Manual — Digital_UNIX Extended_Math_Library_3.4

Section ---

[[empty]] zbcon.3lapack

Section 3DXML

array-math	A library of linear algebra routines
blas1	A library of linear algebra routines
blas1e	A library of linear algebra routines
blas1s	A library of linear algebra routines
blas2	A library of linear algebra routines
blas3	A library of linear algebra routines
caxpyi
cdotci	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
cdotui	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
cgthr	Gathers the specified elements of a vector	[ sgthr, dgthr, cgthr, zgthr ]
cgthrs
cgthrz	Gathers and zeros specified elements of a vector	[ sgthrz, dgthrz, cgthrz, zgthrz ]
csctr	Scatters the elements of a sparse vector	[ ssctr, dsctr, csctr, zsctr ]
csctrs	Scales and scatters the elements of a sparse vector	[ ssctrs, dsctrs, csctrs, zsctrs ]
csumi	Sum of a vector and a sparse vector	[ ssumi, dsumi, csumi, zsumi ]
dapply_diag_all	Apply diagonal preconditioner for any storage scheme (Serial and Parallel Versions)
dapply_ilu_genr_l	Apply incomplete LU preconditioner for general storage by rows
dapply_ilu_genr_u	Apply incomplete LU preconditioner for general storage by rows
dapply_ilu_sdia	Apply ILU preconditioner for symmetric diagonal storage
dapply_ilu_udia_l	Apply ILU preconditioner for unsymmetric diagonal storage
dapply_ilu_udia_u	Apply ILU preconditioner for unsymmetric diagonal storage
dapply_poly_genr	Apply polynomial preconditioner for general storage by rows (Serial and Parallel Versions)
dapply_poly_sdia	Apply polynomial preconditioner for symmetric diagonal storage (Serial and Parallel Versions)
dapply_poly_udia	Apply polynomial preconditioner for unsymmetric diagonal storage (Serial and Parallel Versions)
daxpyi
dcreate_diag_genr	Generate diagonal preconditioner for general storage by rows (Serial and Parallel Versions)
dcreate_diag_sdia	Generate diagonal preconditioner for symmetric diagonal storage (Serial and Parallel Versions)
dcreate_diag_udia	Generate diagonal preconditioner for unsymmetric diagonal storage (Serial and Parallel Versions)
dcreate_ilu_genr	Generate incomplete LU preconditioner for general storage by rows
dcreate_ilu_sdia	Generate incomplete Cholesky preconditioner for symmetric diagonal storage
dcreate_ilu_udia	Generate incomplete LU preconditioner for unsymmetric diagonal storage
dcreate_poly_genr	Generate polynomial preconditioner for general storage by rows (Serial and Parallel Versions)
dcreate_poly_sdia	Generate polynomial preconditioner for symmetric diagonal storage (Serial and Parallel Versions)
dcreate_poly_udia	Generate polynomial preconditioner for unsymmetric diagonal storage (Serial and Parallel Versions)
ddoti	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
dgthr	Gathers the specified elements of a vector	[ sgthr, dgthr, cgthr, zgthr ]
dgthrs
dgthrz	Gathers and zeros specified elements of a vector	[ sgthrz, dgthrz, cgthrz, zgthrz ]
ditsol_defaults	Set default values for iterative solver
ditsol_driver	Driver for sparse iterative solvers (Serial and Parallel Versions)
ditsol_pbcg	Preconditioned bi-conjugate gradient method (Serial and Parallel Versions)
ditsol_pcg	Preconditioned conjugate gradient method (Serial and Parallel Versions)
ditsol_pcgs	Preconditioned conjugate gradient squared method (Serial and Parallel Versions)
ditsol_pgmres	Preconditioned generalized minimum residual method (Serial and Parallel Versions)
ditsol_plscg	Preconditioned least square conjugate gradient method (Serial and Parallel Versions)
ditsol_ptfqmr	Preconditioned transpose-free quasi-minimal method (Serial and Parallel Versions)
dmatvec_genr	Matrix-vector product for general storage by rows (Serial and Parallel Versions)
dmatvec_sdia	Matrix-vector product for symmetric diagonal storage (Serial and Parallel Versions)
dmatvec_udia	Matrix-vector product for unsymmetric diagonal storage (Serial and Parallel Versions)
dpcgs	Preconditioned conjugate gradient squared method
droti	Real givens plane rotation applied to sparse vector	[ sroti, droti ]
dsctr	Scatters the elements of a sparse vector	[ ssctr, dsctr, csctr, zsctr ]
dsctrs	Scales and scatters the elements of a sparse vector	[ ssctrs, dsctrs, csctrs, zsctrs ]
dsskyc	Symmetric sparse matrix condition number estimator using skyline storage scheme
dsskyd
dsskyf	Symmetric sparse matrix factorization using skyline storage scheme (Serial and Parallel Versions)
dsskyn	Symmetric sparse matrix norm evaluation using skyline storage scheme
dsskyr	Symmetric sparse iterative refinement using skyline storage scheme
dsskys	Symmetric sparse matrix solve using skyline storage scheme
dsskyx	Symmetric sparse expert driver using skyline storage scheme
dsumi	Sum of a vector and a sparse vector	[ ssumi, dsumi, csumi, zsumi ]
duskyc	Unsymmetric sparse matrix condition number estimation using skyline storage scheme
duskyd	Unsymmetric sparse simple driver using skyline storage scheme
duskyf
duskyn	Unsymmetric sparse matrix norm evaluation using skyline storage scheme
duskyr	Unsymmetric sparse iterative refinement using skyline storage scheme
duskys	Unsymmetric sparse matrix solve using skyline storage scheme
duskyx	Unsymmetric sparse expert driver using skyline storage scheme
iterative-solvers	A library of sparse linear solvers (iterative)
lapack	A library of linear algebra routines
random-numbers	Random number generator subprograms
saxpyi
sdoti	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
sgthr	Gathers the specified elements of a vector	[ sgthr, dgthr, cgthr, zgthr ]
sgthrs
sgthrz	Gathers and zeros specified elements of a vector	[ sgthrz, dgthrz, cgthrz, zgthrz ]
signal-processing	A library of signal processing routines
skyline-solvers	A library of sparse linear solvers (direct)
sroti	Real givens plane rotation applied to sparse vector	[ sroti, droti ]
ssctr	Scatters the elements of a sparse vector	[ ssctr, dsctr, csctr, zsctr ]
ssctrs	Scales and scatters the elements of a sparse vector	[ ssctrs, dsctrs, csctrs, zsctrs ]
ssumi	Sum of a vector and a sparse vector	[ ssumi, dsumi, csumi, zsumi ]
vcos	Vector cosine
vcos_sin	Vector cosine and sine
vexp	Vector exponential
vlog	Vector logarithm
vrecip	Vector reciprocal
vsin	Vector sine
vsqrt	Vector square root
zaxpyi
zdotci	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
zdotui	Inner product of a vector and a sparse vector	[ sdoti, ddoti, cdotui, zdotui, cdotci, zdotci ]
zgthr	Gathers the specified elements of a vector	[ sgthr, dgthr, cgthr, zgthr ]
zgthrs
zgthrz	Gathers and zeros specified elements of a vector	[ sgthrz, dgthrz, cgthrz, zgthrz ]
zsctr	Scatters the elements of a sparse vector	[ ssctr, dsctr, csctr, zsctr ]
zsctrs	Scales and scatters the elements of a sparse vector	[ ssctrs, dsctrs, csctrs, zsctrs ]
zsumi	Sum of a vector and a sparse vector	[ ssumi, dsumi, csumi, zsumi ]

