m by n matrix A
sgerqf	compute an RQ factorization of a real M-by-N matrix A
sgesl	solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.
sgesv	compute the solution to a real system of linear equations A ∗ X = B,
sgesvd	compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors
sgesvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B,
sgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
sgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
sgetri	compute the inverse of a matrix using the LU factorization computed by SGETRF
sgetrs	solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF
sggbak	form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL
sggbal	balance a pair of general real matrices (A,B)
sggglm	solve a general Gauss-Markov linear model (GLM) problem
sgghrd	reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular
sgglse	solve the linear equality-constrained least squares (LSE) problem
sggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
sggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
sggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
sggsvp	compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0
sgtcon	estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF
sgtrfs	improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
sgtsl	solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.
sgtsv	solve the equation A∗X = B,
sgtsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B,
sgttrf	compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
sgttrs	solve one of the systems of equations A∗X = B or A’∗X = B,
shgeqz	implement a single-shift/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
shsein	use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
shseqr	compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors
sinqb	synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
sinqf	compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
sinqi	initialize the array xWSAVE, which is used in both xSINQF and xSINQB.
sint	compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence.
sinti	initialize the array xWSAVE, which is used in subroutine xSINT.
slabad	take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
slabrd	reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
slacon	estimate the 1-norm of a square, real matrix A
slacpy	copie all or part of a two-dimensional matrix A to another matrix B
sladiv	perform complex division in real arithmetic (p + i∗q) = (a + i∗b) / (c + i∗d) The algorithm is due to Robert L
slae2	compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
slaebz	contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
slaed0	compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
slaed1	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed2	merge the two sets of eigenvalues together into a single sorted set
slaed3	find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP
slaed4	subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
slaed5	subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
slaed6	compute the positive or negative root (closest to the origin) of f(x) = rho + (z(1) / (d(1)-x)) + (z(2) / (d(2)-x)) + (z(3) / (d(3)-x)) It is assumed that if ORGATI = .true
slaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
slaed8	merge the two sets of eigenvalues together into a single sorted set
slaed9	find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
slaeda	compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
slaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
slaev2	compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
slaexc	swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
slag2	compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A-wB, with scaling as necessary to avoid overflow/underflow
slags2	compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) (-SNU CSU ) (-SNV CSV ) (-SNQ CSQ ) Z’ denotes the transpose of Z
slagtf	factorize the matrix (T-lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T-lambda∗I = PLU,
slagtm	perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be zero, one, or minus one
slagts	may be used to solve one of the systems of equations (T-lambda∗I)∗x = y or (T-lambda∗I)’∗x = y,
slahqr	i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
slahrd	reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
slaic1	apply one step of incremental condition estimation in its simplest version
slaln2	solve a system of the form (ca A-wD ) X = s B or (ca A’-wD) X = s B with possible scaling ("s") and perturbation of A
slamch	determine single precision machine parameters
slamrg	will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order
slangb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
slange	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
slangt	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
slanhs	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
slansb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
slansp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
slanst	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
slansy	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
slantb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
slantp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
slantr	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
slanv2	compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
slapll	two column vectors X and Y, let A = ( X Y )
slapmt	rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
slapy2	return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow
slapy3	return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow
slaqgb	equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
slaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
slaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
slaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S
slaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S
slaqtr	solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE
slar2v	apply a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
slarf	apply a real elementary reflector H to a real m by n matrix C, from either the left or the right
slarfb	apply a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right
slarfg	generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I
slarft	form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
slarfx	apply a real elementary reflector H to a real m by n matrix C, from either the left or the right
slargv	generate a vector of real plane rotations, determined by elements of the real vectors x and y
slarnv	return a vector of n random real numbers from a uniform or normal distribution
slartg	generate a plane rotation so that [ CS SN ]
slartv	apply a vector of real plane rotations to elements of the real vectors x and y
slaruv	return a vector of n random real numbers from a uniform (0,1)
slas2	compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
slascl	multiply the M by N real matrix A by the real scalar CTO/CFROM
slaset	initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
slasq1	SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
slasq2	SLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E
slasq3	SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm
slasq4	SLASQ4 estimates TAU, the smallest eigenvalue of a matrix
slasr	perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
slasrt	the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ )
slassq	return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,
slasv2	compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
slaswp	perform a series of row interchanges on the matrix A
slasy2	solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B,
slasyf	compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
slatbs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
slatps	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
slatrd	reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
slatrs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow
slatzm	apply a Householder matrix generated by STZRQF to a matrix
slauu2	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
slauum	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
snrm2	Return the Euclidian norm of a vector.
sopgtr	generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage
sopmtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
soptimal_workspace	Get the optimal amount of workspace for the last routine called that supports varying length real workspace.
sorg2l	generate an m by n real matrix Q with orthonormal columns,
sorg2r	generate an m by n real matrix Q with orthonormal columns,
sorgbr	generate one of the real orthogonal matrices Q or P∗∗T determined by SGEBRD when reducing a real matrix A to bidiagonal form
sorghr	generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD
sorgl2	generate an m by n real matrix Q with orthonormal rows,
sorglq	generate an M-by-N real matrix Q with orthonormal rows,
sorgql	generate an M-by-N real matrix Q with orthonormal columns,
sorgqr	generate an M-by-N real matrix Q with orthonormal columns,
