Digital

Name

dsskyn − Symmetric sparse matrix norm evaluation using skyline storage scheme

FORMAT

DSSKYN (n, au, iaudiag, nau, iparam, rparam, iwrk, rwrk, ierror)

Arguments

ninteger∗4
On entry, the order of the matrix A.
On exit, n is unchanged. 

aureal∗8
On entry, an array of length at least nau, containing the matrix A stored in the skyline storage scheme, using either the profile-in or the diagonal-out storage mode.
On exit,  au is unchanged. 

iaudiaginteger∗4
On entry, an array of length at least n for the profile-in storage mode and n+1 for the diagonal-out storage mode, containing the pointers to the locations of the diagonal elements in array AU.
On exit,  iaudiag is unchanged. 

nauinteger∗4
On entry, the number of elements in array AU. nau is also the envelope size of the symmetric part of the matrix A. For the profile-in storage mode, nau =  IAUDIAG(n).  For the diagonal-out storage mode, nau =  IAUDIAG(n+1) - 1. 
On exit,  nau is unchanged. 

iparaminteger∗4
An array of length at least 100, containing the integer parameters for the evaluation of the matrix norms.

iparam(1): niparam
On entry, defines the length of the array IPARAM.  niparam >= 100.
On exit,  iparam(1) is unchanged. 

iparam(2): nrparam
On entry, defines the length of the array RPARAM. nrparam >= 100.
On exit,  iparam(2) is unchanged. 

iparam(3): niwrk
On entry, defines the size of the integer work array, IWRK.  niwrk >= n.
On exit,  iparam(3) is unchanged. 

iparam(4): nrwrk
On entry, defines the size of the real work array, RWRK.  nrwrk >= n
On exit,  iparam(4) is unchanged. 

iparam(5): iounit
On entry, defines the I/O unit number for printing error messages and information from the routine DSSKYN. The I/O unit must be opened in the calling subprogram. If iounit <= 0, no output is generated. 
On exit,  iparam(5) is unchanged. 

iparam(6): iolevel
On entry, defines the message level that determines the amount of information printed out to iounit, when iounit > 0. 

iolevel = 0 : fatal error messages only

iolevel = 1 : error messages and minimal information

iolevel = 2 : error messages and detailed information

On exit,  iparam(6) is unchanged. 

iparam(7): idefault
On entry, defines if the default values should be used in arrays IPARAM and RPARAM. If idefault = 0, then the following default values are assigned:

IPARAM(1) = niparam = 100

IPARAM(2) = nrparam = 100

IPARAM(6) = iolevel = 0

IPARAM(8) = istore = 1

IPARAM(9) = inorm = 1

If idefault = 1, then you must assign values to the above variables before the call to the DSSKYN routine. 
On exit,  iparam(7) is unchanged. 

iparam(8): istore
On entry, defines the type of storage scheme used for the skyline matrix. If istore = 1, the matrix A is stored using the profile-in storage mode; if istore = 2, the matrix A is stored using the diagonal-out storage mode.  Default: istore = 1. 
On exit,  iparam(8) is unchanged. 

iparam(9): inorm
On entry, defines the matrix quantity to be evaluated:

inorm = 1 : 1-norm of A

inorm = 2 : Infinity-norm of A

inorm = 3 : Frobenius norm of A

inorm = 4 : Maximum absolute value of A

Default: inorm = 1. 
On exit,  iparam(9) is unchanged. 

rparamreal∗8
An array of length at least 100, containing the real parameters for the norm evaluation.

rparam(1): anorm
On entry, an unspecified variable.
On exit,  rparam(1) contains the matrix quantity evaluated, as defined by the value of IPARAM(9) = inorm. 

iwrkinteger∗4
On entry, an array of length at least n used for integer workspace.
On exit,  iwrk contains information used by the routine DSSKYN. This information is not used by any other routine and therefore can be overwritten.

rwrk
 real∗8
On entry, an array of length at least n used for real workspace.
On exit,  rwrk contains information used by the routine DSSKYN. This information is not used by any other routine and therefore can be overwritten.

ierrorinteger∗4
On entry, an unspecified variable.
On exit,  ierror contains the error flag. A value of zero indicates a normal exit from the routine DSSKYN.

Description

DSSKYN evaluates the following quantities for the symmetric matrix A:

•1-norm of (A)

•Infinity-norm of (A)

•Frobenius-norm of (A)

•Largest absolute value of (A)

The last quantity in the above list is not a matrix norm. The quantity evaluated is determined by the value of inorm, with the 1-norm and Infinity-norm being identical for symmetric matrices. 

The real and integer workspace used by the routine DSSKYN do not contain information for use by any other routines, and can therefore be overwritten. 

As the routine DSSKYN requires the matrix A, it should be called prior to a call to the factorization routine DSSKYF, which overwrites the elements of A by its transp(U)∗D∗U factorization.