Section 3dxml

caxpy	Vector plus the product of a scalar and a vector	[ saxpy, daxpy, caxpy, zaxpy ]
cconv_nonperiodic	Nonperiodic convolution	[ sconv_nonperiodic, dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic ]
cconv_nonperiodic_ext	Extended nonperiodic convolution	[ sconv_nonperiodic_ext, dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext ]
cconv_periodic	Periodic concolution	[ sconv_periodic, dconv_periodic, cconv_periodic, zconv_periodic ]
cconv_periodic_ext	Extended periodic convolution	[ sconv_periodic_ext, dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext ]
ccopy	Copy of a vector	[ scopy, dcopy, ccopy, zcopy ]
ccorr_nonperiodic
ccorr_nonperiodic_ext
ccorr_periodic
ccorr_periodic_ext	Extended periodic correlation	[ scorr_periodic_ext, dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext ]
cdotc	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
cdotu	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
cfft	Fast fourier transform in one dimension	[ sfft, dfft, cfft, zfft ]
cfft_2d	Fast fourier transform in two dimensions	[ sfft_2d, dfft_2d, cfft_2d, zfft_2d ]
cfft_3d	Fast fourier transform in three dimensions	[ sfft_3d, dfft_3d, cfft_3d, zfft_3d ]
cfft_apply	Application step for fast fourier transform in one dimension	[ sfft_apply, dfft_apply, cfft_apply, zfft_apply ]
cfft_apply_2d
cfft_apply_3d	Application step for fast fourier transform in three dimensions	[ sfft_apply_3d, dfft_apply_3d, cfft_apply_3d, zfft_apply_3d ]
cfft_apply_grp	Application step for group fast fourier transform in one dimension	[ sfft_apply_grp, dfft_apply_grp, cfft_apply_grp, zfft_apply_grp ]
cfft_exit	Final step for fast fourier transform in one dimension	[ sfft_exit, dfft_exit, cfft_exit, zfft_exit ]
cfft_exit_2d	Final step for fast fourier transform in two dimensions	[ sfft_exit_2d, dfft_exit_2d, cfft_exit_2d, zfft_exit_2d ]
cfft_exit_3d	Final step for fast fourier transfrom in three dimension	[ sfft_exit_3d, dfft_exit_3d, cfft_exit_3d, zfft_exit_3d ]
cfft_exit_grp	Exit step for group fast fourier transform in one dimension	[ sfft_exit_grp, dfft_exit_grp, cfft_exit_grp, zfft_exit_grp ]
cfft_grp	Group fast fourier transform in one dimension	[ sfft_grp, dfft_grp, cfft_grp, zfft_grp ]
cfft_init	Initialization step for fast fourier transform in one dimension	[ sfft_init, dfft_init, cfft_init, zfft_init ]
cfft_init_2d	Initialization step for fast fourier transform in two dimensions	[ sfft_init_2d, dfft_init_2d, cfft_init_2d, zfft_init_2d ]
cfft_init_3d	Initialization step for fast fourier transform in three dimension	[ sfft_init_3d, dfft_init_3d, cfft_init_3d, zfft_init_3d ]
cfft_init_grp	Initialization step for group fast fourier transform in one dimension	[ sfft_init_grp, dfft_init_grp, cfft_init_grp, zfft_init_grp ]
cgbmv	Matrix-vector product for a general band matrix	[ sgbmv, ddbmv, cgbmv, zgbmv ]
cgema	Matrix-matrix addition	[ sgema, dgema, cgema, zgema ]
cgemm	Matrix-matrix product and addition	[ sgemm, dgemm, cgemm, zgemm ]
cgems	Matrix-matrix subtraction	[ sgems, dgems, cgems, zgems ]
cgemt	Matrix-matrix copy	[ sgemt, dgemt, cgemt, zgemt ]
cgemv	Matrix-vector product for a general matrix	[ sgemv, dgemv, cgemv, zgemv ]
cgerc	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
cgeru	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
chbmv	Matrix-vector product for a symmetric or hermitian band matrix	[ ssbmv, dsbmv, chbmv, zhbmv ]
chemm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
chemv	Matrix-vector product for a symmetric or hermitian matrix	[ ssymv, dsymv, chemv, zhemv ]
cher	Rank-one update of a symmetric or hermitian matrix	[ ssyr, dsyr, cher, zher ]
cher2	Rank-two update of a symmetric or hermitian matrix	[ ssyr2, dsyr2, cher2, zher2 ]
cher2k	Rank-2k update of a complex hermitian matrix	[ cher2k, zher2k ]
cherk	Rank-k update of a complex hermitian matrix	[ cherk, zherk ]
chpmv	Matrix-vector product for a symmetric or hermitian matrix stored in packed form	[ sspmv, dspmv, chpmv, zhpmv ]
chpr	Rank-one update of a symmetric or hermitian matrix stored in packed form	[ sspr, dspr, chpr, zhpr ]
chpr2	Rank-two update of a symmetric or hermitian matrix stored in packed form	[ sspr2, dspr2, chpr2, zhpr2 ]
crot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
crotg
cscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
cset	Set all elements of a vector to a scalar	[ sset, dset, cset, zset ]
csrot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
csscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
csum	Sum of the values of the elements of a vector	[ ssum, dsum, csum, zsum ]
csvcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
cswap	Exchange the elements of two vectors	[ sswap, dswap, cswap, zswap ]
csymm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
csyr2k	Rank-2k update of a symmetric matrix	[ ssyr2k, dsyr2k, csyr2k, zsyr2k ]
csyrk	Rank-k update of a symmetric matrix	[ ssyrk, dsyrk, csyrk, zsyrk ]
ctbmv	Matrix-vector product for a triangular band matrix	[ stbmv, dtbmv, ctbmv, ztbmv ]
ctbsv	Solver of a system of linear equations with a triangular band matrix	[ stbsv, dtbsv, ctbsv, ztbsv ]
ctpmv	Matrix-vector product for a triangular matrix in packed form	[ stpmv, dtpmv, ctpmv, ztpmv ]
ctpsv	Solve a system of linear equations with a triangular matrix in packed form	[ stpsv, dtpsv, ctpsv, ztpsv ]
ctrmm	Matrix-matrix product for triangular matrix	[ strmm, dtrmm, ctrmm, ztrmm ]
ctrmv	Marix-vector product for a triangular matrix	[ strmv, dtrmv, ctrmv, ztrmv ]
ctrsm	Solve a triangular system of equations with a triangular coefficient matrix	[ strsm, dtrsm, ctrsm, ztrsm ]
ctrsv	Solver of a system of linear equations with a triangular matrix	[ strsv, dtrsv, ctrsv, ztrsv ]
cvcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
czaxpy	Vector plus the product of a scalar and a vector	[ szaxpy, dzaxpy, czaxpy, zzaxpy ]
damax	Maximum absolute value	[ samax, damax, scamax, dzamax ]
damin
dasum	Sum of the absolute value	[ sasum, dasum, scasum, dzasum ]
daxpy	Vector plus the product of a scalar and a vector	[ saxpy, daxpy, caxpy, zaxpy ]
dconv_nonperiodic	Nonperiodic convolution	[ sconv_nonperiodic, dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic ]
dconv_nonperiodic_ext	Extended nonperiodic convolution	[ sconv_nonperiodic_ext, dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext ]
dconv_periodic	Periodic concolution	[ sconv_periodic, dconv_periodic, cconv_periodic, zconv_periodic ]
dconv_periodic_ext	Extended periodic convolution	[ sconv_periodic_ext, dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext ]
dcopy	Copy of a vector	[ scopy, dcopy, ccopy, zcopy ]
dcorr_nonperiodic
dcorr_nonperiodic_ext
dcorr_periodic
dcorr_periodic_ext	Extended periodic correlation	[ scorr_periodic_ext, dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext ]
ddot	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
dfct	Fast cosine transform in one dimension	[ sfct, dfct ]
dfct_apply	Application step for fast cosine transform in one dimension	[ sfct_apply, dfct_apply ]
dfct_exit	Final step for fast cosine transform in one dimension	[ sfct_exit, dfct_exit ]
dfct_init	Initialization step for fast cosine transform in one dimension	[ sfct_init, dfct_init ]
dfft	Fast fourier transform in one dimension	[ sfft, dfft, cfft, zfft ]
dfft_2d	Fast fourier transform in two dimensions	[ sfft_2d, dfft_2d, cfft_2d, zfft_2d ]
dfft_3d	Fast fourier transform in three dimensions	[ sfft_3d, dfft_3d, cfft_3d, zfft_3d ]
dfft_apply	Application step for fast fourier transform in one dimension	[ sfft_apply, dfft_apply, cfft_apply, zfft_apply ]
dfft_apply_2d
dfft_apply_3d	Application step for fast fourier transform in three dimensions	[ sfft_apply_3d, dfft_apply_3d, cfft_apply_3d, zfft_apply_3d ]
dfft_apply_grp	Application step for group fast fourier transform in one dimension	[ sfft_apply_grp, dfft_apply_grp, cfft_apply_grp, zfft_apply_grp ]
dfft_exit	Final step for fast fourier transform in one dimension	[ sfft_exit, dfft_exit, cfft_exit, zfft_exit ]
dfft_exit_2d	Final step for fast fourier transform in two dimensions	[ sfft_exit_2d, dfft_exit_2d, cfft_exit_2d, zfft_exit_2d ]
dfft_exit_3d	Final step for fast fourier transfrom in three dimension	[ sfft_exit_3d, dfft_exit_3d, cfft_exit_3d, zfft_exit_3d ]
dfft_exit_grp	Exit step for group fast fourier transform in one dimension	[ sfft_exit_grp, dfft_exit_grp, cfft_exit_grp, zfft_exit_grp ]
dfft_grp	Group fast fourier transform in one dimension	[ sfft_grp, dfft_grp, cfft_grp, zfft_grp ]
dfft_init	Initialization step for fast fourier transform in one dimension	[ sfft_init, dfft_init, cfft_init, zfft_init ]
dfft_init_2d	Initialization step for fast fourier transform in two dimensions	[ sfft_init_2d, dfft_init_2d, cfft_init_2d, zfft_init_2d ]
dfft_init_3d	Initialization step for fast fourier transform in three dimension	[ sfft_init_3d, dfft_init_3d, cfft_init_3d, zfft_init_3d ]
dfft_init_grp	Initialization step for group fast fourier transform in one dimension	[ sfft_init_grp, dfft_init_grp, cfft_init_grp, zfft_init_grp ]
dfst	Fast sine transform in one dimension	[ sfst, dfst ]
dfst_apply	Application step for fast sine transform in one dimension	[ sfst_apply, dfst_apply ]
dfst_exit	Final step for fast sine transform in one dimension	[ sfst_exit, dfst_exit ]
dfst_init	Initialization step for fast sine transform in one dimension	[ sfst_init, dfst_init ]
dgbmv	Matrix-vector product for a general band matrix	[ sgbmv, ddbmv, cgbmv, zgbmv ]
dgema	Matrix-matrix addition	[ sgema, dgema, cgema, zgema ]