sorgr2	generate an m by n real matrix Q with orthonormal rows,
sorgrq	generate an M-by-N real matrix Q with orthonormal rows,
sorgtr	generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD
sorm2l	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
sorm2r	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
sormbr	VECT = ’Q’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sormhr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sorml2	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
sormlq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sormql	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sormqr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sormr2	overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’,
sormrq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
sormtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
spbco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
spbcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF
spbdi	compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA.
spbequ	compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
spbfa	compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
spbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
spbsl	section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x.
spbstf	compute a split Cholesky factorization of a real symmetric positive definite band matrix A
spbsv	compute the solution to a real system of linear equations A ∗ X = B,
spbsvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
spbtf2	compute the Cholesky factorization of a real symmetric positive definite band matrix A
spbtrf	compute the Cholesky factorization of a real symmetric positive definite band matrix A
spbtrs	solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF
spoco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
spocon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF
spodi	compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC.
spoequ	compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
spofa	compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
sporfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
sposl	solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x.
sposv	compute the solution to a real system of linear equations A ∗ X = B,
sposvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
spotf2	compute the Cholesky factorization of a real symmetric positive definite matrix A
spotrf	compute the Cholesky factorization of a real symmetric positive definite matrix A
spotri	compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF
spotrs	solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF
sppco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
sppcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF
sppdi	compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA.
sppequ	compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
sppfa	compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
spprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
sppsl	solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x.
sppsv	compute the solution to a real system of linear equations A ∗ X = B,
sppsvx	use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B,
spptrf	compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
spptri	compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF
spptrs	solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF
sptcon	compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF
spteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor
sptrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
sptsl	solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.
sptsv	compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
sptsvx	use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
spttrf	compute the factorization of a real symmetric positive definite tridiagonal matrix A
spttrs	solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF
sqrdc	compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A.
sqrsl	solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x.
srot	Apply a Given’s rotation constructed by SROTG.
srotg	Construct a Given’s plane rotation
srotm	Apply a Gentleman’s modified Given’s rotation constructed by SROTMG.
srotmg	Construct a Gentleman’s modified Given’s plane rotation
srscl	multiply an n-element real vector x by the real scalar 1/a
ssbev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
ssbgst	reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,
ssbgv	compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x
ssbmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
ssbtrd	reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
sscal	Compute y := alpha ∗ y
ssico	compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
ssidi	compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA.
ssifa	compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
ssisl	solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x.
sspco	compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
sspcon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF
sspdi	compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA.
sspev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
sspevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
sspevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
sspfa	compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
sspgst	reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
sspgv	compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
sspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
sspr	perform the symmetric rank 1 operation A := alpha∗x∗x’ + A
sspr2	perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A
ssprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
sspsl	solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x.
sspsv	compute the solution to a real system of linear equations A ∗ X = B,
sspsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
ssptrd	reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
ssptrf	compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
ssptri	compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF
ssptrs	solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF
sstebz	compute the eigenvalues of a symmetric tridiagonal matrix T
sstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
sstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
ssteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
ssterf	compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
sstev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
sstevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
sstevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
sstsv	compute the solution to a system of linear equations A ∗ X = B where A is a symmetric tridiagonal matrix
ssttrf	compute the factorization of a symmetric tridiagonal matrix A
ssttrs	computes the solution to a real system of linear equations A ∗ X = B
ssvdc	compute the singular value decomposition of a general matrix A.
sswap	Exchange vectors x and y.
ssycon	estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF
ssyev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssyevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssyevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
ssygs2	reduce a real symmetric-definite generalized eigenproblem to standard form
ssygst	reduce a real symmetric-definite generalized eigenproblem to standard form
ssygv	compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
ssymm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
ssymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
ssyr	perform the symmetric rank 1 operation A := alpha∗x∗x’ + A
ssyr2	perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A
ssyr2k	perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C
ssyrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
ssyrk	perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C
ssysv	compute the solution to a real system of linear equations A ∗ X = B,
ssysvx	use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B,
ssytd2	reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
ssytf2	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytrd	reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
ssytrf	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
ssytri	compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF
ssytrs	solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF
stbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
stbmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x
stbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
stbsv	solve one of the systems of equations A∗x = b, or A’∗x = b
stbtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
stgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
stgsja	compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
stpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
stpmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x
stprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
