CXML
dsskyc
Symmetric sparse matrix condition number estimator using skyline
storage scheme
FORMAT
DSSKYC
(n, au, iaudiag, nau, iparam, rparam, iwrk, rwrk, ierror)
Arguments
n integer*4
On entry, the order of the matrix A.
On exit, n is unchanged.
au real*8
On entry, an array of length at least nau, containing
the transp(U)*D*U factorization of the matrix A stored
in the skyline storage scheme, using either the
profile-in, or the diagonal-out storage mode. The
factorization has been obtained by a prior call to the
routine DSSKYF. au must remain unchanged between calls
to the routines DSSKYF and DSSKYC.
On exit, au is unchanged.
iaudiag integer*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.
nau integer*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.
iparam integer*4
An array of length at least 100, containing the integer
parameters for the condition number estimator.
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 >=3n.
On exit, iparam(3) is unchanged.
iparam(4): nrwrk
On entry, defines the size of the real work array,
RWRK. nrwrk >= 2n.
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 DSSKYC.
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
If idefault = 1, then you must assign values to the
above variables before the call to the DSSKYC 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. The storage scheme used in the routines
DSSKYF and DSSKYC must be identical. Default: istore
= 1.
On exit, iparam(8) is unchanged.
rparam real*8
An array of length at least 100, containing the real
parameters for the condition number estimator.
rparam(1): anorm
On entry, the 1-norm of the matric A, which has been
obtained by a prior call to routine DSSKYN.
On exit, rparam(1) is unchanged.
rparam(2): ainorm
On entry, an unspecified variable.
On exit, rparam(2) contains the estimate of the 1-norm
of inverse(A)).
rparam(3): rcond
On entry, an unspecified variable.
On exit, rparam(3) contains the reciprocal of the
estimate of the 1-norm condition number of the matrix
A.
iwrk integer*4
On entry, an array of length at least 3n used for
integer workspace. The first 2n elements of iwrk
generated by the routine DSSKYF must be passed
unchanged to the routine DSSKYC.
On exit, the first 2n elements of iwrk are unchanged.
The next n elements are used as integer workspace by
DSSKYC.
rwrk real*8
On entry, an array of length at least 2n used for
integer workspace.
On exit, the first 2n elements of rwrk are
overwritten.
ierror integer*4
On entry, an unspecified variable.
On exit, ierror contains the error flag. A value of
zero indicates a normal exit from the routine DSSKYC.
Description
DSSKYC obtains the reciprocal of the estimate of the 1-norm condition
number of the symmetric matrix A as:
rcond(A) = 1 / (||A|| * ||inverse(A)|| )
The 1-norm of inverse(A) is obtained using the LAPACK routine DLACON, which
uses Higham's modification [Higham 1988] of Hager's method [Hager 1984].
This routine uses reverse communication for the evaluation of matrix-vector
products. As the matrix under consideration is inverse(A)), routine DSSKYC
requires calls to the routine DSSKYS. Hence the first 2n elements of the
integer work array, IWRK, which are generated by the routine DSSKYF, and
used by the routine DSSKYS, must remain unchanged between the calls to the
routines DSSKYF and DSSKYC. The storage scheme used in the routines DSSKYF
and DSSKYC must be identical.
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