dgemm	Matrix-matrix product and addition	[ sgemm, dgemm, cgemm, zgemm ]
dgems	Matrix-matrix subtraction	[ sgems, dgems, cgems, zgems ]
dgemt	Matrix-matrix copy	[ sgemt, dgemt, cgemt, zgemt ]
dgemv	Matrix-vector product for a general matrix	[ sgemv, dgemv, cgemv, zgemv ]
dger	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
dmax	Largest element in a real vector	[ smax, dmax ]
dmin	Minimum value of the elements of a real vector	[ smin, dmin ]
dnorm2	Square root of sum of the squares of the elements of a vector	[ snorm2, dnorm2, scnorm2, dznorm2 ]
dnrm2	Square root of sum of the squares of the elements of a vector	[ snrm2, dnrm2, scnrm2, dznrm2 ]
dnrsq	Sum of the squares of the elements of a vector	[ snrsq, dnrsq, scnrsq, dznrsq ]
drot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
drotg
drotm	Apply modified givens transformation	[ srotm, drotm ]
drotmg	Generate elements for a modified Givens transform	[ srotmg, drotmg ]
dsbmv	Matrix-vector product for a symmetric or hermitian band matrix	[ ssbmv, dsbmv, chbmv, zhbmv ]
dscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
dsdot	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
dset	Set all elements of a vector to a scalar	[ sset, dset, cset, zset ]
dsortq	Sort the elements of a vector	[ isortq, ssortq, dsortq ]
dsortqx	Performs an indexed sort of a vector	[ isortqx, ssortqx, dsortqx ]
dspmv	Matrix-vector product for a symmetric or hermitian matrix stored in packed form	[ sspmv, dspmv, chpmv, zhpmv ]
dspr	Rank-one update of a symmetric or hermitian matrix stored in packed form	[ sspr, dspr, chpr, zhpr ]
dspr2	Rank-two update of a symmetric or hermitian matrix stored in packed form	[ sspr2, dspr2, chpr2, zhpr2 ]
dsum	Sum of the values of the elements of a vector	[ ssum, dsum, csum, zsum ]
dswap	Exchange the elements of two vectors	[ sswap, dswap, cswap, zswap ]
dsymm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
dsymv	Matrix-vector product for a symmetric or hermitian matrix	[ ssymv, dsymv, chemv, zhemv ]
dsyr	Rank-one update of a symmetric or hermitian matrix	[ ssyr, dsyr, cher, zher ]
dsyr2	Rank-two update of a symmetric or hermitian matrix	[ ssyr2, dsyr2, cher2, zher2 ]
dsyr2k	Rank-2k update of a symmetric matrix	[ ssyr2k, dsyr2k, csyr2k, zsyr2k ]
dsyrk	Rank-k update of a symmetric matrix	[ ssyrk, dsyrk, csyrk, zsyrk ]
dtbmv	Matrix-vector product for a triangular band matrix	[ stbmv, dtbmv, ctbmv, ztbmv ]
dtbsv	Solver of a system of linear equations with a triangular band matrix	[ stbsv, dtbsv, ctbsv, ztbsv ]
dtpmv	Matrix-vector product for a triangular matrix in packed form	[ stpmv, dtpmv, ctpmv, ztpmv ]
dtpsv	Solve a system of linear equations with a triangular matrix in packed form	[ stpsv, dtpsv, ctpsv, ztpsv ]
dtrmm	Matrix-matrix product for triangular matrix	[ strmm, dtrmm, ctrmm, ztrmm ]
dtrmv	Marix-vector product for a triangular matrix	[ strmv, dtrmv, ctrmv, ztrmv ]
dtrsm	Solve a triangular system of equations with a triangular coefficient matrix	[ strsm, dtrsm, ctrsm, ztrsm ]
dtrsv	Solver of a system of linear equations with a triangular matrix	[ strsv, dtrsv, ctrsv, ztrsv ]
dvcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
dxml	A library of linear algebra and signal processing routines
dzamax	Maximum absolute value	[ samax, damax, scamax, dzamax ]
dzamin
dzasum	Sum of the absolute value	[ sasum, dasum, scasum, dzasum ]
dzaxpy	Vector plus the product of a scalar and a vector	[ szaxpy, dzaxpy, czaxpy, zzaxpy ]
dznorm2	Square root of sum of the squares of the elements of a vector	[ snorm2, dnorm2, scnorm2, dznorm2 ]
dznrm2	Square root of sum of the squares of the elements of a vector	[ snrm2, dnrm2, scnrm2, dznrm2 ]
dznrsq	Sum of the squares of the elements of a vector	[ snrsq, dnrsq, scnrsq, dznrsq ]
gen_sort	Sort the elements of a vector
gen_sortx	Sort the elements of an indexed vector
icamax	Index of the element of a vector with maximum absolute value	[ isamax, idamax, icamax, izamax ]
icamin
idamax	Index of the element of a vector with maximum absolute value	[ isamax, idamax, icamax, izamax ]
idamin
idmax	Index of the real vector element with maximum value	[ ismax, idmax ]
idmin	Index of the real vector element with minimum value	[ ismin, idmin ]
isamax	Index of the element of a vector with maximum absolute value	[ isamax, idamax, icamax, izamax ]
isamin
ismax	Index of the real vector element with maximum value	[ ismax, idmax ]
ismin	Index of the real vector element with minimum value	[ ismin, idmin ]
isortq	Sort the elements of a vector	[ isortq, ssortq, dsortq ]
isortqx	Performs an indexed sort of a vector	[ isortqx, ssortqx, dsortqx ]
izamax	Index of the element of a vector with maximum absolute value	[ isamax, idamax, icamax, izamax ]
izamin
ran16807	Routine to generate single precision random numbers using a=16807 and m=2∗∗31-1
ran69069	Routine to generate single precision random numbers using a=69069 and m=2∗∗32
ranl	Random number generator based on L’Ecuyer method
ranl_normal	Routine to generate normally distributed random numbers using summation of uniformly distributed random numbers
ranl_skip2	Routine to skip forward 2∗∗d seeds for the RANL and RANL_NORMAL random number generators
ranl_skip64	Routine to skip forward a given number, d, of seeds for the RANL and RANL_NORMAL random number generators
samax	Maximum absolute value	[ samax, damax, scamax, dzamax ]
samin
sasum	Sum of the absolute value	[ sasum, dasum, scasum, dzasum ]
saxpy	Vector plus the product of a scalar and a vector	[ saxpy, daxpy, caxpy, zaxpy ]
scamax	Maximum absolute value	[ samax, damax, scamax, dzamax ]
scamin
scasum	Sum of the absolute value	[ sasum, dasum, scasum, dzasum ]
scnorm2	Square root of sum of the squares of the elements of a vector	[ snorm2, dnorm2, scnorm2, dznorm2 ]
scnrm2	Square root of sum of the squares of the elements of a vector	[ snrm2, dnrm2, scnrm2, dznrm2 ]
scnrsq	Sum of the squares of the elements of a vector	[ snrsq, dnrsq, scnrsq, dznrsq ]
sconv_nonperiodic	Nonperiodic convolution	[ sconv_nonperiodic, dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic ]
sconv_nonperiodic_ext	Extended nonperiodic convolution	[ sconv_nonperiodic_ext, dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext ]
sconv_periodic	Periodic concolution	[ sconv_periodic, dconv_periodic, cconv_periodic, zconv_periodic ]
sconv_periodic_ext	Extended periodic convolution	[ sconv_periodic_ext, dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext ]
scopy	Copy of a vector	[ scopy, dcopy, ccopy, zcopy ]
scorr_nonperiodic
scorr_nonperiodic_ext
scorr_periodic
scorr_periodic_ext	Extended periodic correlation	[ scorr_periodic_ext, dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext ]
sdot	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
sdsdot	Product of scaled vector and vector
sfct	Fast cosine transform in one dimension	[ sfct, dfct ]
sfct_apply	Application step for fast cosine transform in one dimension	[ sfct_apply, dfct_apply ]
sfct_exit	Final step for fast cosine transform in one dimension	[ sfct_exit, dfct_exit ]
sfct_init	Initialization step for fast cosine transform in one dimension	[ sfct_init, dfct_init ]
sfft	Fast fourier transform in one dimension	[ sfft, dfft, cfft, zfft ]
sfft_2d	Fast fourier transform in two dimensions	[ sfft_2d, dfft_2d, cfft_2d, zfft_2d ]
sfft_3d	Fast fourier transform in three dimensions	[ sfft_3d, dfft_3d, cfft_3d, zfft_3d ]
sfft_apply	Application step for fast fourier transform in one dimension	[ sfft_apply, dfft_apply, cfft_apply, zfft_apply ]
sfft_apply_2d
sfft_apply_3d	Application step for fast fourier transform in three dimensions	[ sfft_apply_3d, dfft_apply_3d, cfft_apply_3d, zfft_apply_3d ]
sfft_apply_grp	Application step for group fast fourier transform in one dimension	[ sfft_apply_grp, dfft_apply_grp, cfft_apply_grp, zfft_apply_grp ]
sfft_exit	Final step for fast fourier transform in one dimension	[ sfft_exit, dfft_exit, cfft_exit, zfft_exit ]
sfft_exit_2d	Final step for fast fourier transform in two dimensions	[ sfft_exit_2d, dfft_exit_2d, cfft_exit_2d, zfft_exit_2d ]
sfft_exit_3d	Final step for fast fourier transfrom in three dimension	[ sfft_exit_3d, dfft_exit_3d, cfft_exit_3d, zfft_exit_3d ]
sfft_exit_grp	Exit step for group fast fourier transform in one dimension	[ sfft_exit_grp, dfft_exit_grp, cfft_exit_grp, zfft_exit_grp ]
sfft_grp	Group fast fourier transform in one dimension	[ sfft_grp, dfft_grp, cfft_grp, zfft_grp ]
sfft_init	Initialization step for fast fourier transform in one dimension	[ sfft_init, dfft_init, cfft_init, zfft_init ]
sfft_init_2d	Initialization step for fast fourier transform in two dimensions	[ sfft_init_2d, dfft_init_2d, cfft_init_2d, zfft_init_2d ]
sfft_init_3d	Initialization step for fast fourier transform in three dimension	[ sfft_init_3d, dfft_init_3d, cfft_init_3d, zfft_init_3d ]
sfft_init_grp	Initialization step for group fast fourier transform in one dimension	[ sfft_init_grp, dfft_init_grp, cfft_init_grp, zfft_init_grp ]
sfilter_apply_nonrec	Performs filtering in lowpass, highpass, bandpass, or bandstop (notch) mode by using the working array that was computed by SFILTER_INIT_NONREC.
sfilter_init_nonrec	Computes a working array that is used by sfilter_apply_nonrec routine.
sfilter_nonrec	Performs filtering in lowpass, highpass, bandpass, or bandstop (notch) mode.
sfst	Fast sine transform in one dimension	[ sfst, dfst ]
sfst_apply	Application step for fast sine transform in one dimension	[ sfst_apply, dfst_apply ]
sfst_exit	Final step for fast sine transform in one dimension	[ sfst_exit, dfst_exit ]