stpsv	solve one of the systems of equations A∗x = b, or A’∗x = b
stptri	compute the inverse of a real upper or lower triangular matrix A stored in packed format
stptrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
strans	transpose and scale source matrix
strco	estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
strcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
strdi	compute the determinant and inverse of a triangular matrix A.
strevc	compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
strexc	reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST
strmm	perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A )
strmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x
strrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
strsen	reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
strsl	solve the linear system Ax = b for a triangular matrix A and vectors b and x.
strsm	solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B
strsna	estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal)
strsv	solve one of the systems of equations A∗x = b, or A’∗x = b
strsyl	solve the real Sylvester matrix equation
strti2	compute the inverse of a real upper or lower triangular matrix
strtri	compute the inverse of a real upper or lower triangular matrix A
strtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,
stzrqf	reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
swiener	perform Wiener deconvolution of two signals
use_double_workspace	Provide a block of memory to be used in LAPACK routines that have a real or complex workspace parameter that can vary in length and are called through the C interfaces.
use_int_workspace	Provide a block of memory to be used in LAPACK routines that have a integer workspace parameter that can vary in length and are called through the C interfaces.
use_threads	set the upper bound on the number of threads that the calling thread wants used
use_workspace	Provide a block of memory to be used in LAPACK routines that have a real or complex workspace parameter that can vary in length and are called through the C interfaces.
using_threads	returns the current Use number set by the USE_THREADS subroutine
vcfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vcfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vcffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
vcosqb	synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
vcosqf	compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
vcosqi	initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB.
vcost	compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N-1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence.
vcosti	initialize the array xWSAVE, which is used in xCOST.
vdcosqb	synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
vdcosqf	compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence.
vdcosqi	initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB.
vdcost	compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N-1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence.
vdcosti	initialize the array xWSAVE, which is used in xCOST.
vdfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vdfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vdffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
vdsinqb	synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
vdsinqf	compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
vdsinqi	initialize the array xWSAVE, which is used in both xSINQF and xSINQB.
vdsint	compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence.
vdsinti	initialize the array xWSAVE, which is used in subroutine xSINT.
vrfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vrfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vrffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
vsinqb	synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
vsinqf	compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.
vsinqi	initialize the array xWSAVE, which is used in both xSINQF and xSINQB.
vsint	compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence.
vsinti	initialize the array xWSAVE, which is used in subroutine xSINT.
vzfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vzfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
vzffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
xerbla	error handler for the LAPACK routines
zaxpy	Compute y := alpha ∗ x + y
zbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
zchdc	compute the Cholesky decomposition of a symmetric positive definite matrix A.
zchdd	downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
zchex	compute the Cholesky decomposition of a symmetric positive definite matrix A.
zchud	update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.
zcnvcor	compute the convolution or correlation of double precision complex vectors
zcnvcor2	compute the convolution or correlation of complex matrices
zcopy	Copy x to y
zdotc	Compute the dot product of two vectors x and conjg(y).
zdotu	Compute the dot product of two vectors x and y.
zdrot	Apply a plane rotation
zdrscl	multiply an n-element complex vector x by the real scalar 1/a
zdscal	Compute y := alpha ∗ y
zfft2b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
zfft2f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M∗N.
zfft2i	initialize the array xWSAVE, which is used in both xFFT2F and xFFT2B.
zfft3b	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
zfft3f	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M∗N∗K.
zfft3i	initialize the array xWSAVE, which is used in both xFFT3F and xFFT3B.
zfftb	compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
zfftf	compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence.
zffti	initialize the array xWSAVE, which is used in both xFFTF and xFFTB.
zfftopt	compute the length of the closest fast FFT
zgbbrd	reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
zgbco	compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
zgbcon	estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
zgbdi	compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA.
zgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
zgbfa	compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.
zgbmv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y
zgbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
zgbsl	solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x.
zgbsv	compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices
zgbsvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
zgbtf2	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrf	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
zgbtrs	solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by ZGBTRF
zgebak	form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL
zgebal	balance a general complex matrix A
zgebd2	reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
zgebrd	reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
zgeco	compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A.
zgecon	estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF
zgedi	compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA.
zgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
zgees	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeesx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
zgeev	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgeevx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
zgefa	compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A.
zgegs	compute for a pair of N-by-N complex nonsymmetric matrices A,
zgegv	compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,
zgehd2	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
zgehrd	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
zgelq2	compute an LQ factorization of a complex m by n matrix A
zgelqf	compute an LQ factorization of a complex M-by-N matrix A
zgels	solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
zgelss	compute the minimum norm solution to a complex linear least squares problem
zgelsx	compute the minimum-norm solution to a complex linear least squares problem
zgemm	perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C
zgemv	perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y
zgeql2	compute a QL factorization of a complex m by n matrix A
zgeqlf	compute a QL factorization of a complex M-by-N matrix A
zgeqpf	compute a QR factorization with column pivoting of a complex M-by-N matrix A
zgeqr2	compute a QR factorization of a complex m by n matrix A
zgeqrf	compute a QR factorization of a complex M-by-N matrix A
zgerc	perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A
zgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
zgerq2	compute an RQ factorization of a complex m by n matrix A
zgerqf	compute an RQ factorization of a complex M-by-N matrix A
zgeru	perform the rank 1 operation A := alpha∗x∗y’ + A
zgesl	solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.
zgesv	compute the solution to a complex system of linear equations A ∗ X = B,
zgesvd	compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors
zgesvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B,
zgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
zgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
zgetri	compute the inverse of a matrix using the LU factorization computed by ZGETRF
zgetrs	solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF
zggbak	form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL
zggbal	balance a pair of general complex matrices (A,B)
zggglm	solve a general Gauss-Markov linear model (GLM) problem
zgghrd	reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular
zgglse	solve the linear equality-constrained least squares (LSE) problem
zggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
zggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
zggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
zggsvp	compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0
zgtcon	estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF
zgtrfs	improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
zgtsl	solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.
zgtsv	solve the equation A∗X = B,
zgtsvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
zgttrf	compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
zgttrs	solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
zhbev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
zhbgst	reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,
zhbgv	compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x
zhbmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
zhbtrd	reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhecon	estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF
zheev	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zheevd	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zheevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
zhegs2	reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegst	reduce a complex Hermitian-definite generalized eigenproblem to standard form
zhegv	compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
zhemm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
zhemv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
zher	perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A
zher2	perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A
zher2k	perform one of the hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C
zherfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
zherk	perform one of the hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C
zhesv	compute the solution to a complex system of linear equations A ∗ X = B,
zhesvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,
zhetd2	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhetf2	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetrd	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
zhetrf	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zhetri	compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF
zhetrs	solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF
zhgeqz	implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
zhico	compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.
zhidi	compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA.
zhifa	compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.
zhisl	solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x.
zhpco	compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.
zhpcon	estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF
zhpdi	compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA.
zhpev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
zhpevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
zhpfa	compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.
zhpgst	reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
zhpgv	compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x
zhpmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y
zhpr	perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A
zhpr2	perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A
zhprfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
zhpsl	solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x.
zhpsv	compute the solution to a complex system of linear equations A ∗ X = B,
zhpsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
zhptrd	reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
zhptrf	compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
zhptri	compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF
zhptrs	solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF
zhsein	use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
zhseqr	compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors
zlabrd	reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
zlacgv	conjugate a complex vector of length N
zlacon	estimate the 1-norm of a square, complex matrix A
zlacpy	copie all or part of a two-dimensional matrix A to another matrix B
zlacrm	perform a very simple matrix-matrix multiplication
zlacrt	apply a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex
zladiv	:= X / Y, where X and Y are complex
zlaed0	the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
zlaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
zlaed8	merge the two sets of eigenvalues together into a single sorted set
zlaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
zlaesy	compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
zlaev2	compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
zlags2	compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
zlagtm	perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be zero, one, or minus one
zlahef	compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zlahqr	i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
zlahrd	reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
zlaic1	apply one step of incremental condition estimation in its simplest version
zlangb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
zlange	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
zlangt	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
zlanhb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
zlanhe	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
zlanhp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
zlanhs	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
zlanht	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
zlansb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
zlansp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
zlansy	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
zlantb	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
zlantp	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
zlantr	return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
zlapll	two column vectors X and Y, let A = ( X Y )
zlapmt	rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
zlaqgb	equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
zlaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
zlaqhb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqhe	equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqhp	equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S
zlaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S
zlar2v	apply a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
zlarf	apply a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
zlarfb	apply a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right
zlarfg	generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I
zlarft	form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
zlarfx	apply a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
zlargv	generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
zlarnv	return a vector of n random complex numbers from a uniform or normal distribution
zlartg	generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
zlartv	apply a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
zlascl	multiply the M by N complex matrix A by the real scalar CTO/CFROM
zlaset	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
zlasr	perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
zlassq	return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,
zlaswp	perform a series of row interchanges on the matrix A
zlasyf	compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zlatbs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
zlatps	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
zlatrd	reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
zlatrs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,
zlatzm	apply a Householder matrix generated by ZTZRQF to a matrix
zlauu2	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zlauum	compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zoptimal_workspace	Get the optimal amount of workspace for the last routine called that supports varying length
zpbco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
zpbcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF
zpbdi	compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA.
zpbequ	compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
zpbfa	compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
zpbrfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
zpbsl	section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x.
zpbstf	compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbsv	compute the solution to a complex system of linear equations A ∗ X = B,
zpbsvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
zpbtf2	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrf	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
zpbtrs	solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF
zpoco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
zpocon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF
zpodi	compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC.
zpoequ	compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
zpofa	compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.
zporfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
zposl	solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x.
zposv	compute the solution to a complex system of linear equations A ∗ X = B,
zposvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
zpotf2	compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A
zpotri	compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF
zpotrs	solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF
zppco	compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
zppcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF
zppdi	compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA.
zppequ	compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
zppfa	compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.
zpprfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
zppsl	solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x.
zppsv	compute the solution to a complex system of linear equations A ∗ X = B,
zppsvx	use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B,
zpptrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
zpptri	compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF
zpptrs	solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF
zptcon	compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by ZPTTRF
zpteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidiagonal factor
zptrfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
zptsl	solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.
zptsv	compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices
zptsvx	use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
zpttrf	compute the factorization of a complex Hermitian positive definite tridiagonal matrix A
zpttrs	solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by ZPTTRF
zqrdc	compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A.
zqrsl	solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x.
zrot	apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex
zrotg	Construct a Given’s plane rotation
zscal	Compute y := alpha ∗ y
zsico	compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
zsidi	compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA.
zsifa	compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.
zsisl	solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x.
zspco	compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
zspcon	estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF
zspdi	compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA.
zspfa	compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.
zspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,
zspr	perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A,
zsprfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
zspsl	solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x.
zspsv	compute the solution to a complex system of linear equations A ∗ X = B,
zspsvx	use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
zsptrf	compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
zsptri	compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF
zsptrs	solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF
zstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
zstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
zsteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
zstsv	compute the solution to a complex system of linear equations A ∗ X = B where A is a Hermitian tridiagonal matrix
zsttrf	compute the factorization of a complex Hermitian tridiagonal matrix A
zsttrs	computes the solution to a complex∗16 system of linear equations A ∗ X = B
zsvdc	compute the singular value decomposition of a general matrix A.
zswap	Exchange vectors x and y.
zsycon	estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF
zsymm	perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C
zsymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,
zsyr	perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A,
zsyr2k	perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C
zsyrfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution
zsyrk	perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C
zsysv	compute the solution to a complex system of linear equations A ∗ X = B,
zsysvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,
zsytf2	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytrf	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zsytri	compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF
zsytrs	solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF
ztbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
ztbmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ztbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
ztbsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ztbtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ztgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
ztgsja	compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
ztpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
ztpmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ztprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
ztpsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ztptri	compute the inverse of a complex upper or lower triangular matrix A stored in packed format
ztptrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ztrans	transpose and scale source matrix
ztrco	estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.
ztrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
ztrdi	compute the determinant and inverse of a triangular matrix A.
ztrevc	compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
ztrexc	reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST
ztrmm	perform one of the matrix-matrix operations B := alpha∗op( A )∗B or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ )
ztrmv	perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x
ztrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
ztrsen	reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
ztrsl	solve the linear system Ax = b for a triangular matrix A and vectors b and x.
ztrsm	solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B
ztrsna	estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary)
ztrsv	solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b
ztrsyl	solve the complex Sylvester matrix equation
ztrti2	compute the inverse of a complex upper or lower triangular matrix
ztrtri	compute the inverse of a complex upper or lower triangular matrix A
ztrtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,
ztzrqf	reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
zung2l	generate an m by n complex matrix Q with orthonormal columns,
zung2r	generate an m by n complex matrix Q with orthonormal columns,
zungbr	generate one of the complex unitary matrices Q or P∗∗H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form
zunghr	generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD
zungl2	generate an m-by-n complex matrix Q with orthonormal rows,
zunglq	generate an M-by-N complex matrix Q with orthonormal rows,
zungql	generate an M-by-N complex matrix Q with orthonormal columns,
zungqr	generate an M-by-N complex matrix Q with orthonormal columns,
zungr2	generate an m by n complex matrix Q with orthonormal rows,
zungrq	generate an M-by-N complex matrix Q with orthonormal rows,
zungtr	generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD
zunm2l	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
zunm2r	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
zunmbr	VECT = ’Q’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunmhr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunml2	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
zunmlq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunmql	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunmqr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunmr2	overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’,
zunmrq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zunmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zupgtr	generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage
zupmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’
zvmul	compute the scaled product of complex∗16 vectors