sfst_init	Initialization step for fast sine transform in one dimension	[ sfst_init, dfst_init ]
sgbmv	Matrix-vector product for a general band matrix	[ sgbmv, ddbmv, cgbmv, zgbmv ]
sgema	Matrix-matrix addition	[ sgema, dgema, cgema, zgema ]
sgemm	Matrix-matrix product and addition	[ sgemm, dgemm, cgemm, zgemm ]
sgems	Matrix-matrix subtraction	[ sgems, dgems, cgems, zgems ]
sgemt	Matrix-matrix copy	[ sgemt, dgemt, cgemt, zgemt ]
sgemv	Matrix-vector product for a general matrix	[ sgemv, dgemv, cgemv, zgemv ]
sger	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
smax	Largest element in a real vector	[ smax, dmax ]
smin	Minimum value of the elements of a real vector	[ smin, dmin ]
snorm2	Square root of sum of the squares of the elements of a vector	[ snorm2, dnorm2, scnorm2, dznorm2 ]
snrm2	Square root of sum of the squares of the elements of a vector	[ snrm2, dnrm2, scnrm2, dznrm2 ]
snrsq	Sum of the squares of the elements of a vector	[ snrsq, dnrsq, scnrsq, dznrsq ]
sorts	A library of sort routines
srot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
srotg
srotm	Apply modified givens transformation	[ srotm, drotm ]
srotmg	Generate elements for a modified Givens transform	[ srotmg, drotmg ]
ssbmv	Matrix-vector product for a symmetric or hermitian band matrix	[ ssbmv, dsbmv, chbmv, zhbmv ]
sscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
sset	Set all elements of a vector to a scalar	[ sset, dset, cset, zset ]
ssortq	Sort the elements of a vector	[ isortq, ssortq, dsortq ]
ssortqx	Performs an indexed sort of a vector	[ isortqx, ssortqx, dsortqx ]
sspmv	Matrix-vector product for a symmetric or hermitian matrix stored in packed form	[ sspmv, dspmv, chpmv, zhpmv ]
sspr	Rank-one update of a symmetric or hermitian matrix stored in packed form	[ sspr, dspr, chpr, zhpr ]
sspr2	Rank-two update of a symmetric or hermitian matrix stored in packed form	[ sspr2, dspr2, chpr2, zhpr2 ]
ssum	Sum of the values of the elements of a vector	[ ssum, dsum, csum, zsum ]
sswap	Exchange the elements of two vectors	[ sswap, dswap, cswap, zswap ]
ssymm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
ssymv	Matrix-vector product for a symmetric or hermitian matrix	[ ssymv, dsymv, chemv, zhemv ]
ssyr	Rank-one update of a symmetric or hermitian matrix	[ ssyr, dsyr, cher, zher ]
ssyr2	Rank-two update of a symmetric or hermitian matrix	[ ssyr2, dsyr2, cher2, zher2 ]
ssyr2k	Rank-2k update of a symmetric matrix	[ ssyr2k, dsyr2k, csyr2k, zsyr2k ]
ssyrk	Rank-k update of a symmetric matrix	[ ssyrk, dsyrk, csyrk, zsyrk ]
stbmv	Matrix-vector product for a triangular band matrix	[ stbmv, dtbmv, ctbmv, ztbmv ]
stbsv	Solver of a system of linear equations with a triangular band matrix	[ stbsv, dtbsv, ctbsv, ztbsv ]
stpmv	Matrix-vector product for a triangular matrix in packed form	[ stpmv, dtpmv, ctpmv, ztpmv ]
stpsv	Solve a system of linear equations with a triangular matrix in packed form	[ stpsv, dtpsv, ctpsv, ztpsv ]
strmm	Matrix-matrix product for triangular matrix	[ strmm, dtrmm, ctrmm, ztrmm ]
strmv	Marix-vector product for a triangular matrix	[ strmv, dtrmv, ctrmv, ztrmv ]
strsm	Solve a triangular system of equations with a triangular coefficient matrix	[ strsm, dtrsm, ctrsm, ztrsm ]
strsv	Solver of a system of linear equations with a triangular matrix	[ strsv, dtrsv, ctrsv, ztrsv ]
svcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
szaxpy	Vector plus the product of a scalar and a vector	[ szaxpy, dzaxpy, czaxpy, zzaxpy ]
vxworks_dxml	Using DXML on VxWorks
zaxpy	Vector plus the product of a scalar and a vector	[ saxpy, daxpy, caxpy, zaxpy ]
zconv_nonperiodic	Nonperiodic convolution	[ sconv_nonperiodic, dconv_nonperiodic, cconv_nonperiodic, zconv_nonperiodic ]
zconv_nonperiodic_ext	Extended nonperiodic convolution	[ sconv_nonperiodic_ext, dconv_nonperiodic_ext, cconv_nonperiodic_ext, zconv_nonperiodic_ext ]
zconv_periodic	Periodic concolution	[ sconv_periodic, dconv_periodic, cconv_periodic, zconv_periodic ]
zconv_periodic_ext	Extended periodic convolution	[ sconv_periodic_ext, dconv_periodic_ext, cconv_periodic_ext, zconv_periodic_ext ]
zcopy	Copy of a vector	[ scopy, dcopy, ccopy, zcopy ]
zcorr_nonperiodic
zcorr_nonperiodic_ext
zcorr_periodic
zcorr_periodic_ext	Extended periodic correlation	[ scorr_periodic_ext, dcorr_periodic_ext, ccorr_periodic_ext, zcorr_periodic_ext ]
zdotc	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
zdotu	INNER PRODUCT OF TWO VECTORS	[ sdot, ddot, dsdot, cdotc, zdotc, cdotu, zdotu ]
zdrot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
zdscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
zdvcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
zfft	Fast fourier transform in one dimension	[ sfft, dfft, cfft, zfft ]
zfft_2d	Fast fourier transform in two dimensions	[ sfft_2d, dfft_2d, cfft_2d, zfft_2d ]
zfft_3d	Fast fourier transform in three dimensions	[ sfft_3d, dfft_3d, cfft_3d, zfft_3d ]
zfft_apply	Application step for fast fourier transform in one dimension	[ sfft_apply, dfft_apply, cfft_apply, zfft_apply ]
zfft_apply_2d
zfft_apply_3d	Application step for fast fourier transform in three dimensions	[ sfft_apply_3d, dfft_apply_3d, cfft_apply_3d, zfft_apply_3d ]
zfft_apply_grp	Application step for group fast fourier transform in one dimension	[ sfft_apply_grp, dfft_apply_grp, cfft_apply_grp, zfft_apply_grp ]
zfft_exit	Final step for fast fourier transform in one dimension	[ sfft_exit, dfft_exit, cfft_exit, zfft_exit ]
zfft_exit_2d	Final step for fast fourier transform in two dimensions	[ sfft_exit_2d, dfft_exit_2d, cfft_exit_2d, zfft_exit_2d ]
zfft_exit_3d	Final step for fast fourier transfrom in three dimension	[ sfft_exit_3d, dfft_exit_3d, cfft_exit_3d, zfft_exit_3d ]
zfft_exit_grp	Exit step for group fast fourier transform in one dimension	[ sfft_exit_grp, dfft_exit_grp, cfft_exit_grp, zfft_exit_grp ]
zfft_grp	Group fast fourier transform in one dimension	[ sfft_grp, dfft_grp, cfft_grp, zfft_grp ]
zfft_init	Initialization step for fast fourier transform in one dimension	[ sfft_init, dfft_init, cfft_init, zfft_init ]
zfft_init_2d	Initialization step for fast fourier transform in two dimensions	[ sfft_init_2d, dfft_init_2d, cfft_init_2d, zfft_init_2d ]
zfft_init_3d	Initialization step for fast fourier transform in three dimension	[ sfft_init_3d, dfft_init_3d, cfft_init_3d, zfft_init_3d ]
zfft_init_grp	Initialization step for group fast fourier transform in one dimension	[ sfft_init_grp, dfft_init_grp, cfft_init_grp, zfft_init_grp ]
zgbmv	Matrix-vector product for a general band matrix	[ sgbmv, ddbmv, cgbmv, zgbmv ]
zgema	Matrix-matrix addition	[ sgema, dgema, cgema, zgema ]
zgemm	Matrix-matrix product and addition	[ sgemm, dgemm, cgemm, zgemm ]
zgems	Matrix-matrix subtraction	[ sgems, dgems, cgems, zgems ]
zgemt	Matrix-matrix copy	[ sgemt, dgemt, cgemt, zgemt ]
zgemv	Matrix-vector product for a general matrix	[ sgemv, dgemv, cgemv, zgemv ]
zgerc	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
zgeru	Rank-one update of a general matrix	[ sger, dger, cgerc, zgerc, cgeru, zgeru ]
zhbmv	Matrix-vector product for a symmetric or hermitian band matrix	[ ssbmv, dsbmv, chbmv, zhbmv ]
zhemm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
zhemv	Matrix-vector product for a symmetric or hermitian matrix	[ ssymv, dsymv, chemv, zhemv ]
zher	Rank-one update of a symmetric or hermitian matrix	[ ssyr, dsyr, cher, zher ]
zher2	Rank-two update of a symmetric or hermitian matrix	[ ssyr2, dsyr2, cher2, zher2 ]
zher2k	Rank-2k update of a complex hermitian matrix	[ cher2k, zher2k ]
zherk	Rank-k update of a complex hermitian matrix	[ cherk, zherk ]
zhpmv	Matrix-vector product for a symmetric or hermitian matrix stored in packed form	[ sspmv, dspmv, chpmv, zhpmv ]
zhpr	Rank-one update of a symmetric or hermitian matrix stored in packed form	[ sspr, dspr, chpr, zhpr ]
zhpr2	Rank-two update of a symmetric or hermitian matrix stored in packed form	[ sspr2, dspr2, chpr2, zhpr2 ]
zrot	Apply givens plane rotation	[ srot, drot, crot, zrot, csrot, zdrot ]
zrotg
zscal	Product of a scalar and a vector	[ sscal, dscal, cscal, zscal, csscal, zdscal ]
zset	Set all elements of a vector to a scalar	[ sset, dset, cset, zset ]
zsum	Sum of the values of the elements of a vector	[ ssum, dsum, csum, zsum ]
zswap	Exchange the elements of two vectors	[ sswap, dswap, cswap, zswap ]
zsymm	Matrix-matrix product and addition for a symmetric or hermitian matrix	[ ssymm, dsymm, csymm, zsymm, chemm, zhemm ]
zsyr2k	Rank-2k update of a symmetric matrix	[ ssyr2k, dsyr2k, csyr2k, zsyr2k ]
zsyrk	Rank-k update of a symmetric matrix	[ ssyrk, dsyrk, csyrk, zsyrk ]
ztbmv	Matrix-vector product for a triangular band matrix	[ stbmv, dtbmv, ctbmv, ztbmv ]
ztbsv	Solver of a system of linear equations with a triangular band matrix	[ stbsv, dtbsv, ctbsv, ztbsv ]
ztpmv	Matrix-vector product for a triangular matrix in packed form	[ stpmv, dtpmv, ctpmv, ztpmv ]
ztpsv	Solve a system of linear equations with a triangular matrix in packed form	[ stpsv, dtpsv, ctpsv, ztpsv ]
ztrmm	Matrix-matrix product for triangular matrix	[ strmm, dtrmm, ctrmm, ztrmm ]
ztrmv	Marix-vector product for a triangular matrix	[ strmv, dtrmv, ctrmv, ztrmv ]
ztrsm	Solve a triangular system of equations with a triangular coefficient matrix	[ strsm, dtrsm, ctrsm, ztrsm ]
ztrsv	Solver of a system of linear equations with a triangular matrix	[ strsv, dtrsv, ctrsv, ztrsv ]
zvcal	Product of a scalar and a vector	[ svcal, dvcal, cvcal, zvcal, csvcal, zdvcal ]
zzaxpy	Vector plus the product of a scalar and a vector	[ szaxpy, dzaxpy, czaxpy, zzaxpy ]

Section 3lapack

csrot		[ ]
zdrot		[ ]
zsrot		[ ]

Section l

cbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B	[ CBDSQR ]
cgbbrd	reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation	[ CGBBRD ]
cgbcon	estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,	[ CGBCON ]
cgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number	[ CGBEQU ]
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	[ CGBRFS ]
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	[ CGBSV ]
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,	[ CGBSVX ]
cgbtf2	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges	[ CGBTF2 ]
cgbtrf	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges	[ CGBTRF ]
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	[ CGBTRS ]
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	[ CGEBAK ]
cgebal	balance a general complex matrix A	[ CGEBAL ]
cgebd2	reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation	[ CGEBD2 ]
cgebrd	reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation	[ CGEBRD ]
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	[ CGECON ]
cgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number	[ CGEEQU ]
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	[ CGEES ]
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	[ CGEESX ]
cgeev	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ CGEEV ]
cgeevx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ CGEEVX ]
cgegs	compute for a pair of N-by-N complex nonsymmetric matrices A,	[ CGEGS ]
cgegv	compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,	[ CGEGV ]
cgehd2	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation	[ CGEHD2 ]
cgehrd	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation	[ CGEHRD ]
cgelq2	compute an LQ factorization of a complex m by n matrix A	[ CGELQ2 ]
cgelqf	compute an LQ factorization of a complex M-by-N matrix A	[ CGELQF ]
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	[ CGELS ]
cgelss	compute the minimum norm solution to a complex linear least squares problem	[ CGELSS ]
cgelsx	compute the minimum-norm solution to a complex linear least squares problem	[ CGELSX ]
cgeql2	compute a QL factorization of a complex m by n matrix A	[ CGEQL2 ]
cgeqlf	compute a QL factorization of a complex M-by-N matrix A	[ CGEQLF ]
cgeqpf	compute a QR factorization with column pivoting of a complex M-by-N matrix A	[ CGEQPF ]
cgeqr2	compute a QR factorization of a complex m by n matrix A	[ CGEQR2 ]
cgeqrf	compute a QR factorization of a complex M-by-N matrix A	[ CGEQRF ]
cgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution	[ CGERFS ]
cgerq2	compute an RQ factorization of a complex m by n matrix A	[ CGERQ2 ]
cgerqf	compute an RQ factorization of a complex M-by-N matrix A	[ CGERQF ]
cgesv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CGESV ]
cgesvd	compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors	[ CGESVD ]
cgesvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ CGESVX ]
cgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges	[ CGETF2 ]
cgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges	[ CGETRF ]
cgetri	compute the inverse of a matrix using the LU factorization computed by CGETRF	[ CGETRI ]
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	[ CGETRS ]
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	[ CGGBAK ]
cggbal	balance a pair of general complex matrices (A,B)	[ CGGBAL ]
cggglm	solve a general Gauss-Markov linear model (GLM) problem	[ CGGGLM ]
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	[ CGGHRD ]
cgglse	solve the linear equality-constrained least squares (LSE) problem	[ CGGLSE ]
cggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B	[ CGGQRF ]
cggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B	[ CGGRQF ]
cggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B	[ CGGSVD ]
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	[ CGGSVP ]
cgtcon	estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF	[ CGTCON ]
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	[ CGTRFS ]
cgtsv	solve the equation A∗X = B,	[ CGTSV ]
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,	[ CGTSVX ]
cgttrf	compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges	[ CGTTRF ]
cgttrs	solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ CGTTRS ]
chbev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ CHBEV ]
chbevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ CHBEVD ]
chbevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ CHBEVX ]
chbgst	reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,	[ CHBGST ]
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	[ CHBGV ]
chbtrd	reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ CHBTRD ]
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	[ CHECON ]
cheev	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ CHEEV ]
cheevd	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ CHEEVD ]
cheevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ CHEEVX ]
chegs2	reduce a complex Hermitian-definite generalized eigenproblem to standard form	[ CHEGS2 ]
chegst	reduce a complex Hermitian-definite generalized eigenproblem to standard form	[ CHEGST ]
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	[ CHEGV ]
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	[ CHERFS ]
chesv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CHESV ]
chesvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ CHESVX ]
chetd2	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ CHETD2 ]
chetf2	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ CHETF2 ]
chetrd	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ CHETRD ]
chetrf	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ CHETRF ]
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	[ CHETRI ]
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	[ CHETRS ]
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	[ CHGEQZ ]
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	[ CHPCON ]
chpev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage	[ CHPEV ]
chpevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage	[ CHPEVD ]
chpevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage	[ CHPEVX ]
chpgst	reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage	[ CHPGST ]
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	[ CHPGV ]
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	[ CHPRFS ]
chpsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CHPSV ]
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	[ CHPSVX ]
chptrd	reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation	[ CHPTRD ]
chptrf	compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method	[ CHPTRF ]
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	[ CHPTRI ]
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	[ CHPTRS ]
chsein	use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H	[ CHSEIN ]
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	[ CHSEQR ]
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	[ CLABRD ]
clacgv	conjugate a complex vector of length N	[ CLACGV ]
clacon	estimate the 1-norm of a square, complex matrix A	[ CLACON ]
clacpy	copie all or part of a two-dimensional matrix A to another matrix B	[ CLACPY ]
clacrm	perform a very simple matrix-matrix multiplication	[ CLACRM ]
clacrt	applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex	[ CLACRT ]
cladiv	:= X / Y, where X and Y are complex	[ CLADIV ]
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	[ CLAED0 ]
claed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ CLAED7 ]
claed8	merge the two sets of eigenvalues together into a single sorted set	[ CLAED8 ]
claein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H	[ CLAEIN ]
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	[ CLAESY ]
claev2	compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]	[ CLAEV2 ]
clags2
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 0., 1., or -1	[ CLAGTM ]
clahef	compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ CLAHEF ]
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	[ CLAHQR ]
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	[ CLAHRD ]
claic1	applie one step of incremental condition estimation in its simplest version	[ CLAIC1 ]
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	[ CLANGB ]
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	[ CLANGE ]
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	[ CLANGT ]
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	[ CLANHB ]
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	[ CLANHE ]
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	[ CLANHP ]
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	[ CLANHS ]
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	[ CLANHT ]
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	[ CLANSB ]
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	[ CLANSP ]
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	[ CLANSY ]
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	[ CLANTB ]
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	[ CLANTP ]
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	[ CLANTR ]
clapll	two column vectors X and Y, let A = ( X Y )	[ CLAPLL ]
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	[ CLAPMT ]
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	[ CLAQGB ]
claqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C	[ CLAQGE ]
claqhb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ CLAQHB ]
claqhe	equilibrate a Hermitian matrix A using the scaling factors in the vector S	[ CLAQHE ]
claqhp	equilibrate a Hermitian matrix A using the scaling factors in the vector S	[ CLAQHP ]
claqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ CLAQSB ]
claqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ CLAQSP ]
claqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ CLAQSY ]
clar2v	applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,	[ CLAR2V ]
clarf	applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right	[ CLARF ]
clarfb	applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right	[ CLARFB ]
clarfg	generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I	[ CLARFG ]
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	[ CLARFT ]
clarfx	applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right	[ CLARFX ]
clargv	generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y	[ CLARGV ]
clarnv	return a vector of n random complex numbers from a uniform or normal distribution	[ CLARNV ]
clartg	generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]	[ CLARTG ]
clartv	applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y	[ CLARTV ]
clascl	multiplie the M by N complex matrix A by the real scalar CTO/CFROM	[ CLASCL ]
claset	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ CLASET ]
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,	[ CLASR ]
classq	return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,	[ CLASSQ ]
claswp	perform a series of row interchanges on the matrix A	[ CLASWP ]
clasyf	compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ CLASYF ]
clatbs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ CLATBS ]
clatps	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ CLATPS ]
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	[ CLATRD ]
clatrs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ CLATRS ]
clatzm	applie a Householder matrix generated by CTZRQF to a matrix	[ CLATZM ]
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	[ CLAUU2 ]
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	[ CLAUUM ]
clazro	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ CLAZRO ]
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	[ CPBCON ]
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)	[ CPBEQU ]
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	[ CPBRFS ]
cpbstf	compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A	[ CPBSTF ]
cpbsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CPBSV ]
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,	[ CPBSVX ]
cpbtf2	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A	[ CPBTF2 ]
cpbtrf	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A	[ CPBTRF ]
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	[ CPBTRS ]
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	[ CPOCON ]
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)	[ CPOEQU ]
cporfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,	[ CPORFS ]
cposv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CPOSV ]
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,	[ CPOSVX ]
cpotf2	compute the Cholesky factorization of a complex Hermitian positive definite matrix A	[ CPOTF2 ]
cpotrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A	[ CPOTRF ]
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	[ CPOTRI ]
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	[ CPOTRS ]
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	[ CPPCON ]
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)	[ CPPEQU ]
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	[ CPPRFS ]
cppsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CPPSV ]
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,	[ CPPSVX ]
cpptrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format	[ CPPTRF ]
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	[ CPPTRI ]
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	[ CPPTRS ]
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	[ CPTCON ]
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	[ CPTEQR ]
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	[ CPTRFS ]
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	[ CPTSV ]
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	[ CPTSVX ]
cpttrf	compute the factorization of a complex Hermitian positive definite tridiagonal matrix A	[ CPTTRF ]
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	[ CPTTRS ]
crot	applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex	[ CROT ]
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	[ CSPCON ]
cspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,	[ CSPMV ]
cspr	perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A,	[ CSPR ]
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	[ CSPRFS ]
cspsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CSPSV ]
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	[ CSPSVX ]
csptrf	compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method	[ CSPTRF ]
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	[ CSPTRI ]
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	[ CSPTRS ]
csrscl	multiplie an n-element complex vector x by the real scalar 1/a	[ CSRSCL ]
cstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ CSTEDC ]
cstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration	[ CSTEIN ]
csteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method	[ CSTEQR ]
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	[ CSYCON ]
csymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,	[ CSYMV ]
csyr	perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A,	[ CSYR ]
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	[ CSYRFS ]
csysv	compute the solution to a complex system of linear equations A ∗ X = B,	[ CSYSV ]
csysvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ CSYSVX ]
csytf2	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ CSYTF2 ]
csytrf	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ CSYTRF ]
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	[ CSYTRI ]
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	[ CSYTRS ]
ctbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm	[ CTBCON ]
ctbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix	[ CTBRFS ]
ctbtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ CTBTRS ]
ctgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)	[ CTGEVC ]
ctgsja	compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B	[ CTGSJA ]
ctpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm	[ CTPCON ]
ctprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix	[ CTPRFS ]
ctptri	compute the inverse of a complex upper or lower triangular matrix A stored in packed format	[ CTPTRI ]
ctptrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ CTPTRS ]
ctrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm	[ CTRCON ]
ctrevc	compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T	[ CTREVC ]
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	[ CTREXC ]
ctrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix	[ CTRRFS ]
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	[ CTRSEN ]
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)	[ CTRSNA ]
ctrsyl	solve the complex Sylvester matrix equation	[ CTRSYL ]
ctrti2	compute the inverse of a complex upper or lower triangular matrix	[ CTRTI2 ]
ctrtri	compute the inverse of a complex upper or lower triangular matrix A	[ CTRTRI ]
ctrtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ CTRTRS ]
ctzrqf	reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations	[ CTZRQF ]
cung2l	generate an m by n complex matrix Q with orthonormal columns,	[ CUNG2L ]
cung2r	generate an m by n complex matrix Q with orthonormal columns,	[ CUNG2R ]
cungbr	generate one of the complex unitary matrices Q or P∗∗H determined by CGEBRD when reducing a complex matrix A to bidiagonal form	[ CUNGBR ]
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	[ CUNGHR ]
cungl2	generate an m-by-n complex matrix Q with orthonormal rows,	[ CUNGL2 ]
cunglq	generate an M-by-N complex matrix Q with orthonormal rows,	[ CUNGLQ ]
cungql	generate an M-by-N complex matrix Q with orthonormal columns,	[ CUNGQL ]
cungqr	generate an M-by-N complex matrix Q with orthonormal columns,	[ CUNGQR ]
cungr2	generate an m by n complex matrix Q with orthonormal rows,	[ CUNGR2 ]
cungrq	generate an M-by-N complex matrix Q with orthonormal rows,	[ CUNGRQ ]
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	[ CUNGTR ]
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’,	[ CUNM2L ]
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’,	[ CUNM2R ]
cunmbr	VECT = ’Q’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMBR ]
cunmhr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMHR ]
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’,	[ CUNML2 ]
cunmlq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMLQ ]
cunmql	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMQL ]
cunmqr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMQR ]
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’,	[ CUNMR2 ]
cunmrq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMRQ ]
cunmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUNMTR ]
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	[ CUPGTR ]
cupmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ CUPMTR ]
dbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B	[ DBDSQR ]
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	[ DDISNA ]
dgbbrd	reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation	[ DGBBRD ]
dgbcon	estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,	[ DGBCON ]
dgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number	[ DGBEQU ]
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	[ DGBRFS ]
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	[ DGBSV ]
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,	[ DGBSVX ]
dgbtf2	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges	[ DGBTF2 ]
dgbtrf	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges	[ DGBTRF ]
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	[ DGBTRS ]