3m. Math Library

List

3x. Miscellaneous Libraries

_rtc_check_free	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_check_malloc	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_check_malloc_result	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_check_realloc	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_check_realloc_result	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_hide_region	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_off	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_on	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_record_free	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_record_malloc	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_record_realloc	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
_rtc_report_error	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]
rtc_api	Runtime Checking (RTC) API for the use of private memory allocators.	[ _rtc_check_free, _rtc_check_malloc, _rtc_check_realloc, _rtc_check_malloc_result, _rtc_check_realloc_result, _rtc_hide_region, _rtc_off, _rtc_on, _rtc_record_free, _rtc_record_malloc, _rtc_record_realloc, _rtc_report_error, rtc_api ]

4. File Formats

access_control	TeamWare access control file
args	TeamWare argument caching file
children	List of a workspace’s child workspaces
conflicts	List of files in conflict in a workspace
dbxinit	commands to dbx	[ dbxinit, .dbxinit ]
dbxrc	commands to dbx	[ dbxrc, .dbxrc ]
freezepointfile	format of a freezepoint file
locks	TeamWare locks file
nametable	CodeManager file name table
notification	TeamWare notification file
parent	Path name of a workspace’s parent
putback.cmt	Putback transaction comment log file
sbinit	directives to SourceBrowser and compilers

Museum

Anchors

Manual — unbundled WorkShop_5.0

Section (4)

1. Commands (intro)

3. Functions and Libraries

Section 3C++

Section 3F (intro)

3M. Math Library (intro)

Section 3P

3m. Math Library

3x. Miscellaneous Libraries

4. File Formats