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	[ DGEBAK ]
dgebal	balance a general real matrix A	[ DGEBAL ]
dgebd2	reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation	[ DGEBD2 ]
dgebrd	reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation	[ DGEBRD ]
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	[ DGECON ]
dgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number	[ DGEEQU ]
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	[ DGEES ]
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	[ DGEESX ]
dgeev	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ DGEEV ]
dgeevx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ DGEEVX ]
dgegs	compute for a pair of N-by-N real nonsymmetric matrices A, B	[ DGEGS ]
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)	[ DGEGV ]
dgehd2	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation	[ DGEHD2 ]
dgehrd	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation	[ DGEHRD ]
dgelq2	compute an LQ factorization of a real m by n matrix A	[ DGELQ2 ]
dgelqf	compute an LQ factorization of a real M-by-N matrix A	[ DGELQF ]
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	[ DGELS ]
dgelss	compute the minimum norm solution to a real linear least squares problem	[ DGELSS ]
dgelsx	compute the minimum-norm solution to a real linear least squares problem	[ DGELSX ]
dgeql2	compute a QL factorization of a real m by n matrix A	[ DGEQL2 ]
dgeqlf	compute a QL factorization of a real M-by-N matrix A	[ DGEQLF ]
dgeqpf	compute a QR factorization with column pivoting of a real M-by-N matrix A	[ DGEQPF ]
dgeqr2	compute a QR factorization of a real m by n matrix A	[ DGEQR2 ]
dgeqrf	compute a QR factorization of a real M-by-N matrix A	[ DGEQRF ]
dgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution	[ DGERFS ]
dgerq2	compute an RQ factorization of a real m by n matrix A	[ DGERQ2 ]
dgerqf	compute an RQ factorization of a real M-by-N matrix A	[ DGERQF ]
dgesv	compute the solution to a real system of linear equations A ∗ X = B,	[ DGESV ]
dgesvd	compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors	[ DGESVD ]
dgesvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B,	[ DGESVX ]
dgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges	[ DGETF2 ]
dgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges	[ DGETRF ]
dgetri	compute the inverse of a matrix using the LU factorization computed by DGETRF	[ DGETRI ]
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	[ DGETRS ]
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	[ DGGBAK ]
dggbal	balance a pair of general real matrices (A,B)	[ DGGBAL ]
dggglm	solve a general Gauss-Markov linear model (GLM) problem	[ DGGGLM ]
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	[ DGGHRD ]
dgglse	solve the linear equality-constrained least squares (LSE) problem	[ DGGLSE ]
dggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B	[ DGGQRF ]
dggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B	[ DGGRQF ]
dggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B	[ DGGSVD ]
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	[ DGGSVP ]
dgtcon	estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF	[ DGTCON ]
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	[ DGTRFS ]
dgtsv	solve the equation A∗X = B,	[ DGTSV ]
dgtsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B,	[ DGTSVX ]
dgttrf	compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges	[ DGTTRF ]
dgttrs	solve one of the systems of equations A∗X = B or A’∗X = B,	[ DGTTRS ]
dhgeqz	implement a single-/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	[ DHGEQZ ]
dhsein	use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H	[ DHSEIN ]
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	[ DHSEQR ]
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	[ DLABAD ]
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	[ DLABRD ]
dlacon	estimate the 1-norm of a square, real matrix A	[ DLACON ]
dlacpy	copie all or part of a two-dimensional matrix A to another matrix B	[ DLACPY ]
dladiv	perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L	[ DLADIV ]
dlae2	compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]	[ DLAE2 ]
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	[ DLAEBZ ]
dlaed0	compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ DLAED0 ]
dlaed1	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ DLAED1 ]
dlaed2	merge the two sets of eigenvalues together into a single sorted set	[ DLAED2 ]
dlaed3	find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP	[ DLAED3 ]
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	[ DLAED4 ]
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	[ DLAED5 ]
dlaed6	compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true	[ DLAED6 ]
dlaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ DLAED7 ]
dlaed8	merge the two sets of eigenvalues together into a single sorted set	[ DLAED8 ]
dlaed9	find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP	[ DLAED9 ]
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	[ DLAEDA ]
dlaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H	[ DLAEIN ]
dlaev2	compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]	[ DLAEV2 ]
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	[ DLAEXC ]
dlag2	compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow	[ DLAG2 ]
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,	[ DLAGTF ]
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 0., 1., or -1	[ DLAGTM ]
dlagts	may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y,	[ DLAGTS ]
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	[ DLAHQR ]
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	[ DLAHRD ]
dlaic1	applie one step of incremental condition estimation in its simplest version	[ DLAIC1 ]
dlaln2	solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A	[ DLALN2 ]
dlamch	determine double precision machine parameters	[ DLAMCH ]
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	[ DLAMRG ]
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	[ DLANGB ]
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	[ DLANGE ]
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	[ DLANGT ]
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	[ DLANHS ]
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	[ DLANSB ]
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	[ DLANSP ]
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	[ DLANST ]
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	[ DLANSY ]
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	[ DLANTB ]
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	[ DLANTP ]
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	[ DLANTR ]
dlanv2	compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form	[ DLANV2 ]
dlapll	two column vectors X and Y, let A = ( X Y )	[ DLAPLL ]
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	[ DLAPMT ]
dlapy2	return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow	[ DLAPY2 ]
dlapy3	return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow	[ DLAPY3 ]
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	[ DLAQGB ]
dlaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C	[ DLAQGE ]
dlaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ DLAQSB ]
dlaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ DLAQSP ]
dlaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ DLAQSY ]
dlaqtr	solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE	[ DLAQTR ]
dlar2v	applie 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	[ DLAR2V ]
dlarf	applie a real elementary reflector H to a real m by n matrix C, from either the left or the right	[ DLARF ]
dlarfb	applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right	[ DLARFB ]
dlarfg	generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I	[ DLARFG ]
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	[ DLARFT ]
dlarfx	applie a real elementary reflector H to a real m by n matrix C, from either the left or the right	[ DLARFX ]
dlargv	generate a vector of real plane rotations, determined by elements of the real vectors x and y	[ DLARGV ]
dlarnv	return a vector of n random real numbers from a uniform or normal distribution	[ DLARNV ]
dlartg	generate a plane rotation so that [ CS SN ]	[ DLARTG ]
dlartv	applie a vector of real plane rotations to elements of the real vectors x and y	[ DLARTV ]
dlaruv	return a vector of n random real numbers from a uniform (0,1)	[ DLARUV ]
dlas2	compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]	[ DLAS2 ]
dlascl	multiplie the M by N real matrix A by the real scalar CTO/CFROM	[ DLASCL ]
dlaset	initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals	[ DLASET ]
dlasq1	DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E	[ DLASQ1 ]
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	[ DLASQ2 ]
dlasq3	DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm	[ DLASQ3 ]
dlasq4	DLASQ4 estimates TAU, the smallest eigenvalue of a matrix	[ DLASQ4 ]
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,	[ DLASR ]
dlasrt	the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ )	[ DLASRT ]
dlassq	return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,	[ DLASSQ ]
dlasv2	compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]	[ DLASV2 ]
dlaswp	perform a series of row interchanges on the matrix A	[ DLASWP ]
dlasy2	solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B,	[ DLASY2 ]
dlasyf	compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ DLASYF ]
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	[ DLATBS ]
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	[ DLATPS ]
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	[ DLATRD ]
dlatrs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow	[ DLATRS ]
dlatzm	applie a Householder matrix generated by DTZRQF to a matrix	[ DLATZM ]
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	[ DLAUU2 ]
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	[ DLAUUM ]
dlazro	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ DLAZRO ]
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	[ DOPGTR ]
dopmtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DOPMTR ]
dorg2l	generate an m by n real matrix Q with orthonormal columns,	[ DORG2L ]
dorg2r	generate an m by n real matrix Q with orthonormal columns,	[ DORG2R ]
dorgbr	generate one of the real orthogonal matrices Q or P∗∗T determined by DGEBRD when reducing a real matrix A to bidiagonal form	[ DORGBR ]
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	[ DORGHR ]
dorgl2	generate an m by n real matrix Q with orthonormal rows,	[ DORGL2 ]
dorglq	generate an M-by-N real matrix Q with orthonormal rows,	[ DORGLQ ]
dorgql	generate an M-by-N real matrix Q with orthonormal columns,	[ DORGQL ]
dorgqr	generate an M-by-N real matrix Q with orthonormal columns,	[ DORGQR ]
dorgr2	generate an m by n real matrix Q with orthonormal rows,	[ DORGR2 ]
dorgrq	generate an M-by-N real matrix Q with orthonormal rows,	[ DORGRQ ]
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	[ DORGTR ]
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’,	[ DORM2L ]
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’,	[ DORM2R ]
dormbr	VECT = ’Q’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMBR ]
dormhr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMHR ]
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’,	[ DORML2 ]
dormlq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMLQ ]
dormql	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMQL ]
dormqr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMQR ]
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’,	[ DORMR2 ]
dormrq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMRQ ]
dormtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ DORMTR ]
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	[ DPBCON ]
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)	[ DPBEQU ]
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	[ DPBRFS ]
dpbstf	compute a split Cholesky factorization of a real symmetric positive definite band matrix A	[ DPBSTF ]
dpbsv	compute the solution to a real system of linear equations A ∗ X = B,	[ DPBSV ]
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,	[ DPBSVX ]
dpbtf2	compute the Cholesky factorization of a real symmetric positive definite band matrix A	[ DPBTF2 ]
dpbtrf	compute the Cholesky factorization of a real symmetric positive definite band matrix A	[ DPBTRF ]
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	[ DPBTRS ]
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	[ DPOCON ]
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)	[ DPOEQU ]
dporfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,	[ DPORFS ]
dposv	compute the solution to a real system of linear equations A ∗ X = B,	[ DPOSV ]
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,	[ DPOSVX ]
dpotf2	compute the Cholesky factorization of a real symmetric positive definite matrix A	[ DPOTF2 ]
dpotrf	compute the Cholesky factorization of a real symmetric positive definite matrix A	[ DPOTRF ]
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	[ DPOTRI ]
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	[ DPOTRS ]
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	[ DPPCON ]
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)	[ DPPEQU ]
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	[ DPPRFS ]
dppsv	compute the solution to a real system of linear equations A ∗ X = B,	[ DPPSV ]
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,	[ DPPSVX ]
dpptrf	compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format	[ DPPTRF ]
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	[ DPPTRI ]
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	[ DPPTRS ]
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	[ DPTCON ]
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	[ DPTEQR ]
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	[ DPTRFS ]
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	[ DPTSV ]
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	[ DPTSVX ]
dpttrf	compute the factorization of a real symmetric positive definite tridiagonal matrix A	[ DPTTRF ]
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	[ DPTTRS ]
drscl	multiplie an n-element real vector x by the real scalar 1/a	[ DRSCL ]
dsbev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ DSBEV ]
dsbevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ DSBEVD ]
dsbevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ DSBEVX ]
dsbgst	reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,	[ DSBGST ]
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	[ DSBGV ]
dsbtrd	reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation	[ DSBTRD ]
dsecnd	return the user time for a process in seconds	[ DSECND ]
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	[ DSPCON ]
dspev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ DSPEV ]
dspevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ DSPEVD ]
dspevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ DSPEVX ]
dspgst	reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage	[ DSPGST ]
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	[ DSPGV ]
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	[ DSPRFS ]
dspsv	compute the solution to a real system of linear equations A ∗ X = B,	[ DSPSV ]
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	[ DSPSVX ]
dsptrd	reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation	[ DSPTRD ]
dsptrf	compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method	[ DSPTRF ]
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	[ DSPTRI ]
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	[ DSPTRS ]
dstebz	compute the eigenvalues of a symmetric tridiagonal matrix T	[ DSTEBZ ]
dstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ DSTEDC ]
dstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration	[ DSTEIN ]
dsteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method	[ DSTEQR ]
dsterf	compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm	[ DSTERF ]
dstev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A	[ DSTEV ]
dstevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix	[ DSTEVD ]
dstevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A	[ DSTEVX ]
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	[ DSYCON ]
dsyev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ DSYEV ]
dsyevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ DSYEVD ]
dsyevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ DSYEVX ]
dsygs2	reduce a real symmetric-definite generalized eigenproblem to standard form	[ DSYGS2 ]
dsygst	reduce a real symmetric-definite generalized eigenproblem to standard form	[ DSYGST ]
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	[ DSYGV ]
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	[ DSYRFS ]
dsysv	compute the solution to a real system of linear equations A ∗ X = B,	[ DSYSV ]
dsysvx	use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B,	[ DSYSVX ]
dsytd2	reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation	[ DSYTD2 ]
dsytf2	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ DSYTF2 ]
dsytrd	reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation	[ DSYTRD ]
dsytrf	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ DSYTRF ]
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	[ DSYTRI ]
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	[ DSYTRS ]
dtbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm	[ DTBCON ]
dtbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix	[ DTBRFS ]
dtbtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ DTBTRS ]
dtgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)	[ DTGEVC ]
dtgsja	compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B	[ DTGSJA ]
dtpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm	[ DTPCON ]
dtprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix	[ DTPRFS ]
dtptri	compute the inverse of a real upper or lower triangular matrix A stored in packed format	[ DTPTRI ]
dtptrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ DTPTRS ]
dtrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm	[ DTRCON ]
dtrevc	compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T	[ DTREVC ]
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	[ DTREXC ]
dtrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix	[ DTRRFS ]
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,	[ DTRSEN ]
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)	[ DTRSNA ]
dtrsyl	solve the real Sylvester matrix equation	[ DTRSYL ]
dtrti2	compute the inverse of a real upper or lower triangular matrix	[ DTRTI2 ]
dtrtri	compute the inverse of a real upper or lower triangular matrix A	[ DTRTRI ]
dtrtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ DTRTRS ]
dtzrqf	reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations	[ DTZRQF ]
dzsum1	take the sum of the absolute values of a complex vector and returns a double precision result	[ DZSUM1 ]
icmax1	find the index of the element whose real part has maximum absolute value	[ ICMAX1 ]
ilaenv	i called from the LAPACK routines to choose problem-dependent parameters for the local environment	[ ILAENV ]
izmax1	find the index of the element whose real part has maximum absolute value	[ IZMAX1 ]
lapack
lsame	return .TRUE	[ LSAME ]
lsamen	test if the first N letters of CA are the same as the first N letters of CB, regardless of case	[ LSAMEN ]
sbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B	[ SBDSQR ]
scsum1	take the sum of the absolute values of a complex vector and returns a single precision result	[ SCSUM1 ]
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	[ SDISNA ]
second	return the user time for a process in seconds	[ SECOND ]
sgbbrd	reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation	[ SGBBRD ]
sgbcon	estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,	[ SGBCON ]
sgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number	[ SGBEQU ]
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	[ SGBRFS ]
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	[ SGBSV ]
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,	[ SGBSVX ]
sgbtf2	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges	[ SGBTF2 ]
sgbtrf	compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges	[ SGBTRF ]
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	[ SGBTRS ]
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	[ SGEBAK ]
sgebal	balance a general real matrix A	[ SGEBAL ]
sgebd2	reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation	[ SGEBD2 ]
sgebrd	reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation	[ SGEBRD ]
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	[ SGECON ]
sgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number	[ SGEEQU ]
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	[ SGEES ]
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	[ SGEESX ]
sgeev	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ SGEEV ]
sgeevx	compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ SGEEVX ]
sgegs	compute for a pair of N-by-N real nonsymmetric matrices A, B	[ SGEGS ]
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)	[ SGEGV ]
sgehd2	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation	[ SGEHD2 ]
sgehrd	reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation	[ SGEHRD ]
sgelq2	compute an LQ factorization of a real m by n matrix A	[ SGELQ2 ]
sgelqf	compute an LQ factorization of a real M-by-N matrix A	[ SGELQF ]
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	[ SGELS ]
sgelss	compute the minimum norm solution to a real linear least squares problem	[ SGELSS ]
sgelsx	compute the minimum-norm solution to a real linear least squares problem	[ SGELSX ]
sgeql2	compute a QL factorization of a real m by n matrix A	[ SGEQL2 ]
sgeqlf	compute a QL factorization of a real M-by-N matrix A	[ SGEQLF ]
sgeqpf	compute a QR factorization with column pivoting of a real M-by-N matrix A	[ SGEQPF ]
sgeqr2	compute a QR factorization of a real m by n matrix A	[ SGEQR2 ]
sgeqrf	compute a QR factorization of a real M-by-N matrix A	[ SGEQRF ]
sgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution	[ SGERFS ]
sgerq2	compute an RQ factorization of a real m by n matrix A	[ SGERQ2 ]
sgerqf	compute an RQ factorization of a real M-by-N matrix A	[ SGERQF ]
sgesv	compute the solution to a real system of linear equations A ∗ X = B,	[ SGESV ]
sgesvd	compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors	[ SGESVD ]
sgesvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B,	[ SGESVX ]
sgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges	[ SGETF2 ]
sgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges	[ SGETRF ]
sgetri	compute the inverse of a matrix using the LU factorization computed by SGETRF	[ SGETRI ]
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	[ SGETRS ]
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	[ SGGBAK ]
sggbal	balance a pair of general real matrices (A,B)	[ SGGBAL ]
sggglm	solve a general Gauss-Markov linear model (GLM) problem	[ SGGGLM ]
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	[ SGGHRD ]
sgglse	solve the linear equality-constrained least squares (LSE) problem	[ SGGLSE ]
sggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B	[ SGGQRF ]
sggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B	[ SGGRQF ]
sggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B	[ SGGSVD ]
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	[ SGGSVP ]
sgtcon	estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF	[ SGTCON ]
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	[ SGTRFS ]
sgtsv	solve the equation A∗X = B,	[ SGTSV ]
sgtsvx	use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B,	[ SGTSVX ]
sgttrf	compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges	[ SGTTRF ]
sgttrs	solve one of the systems of equations A∗X = B or A’∗X = B,	[ SGTTRS ]
shgeqz	implement a single-/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	[ SHGEQZ ]
shsein	use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H	[ SHSEIN ]
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	[ SHSEQR ]
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	[ SLABAD ]
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	[ SLABRD ]
slacon	estimate the 1-norm of a square, real matrix A	[ SLACON ]
slacpy	copie all or part of a two-dimensional matrix A to another matrix B	[ SLACPY ]
sladiv	perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L	[ SLADIV ]
slae2	compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]	[ SLAE2 ]
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	[ SLAEBZ ]
slaed0	compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ SLAED0 ]
slaed1	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ SLAED1 ]
slaed2	merge the two sets of eigenvalues together into a single sorted set	[ SLAED2 ]
slaed3	find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP	[ SLAED3 ]
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	[ SLAED4 ]
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	[ SLAED5 ]
slaed6	compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true	[ SLAED6 ]
slaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ SLAED7 ]
slaed8	merge the two sets of eigenvalues together into a single sorted set	[ SLAED8 ]
slaed9	find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP	[ SLAED9 ]
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	[ SLAEDA ]
slaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H	[ SLAEIN ]
slaev2	compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]	[ SLAEV2 ]
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	[ SLAEXC ]
slag2	compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow	[ SLAG2 ]
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,	[ SLAGTF ]
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 0., 1., or -1	[ SLAGTM ]
slagts	may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y,	[ SLAGTS ]
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	[ SLAHQR ]
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	[ SLAHRD ]
slaic1	applie one step of incremental condition estimation in its simplest version	[ SLAIC1 ]
slaln2	solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A	[ SLALN2 ]
slamch	determine single precision machine parameters	[ SLAMCH ]
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	[ SLAMRG ]
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	[ SLANGB ]
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	[ SLANGE ]
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	[ SLANGT ]
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	[ SLANHS ]
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	[ SLANSB ]
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	[ SLANSP ]
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	[ SLANST ]
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	[ SLANSY ]
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	[ SLANTB ]
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	[ SLANTP ]
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	[ SLANTR ]
slanv2	compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form	[ SLANV2 ]
slapll	two column vectors X and Y, let A = ( X Y )	[ SLAPLL ]
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	[ SLAPMT ]
slapy2	return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow	[ SLAPY2 ]
slapy3	return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow	[ SLAPY3 ]
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	[ SLAQGB ]
slaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C	[ SLAQGE ]
slaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ SLAQSB ]
slaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ SLAQSP ]
slaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ SLAQSY ]
slaqtr	solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE	[ SLAQTR ]
slar2v	applie 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	[ SLAR2V ]
slarf	applie a real elementary reflector H to a real m by n matrix C, from either the left or the right	[ SLARF ]
slarfb	applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right	[ SLARFB ]
slarfg	generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I	[ SLARFG ]
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	[ SLARFT ]
slarfx	applie a real elementary reflector H to a real m by n matrix C, from either the left or the right	[ SLARFX ]
slargv	generate a vector of real plane rotations, determined by elements of the real vectors x and y	[ SLARGV ]
slarnv	return a vector of n random real numbers from a uniform or normal distribution	[ SLARNV ]
slartg	generate a plane rotation so that [ CS SN ]	[ SLARTG ]
slartv	applie a vector of real plane rotations to elements of the real vectors x and y	[ SLARTV ]
slaruv	return a vector of n random real numbers from a uniform (0,1)	[ SLARUV ]
slas2	compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]	[ SLAS2 ]
slascl	multiplie the M by N real matrix A by the real scalar CTO/CFROM	[ SLASCL ]
slaset	initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals	[ SLASET ]
slasq1	SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E	[ SLASQ1 ]
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	[ SLASQ2 ]
slasq3	SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm	[ SLASQ3 ]
slasq4	SLASQ4 estimates TAU, the smallest eigenvalue of a matrix	[ SLASQ4 ]
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,	[ SLASR ]
slasrt	the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ )	[ SLASRT ]
slassq	return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,	[ SLASSQ ]
slasv2	compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]	[ SLASV2 ]
slaswp	perform a series of row interchanges on the matrix A	[ SLASWP ]
slasy2	solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B,	[ SLASY2 ]
slasyf	compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ SLASYF ]
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	[ SLATBS ]
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	[ SLATPS ]
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	[ SLATRD ]
slatrs	solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow	[ SLATRS ]
slatzm	applie a Householder matrix generated by STZRQF to a matrix	[ SLATZM ]
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	[ SLAUU2 ]
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	[ SLAUUM ]
slazro	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ SLAZRO ]
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	[ SOPGTR ]
sopmtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SOPMTR ]
sorg2l	generate an m by n real matrix Q with orthonormal columns,	[ SORG2L ]
sorg2r	generate an m by n real matrix Q with orthonormal columns,	[ SORG2R ]
sorgbr	generate one of the real orthogonal matrices Q or P∗∗T determined by SGEBRD when reducing a real matrix A to bidiagonal form	[ SORGBR ]
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	[ SORGHR ]
sorgl2	generate an m by n real matrix Q with orthonormal rows,	[ SORGL2 ]
sorglq	generate an M-by-N real matrix Q with orthonormal rows,	[ SORGLQ ]
sorgql	generate an M-by-N real matrix Q with orthonormal columns,	[ SORGQL ]
sorgqr	generate an M-by-N real matrix Q with orthonormal columns,	[ SORGQR ]
sorgr2	generate an m by n real matrix Q with orthonormal rows,	[ SORGR2 ]
sorgrq	generate an M-by-N real matrix Q with orthonormal rows,	[ SORGRQ ]
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	[ SORGTR ]
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’,	[ SORM2L ]
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’,	[ SORM2R ]
sormbr	VECT = ’Q’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMBR ]
sormhr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMHR ]
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’,	[ SORML2 ]
sormlq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMLQ ]
sormql	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMQL ]
sormqr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMQR ]
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’,	[ SORMR2 ]
sormrq	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMRQ ]
sormtr	overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ SORMTR ]
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	[ SPBCON ]
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)	[ SPBEQU ]
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	[ SPBRFS ]
spbstf	compute a split Cholesky factorization of a real symmetric positive definite band matrix A	[ SPBSTF ]
spbsv	compute the solution to a real system of linear equations A ∗ X = B,	[ SPBSV ]
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,	[ SPBSVX ]
spbtf2	compute the Cholesky factorization of a real symmetric positive definite band matrix A	[ SPBTF2 ]
spbtrf	compute the Cholesky factorization of a real symmetric positive definite band matrix A	[ SPBTRF ]
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	[ SPBTRS ]
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	[ SPOCON ]
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)	[ SPOEQU ]
sporfs	improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,	[ SPORFS ]
sposv	compute the solution to a real system of linear equations A ∗ X = B,	[ SPOSV ]
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,	[ SPOSVX ]
spotf2	compute the Cholesky factorization of a real symmetric positive definite matrix A	[ SPOTF2 ]
spotrf	compute the Cholesky factorization of a real symmetric positive definite matrix A	[ SPOTRF ]
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	[ SPOTRI ]
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	[ SPOTRS ]
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	[ SPPCON ]
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)	[ SPPEQU ]
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	[ SPPRFS ]
sppsv	compute the solution to a real system of linear equations A ∗ X = B,	[ SPPSV ]
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,	[ SPPSVX ]
spptrf	compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format	[ SPPTRF ]
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	[ SPPTRI ]
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	[ SPPTRS ]
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	[ SPTCON ]
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	[ SPTEQR ]
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	[ SPTRFS ]
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	[ SPTSV ]
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	[ SPTSVX ]
spttrf	compute the factorization of a real symmetric positive definite tridiagonal matrix A	[ SPTTRF ]
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	[ SPTTRS ]
srscl	multiplie an n-element real vector x by the real scalar 1/a	[ SRSCL ]
ssbev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ SSBEV ]
ssbevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ SSBEVD ]
ssbevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A	[ SSBEVX ]
ssbgst	reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,	[ SSBGST ]
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	[ SSBGV ]
ssbtrd	reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation	[ SSBTRD ]
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	[ SSPCON ]
sspev	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ SSPEV ]
sspevd	compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ SSPEVD ]
sspevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage	[ SSPEVX ]
sspgst	reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage	[ SSPGST ]
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	[ SSPGV ]
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	[ SSPRFS ]
sspsv	compute the solution to a real system of linear equations A ∗ X = B,	[ SSPSV ]
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	[ SSPSVX ]
ssptrd	reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation	[ SSPTRD ]
ssptrf	compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method	[ SSPTRF ]
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	[ SSPTRI ]
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	[ SSPTRS ]
sstebz	compute the eigenvalues of a symmetric tridiagonal matrix T	[ SSTEBZ ]
sstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ SSTEDC ]
sstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration	[ SSTEIN ]
ssteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method	[ SSTEQR ]
ssterf	compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm	[ SSTERF ]
sstev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A	[ SSTEV ]
sstevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix	[ SSTEVD ]
sstevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A	[ SSTEVX ]
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	[ SSYCON ]
ssyev	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ SSYEV ]
ssyevd	compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ SSYEVD ]
ssyevx	compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A	[ SSYEVX ]
ssygs2	reduce a real symmetric-definite generalized eigenproblem to standard form	[ SSYGS2 ]
ssygst	reduce a real symmetric-definite generalized eigenproblem to standard form	[ SSYGST ]
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	[ SSYGV ]
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	[ SSYRFS ]
ssysv	compute the solution to a real system of linear equations A ∗ X = B,	[ SSYSV ]
ssysvx	use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B,	[ SSYSVX ]
ssytd2	reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation	[ SSYTD2 ]
ssytf2	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ SSYTF2 ]
ssytrd	reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation	[ SSYTRD ]
ssytrf	compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ SSYTRF ]
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	[ SSYTRI ]
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	[ SSYTRS ]
stbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm	[ STBCON ]
stbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix	[ STBRFS ]
stbtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ STBTRS ]
stgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)	[ STGEVC ]
stgsja	compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B	[ STGSJA ]
stpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm	[ STPCON ]
stprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix	[ STPRFS ]
stptri	compute the inverse of a real upper or lower triangular matrix A stored in packed format	[ STPTRI ]
stptrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ STPTRS ]
strcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm	[ STRCON ]
strevc	compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T	[ STREVC ]
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	[ STREXC ]
strrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix	[ STRRFS ]
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,	[ STRSEN ]
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)	[ STRSNA ]
strsyl	solve the real Sylvester matrix equation	[ STRSYL ]
strti2	compute the inverse of a real upper or lower triangular matrix	[ STRTI2 ]
strtri	compute the inverse of a real upper or lower triangular matrix A	[ STRTRI ]
strtrs	solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B,	[ STRTRS ]
stzrqf	reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations	[ STZRQF ]
xerbla	i an error handler for the LAPACK routines	[ XERBLA ]
zbdsqr	compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B	[ ZBDSQR ]
zdrscl	multiplie an n-element complex vector x by the real scalar 1/a	[ ZDRSCL ]
zgbbrd	reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation	[ ZGBBRD ]
zgbcon	estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,	[ ZGBCON ]
zgbequ	compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number	[ ZGBEQU ]
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	[ ZGBRFS ]
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	[ ZGBSV ]
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,	[ ZGBSVX ]
zgbtf2	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges	[ ZGBTF2 ]
zgbtrf	compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges	[ ZGBTRF ]
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	[ ZGBTRS ]
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	[ ZGEBAK ]
zgebal	balance a general complex matrix A	[ ZGEBAL ]
zgebd2	reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation	[ ZGEBD2 ]
zgebrd	reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation	[ ZGEBRD ]
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	[ ZGECON ]
zgeequ	compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number	[ ZGEEQU ]
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	[ ZGEES ]
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	[ ZGEESX ]
zgeev	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ ZGEEV ]
zgeevx	compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors	[ ZGEEVX ]
zgegs	compute for a pair of N-by-N complex nonsymmetric matrices A,	[ ZGEGS ]
zgegv	compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally,	[ ZGEGV ]
zgehd2	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation	[ ZGEHD2 ]
zgehrd	reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation	[ ZGEHRD ]
zgelq2	compute an LQ factorization of a complex m by n matrix A	[ ZGELQ2 ]
zgelqf	compute an LQ factorization of a complex M-by-N matrix A	[ ZGELQF ]
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	[ ZGELS ]
zgelss	compute the minimum norm solution to a complex linear least squares problem	[ ZGELSS ]
zgelsx	compute the minimum-norm solution to a complex linear least squares problem	[ ZGELSX ]
zgeql2	compute a QL factorization of a complex m by n matrix A	[ ZGEQL2 ]
zgeqlf	compute a QL factorization of a complex M-by-N matrix A	[ ZGEQLF ]
zgeqpf	compute a QR factorization with column pivoting of a complex M-by-N matrix A	[ ZGEQPF ]
zgeqr2	compute a QR factorization of a complex m by n matrix A	[ ZGEQR2 ]
zgeqrf	compute a QR factorization of a complex M-by-N matrix A	[ ZGEQRF ]
zgerfs	improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution	[ ZGERFS ]
zgerq2	compute an RQ factorization of a complex m by n matrix A	[ ZGERQ2 ]
zgerqf	compute an RQ factorization of a complex M-by-N matrix A	[ ZGERQF ]
zgesv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZGESV ]
zgesvd	compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors	[ ZGESVD ]
zgesvx	use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ ZGESVX ]
zgetf2	compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges	[ ZGETF2 ]
zgetrf	compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges	[ ZGETRF ]
zgetri	compute the inverse of a matrix using the LU factorization computed by ZGETRF	[ ZGETRI ]
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	[ ZGETRS ]
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	[ ZGGBAK ]
zggbal	balance a pair of general complex matrices (A,B)	[ ZGGBAL ]
zggglm	solve a general Gauss-Markov linear model (GLM) problem	[ ZGGGLM ]
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	[ ZGGHRD ]
zgglse	solve the linear equality-constrained least squares (LSE) problem	[ ZGGLSE ]
zggqrf	compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B	[ ZGGQRF ]
zggrqf	compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B	[ ZGGRQF ]
zggsvd	compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B	[ ZGGSVD ]
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	[ ZGGSVP ]
zgtcon	estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF	[ ZGTCON ]
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	[ ZGTRFS ]
zgtsv	solve the equation A∗X = B,	[ ZGTSV ]
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,	[ ZGTSVX ]
zgttrf	compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges	[ ZGTTRF ]
zgttrs	solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ ZGTTRS ]
zhbev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ ZHBEV ]
zhbevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ ZHBEVD ]
zhbevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A	[ ZHBEVX ]
zhbgst	reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y,	[ ZHBGST ]
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	[ ZHBGV ]
zhbtrd	reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ ZHBTRD ]
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	[ ZHECON ]
zheev	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ ZHEEV ]
zheevd	compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ ZHEEVD ]
zheevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A	[ ZHEEVX ]
zhegs2	reduce a complex Hermitian-definite generalized eigenproblem to standard form	[ ZHEGS2 ]
zhegst	reduce a complex Hermitian-definite generalized eigenproblem to standard form	[ ZHEGST ]
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	[ ZHEGV ]
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	[ ZHERFS ]
zhesv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZHESV ]
zhesvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ ZHESVX ]
zhetd2	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ ZHETD2 ]
zhetf2	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZHETF2 ]
zhetrd	reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation	[ ZHETRD ]
zhetrf	compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZHETRF ]
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	[ ZHETRI ]
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	[ ZHETRS ]
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	[ ZHGEQZ ]
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	[ ZHPCON ]
zhpev	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage	[ ZHPEV ]
zhpevd	compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage	[ ZHPEVD ]
zhpevx	compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage	[ ZHPEVX ]
zhpgst	reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage	[ ZHPGST ]
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	[ ZHPGV ]
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	[ ZHPRFS ]
zhpsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZHPSV ]
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	[ ZHPSVX ]
zhptrd	reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation	[ ZHPTRD ]
zhptrf	compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZHPTRF ]
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	[ ZHPTRI ]
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	[ ZHPTRS ]
zhsein	use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H	[ ZHSEIN ]
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	[ ZHSEQR ]
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	[ ZLABRD ]
zlacgv	conjugate a complex vector of length N	[ ZLACGV ]
zlacon	estimate the 1-norm of a square, complex matrix A	[ ZLACON ]
zlacpy	copie all or part of a two-dimensional matrix A to another matrix B	[ ZLACPY ]
zlacrm	perform a very simple matrix-matrix multiplication	[ ZLACRM ]
zlacrt	applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex	[ ZLACRT ]
zladiv	:= X / Y, where X and Y are complex	[ ZLADIV ]
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	[ ZLAED0 ]
zlaed7	compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix	[ ZLAED7 ]
zlaed8	merge the two sets of eigenvalues together into a single sorted set	[ ZLAED8 ]
zlaein	use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H	[ ZLAEIN ]
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	[ ZLAESY ]
zlaev2	compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]	[ ZLAEV2 ]
zlags2
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 0., 1., or -1	[ ZLAGTM ]
zlahef	compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZLAHEF ]
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	[ ZLAHQR ]
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	[ ZLAHRD ]
zlaic1	applie one step of incremental condition estimation in its simplest version	[ ZLAIC1 ]
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	[ ZLANGB ]
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	[ ZLANGE ]
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	[ ZLANGT ]
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	[ ZLANHB ]
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	[ ZLANHE ]
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	[ ZLANHP ]
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	[ ZLANHS ]
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	[ ZLANHT ]
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	[ ZLANSB ]
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	[ ZLANSP ]
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	[ ZLANSY ]
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	[ ZLANTB ]
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	[ ZLANTP ]
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	[ ZLANTR ]
zlapll	two column vectors X and Y, let A = ( X Y )	[ ZLAPLL ]
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	[ ZLAPMT ]
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	[ ZLAQGB ]
zlaqge	equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C	[ ZLAQGE ]
zlaqhb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ ZLAQHB ]
zlaqhe	equilibrate a Hermitian matrix A using the scaling factors in the vector S	[ ZLAQHE ]
zlaqhp	equilibrate a Hermitian matrix A using the scaling factors in the vector S	[ ZLAQHP ]
zlaqsb	equilibrate a symmetric band matrix A using the scaling factors in the vector S	[ ZLAQSB ]
zlaqsp	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ ZLAQSP ]
zlaqsy	equilibrate a symmetric matrix A using the scaling factors in the vector S	[ ZLAQSY ]
zlar2v	applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,	[ ZLAR2V ]
zlarf	applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right	[ ZLARF ]
zlarfb	applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right	[ ZLARFB ]
zlarfg	generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I	[ ZLARFG ]
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	[ ZLARFT ]
zlarfx	applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right	[ ZLARFX ]
zlargv	generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y	[ ZLARGV ]
zlarnv	return a vector of n random complex numbers from a uniform or normal distribution	[ ZLARNV ]
zlartg	generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]	[ ZLARTG ]
zlartv	applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y	[ ZLARTV ]
zlascl	multiplie the M by N complex matrix A by the real scalar CTO/CFROM	[ ZLASCL ]
zlaset	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ ZLASET ]
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,	[ ZLASR ]
zlassq	return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq,	[ ZLASSQ ]
zlaswp	perform a series of row interchanges on the matrix A	[ ZLASWP ]
zlasyf	compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZLASYF ]
zlatbs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ ZLATBS ]
zlatps	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ ZLATPS ]
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	[ ZLATRD ]
zlatrs	solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b,	[ ZLATRS ]
zlatzm	applie a Householder matrix generated by ZTZRQF to a matrix	[ ZLATZM ]
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	[ ZLAUU2 ]
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	[ ZLAUUM ]
zlazro	initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals	[ ZLAZRO ]
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	[ ZPBCON ]
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)	[ ZPBEQU ]
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	[ ZPBRFS ]
zpbstf	compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A	[ ZPBSTF ]
zpbsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZPBSV ]
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,	[ ZPBSVX ]
zpbtf2	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A	[ ZPBTF2 ]
zpbtrf	compute the Cholesky factorization of a complex Hermitian positive definite band matrix A	[ ZPBTRF ]
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	[ ZPBTRS ]
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	[ ZPOCON ]
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)	[ ZPOEQU ]
zporfs	improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,	[ ZPORFS ]
zposv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZPOSV ]
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,	[ ZPOSVX ]
zpotf2	compute the Cholesky factorization of a complex Hermitian positive definite matrix A	[ ZPOTF2 ]
zpotrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A	[ ZPOTRF ]
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	[ ZPOTRI ]
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	[ ZPOTRS ]
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	[ ZPPCON ]
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)	[ ZPPEQU ]
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	[ ZPPRFS ]
zppsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZPPSV ]
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,	[ ZPPSVX ]
zpptrf	compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format	[ ZPPTRF ]
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	[ ZPPTRI ]
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	[ ZPPTRS ]
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	[ ZPTCON ]
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	[ ZPTEQR ]
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	[ ZPTRFS ]
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	[ ZPTSV ]
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	[ ZPTSVX ]
zpttrf	compute the factorization of a complex Hermitian positive definite tridiagonal matrix A	[ ZPTTRF ]
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	[ ZPTTRS ]
zrot	applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex	[ ZROT ]
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	[ ZSPCON ]
zspmv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,	[ ZSPMV ]
zspr	perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A,	[ ZSPR ]
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	[ ZSPRFS ]
zspsv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZSPSV ]
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	[ ZSPSVX ]
zsptrf	compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method	[ ZSPTRF ]
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	[ ZSPTRI ]
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	[ ZSPTRS ]
zsrscl	multiplie an n-element complex vector x by the real scalar 1/a	[ ZSRSCL ]
zstedc	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method	[ ZSTEDC ]
zstein	compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration	[ ZSTEIN ]
zsteqr	compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method	[ ZSTEQR ]
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	[ ZSYCON ]
zsymv	perform the matrix-vector operation y := alpha∗A∗x + beta∗y,	[ ZSYMV ]
zsyr	perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A,	[ ZSYR ]
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	[ ZSYRFS ]
zsysv	compute the solution to a complex system of linear equations A ∗ X = B,	[ ZSYSV ]
zsysvx	use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B,	[ ZSYSVX ]
zsytf2	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZSYTF2 ]
zsytrf	compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method	[ ZSYTRF ]
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	[ ZSYTRI ]
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	[ ZSYTRS ]
ztbcon	estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm	[ ZTBCON ]
ztbrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix	[ ZTBRFS ]
ztbtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ ZTBTRS ]
ztgevc	compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)	[ ZTGEVC ]
ztgsja	compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B	[ ZTGSJA ]
ztpcon	estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm	[ ZTPCON ]
ztprfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix	[ ZTPRFS ]
ztptri	compute the inverse of a complex upper or lower triangular matrix A stored in packed format	[ ZTPTRI ]
ztptrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ ZTPTRS ]
ztrcon	estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm	[ ZTRCON ]
ztrevc	compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T	[ ZTREVC ]
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	[ ZTREXC ]
ztrrfs	provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix	[ ZTRRFS ]
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	[ ZTRSEN ]
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)	[ ZTRSNA ]
ztrsyl	solve the complex Sylvester matrix equation	[ ZTRSYL ]
ztrti2	compute the inverse of a complex upper or lower triangular matrix	[ ZTRTI2 ]
ztrtri	compute the inverse of a complex upper or lower triangular matrix A	[ ZTRTRI ]
ztrtrs	solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B,	[ ZTRTRS ]
ztzrqf	reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations	[ ZTZRQF ]
zung2l	generate an m by n complex matrix Q with orthonormal columns,	[ ZUNG2L ]
zung2r	generate an m by n complex matrix Q with orthonormal columns,	[ ZUNG2R ]
zungbr	generate one of the complex unitary matrices Q or P∗∗H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form	[ ZUNGBR ]
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	[ ZUNGHR ]
zungl2	generate an m-by-n complex matrix Q with orthonormal rows,	[ ZUNGL2 ]
zunglq	generate an M-by-N complex matrix Q with orthonormal rows,	[ ZUNGLQ ]
zungql	generate an M-by-N complex matrix Q with orthonormal columns,	[ ZUNGQL ]
zungqr	generate an M-by-N complex matrix Q with orthonormal columns,	[ ZUNGQR ]
zungr2	generate an m by n complex matrix Q with orthonormal rows,	[ ZUNGR2 ]
zungrq	generate an M-by-N complex matrix Q with orthonormal rows,	[ ZUNGRQ ]
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	[ ZUNGTR ]
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’,	[ ZUNM2L ]
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’,	[ ZUNM2R ]
zunmbr	VECT = ’Q’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMBR ]
zunmhr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMHR ]
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’,	[ ZUNML2 ]
zunmlq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMLQ ]
zunmql	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMQL ]
zunmqr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMQR ]
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’,	[ ZUNMR2 ]
zunmrq	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMRQ ]
zunmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUNMTR ]
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	[ ZUPGTR ]
zupmtr	overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’	[ ZUPMTR ]

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Anchors

Manual — Digital_UNIX Extended_Math_Library_3.4

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Section 3DXML

Section 3dxml

Section 3lapack

Section l