Purpose
To solve a system of equations in quasi-Hessenberg form (Hessenberg form plus two consecutive offdiagonals) with two right-hand sides.Specification
SUBROUTINE SB04RX( RC, UL, M, A, LDA, LAMBD1, LAMBD2, LAMBD3,
$ LAMBD4, D, TOL, IWORK, DWORK, LDDWOR, INFO )
C .. Scalar Arguments ..
CHARACTER RC, UL
INTEGER INFO, LDA, LDDWOR, M
DOUBLE PRECISION LAMBD1, LAMBD2, LAMBD3, LAMBD4, TOL
C .. Array Arguments ..
INTEGER IWORK(*)
DOUBLE PRECISION A(LDA,*), D(*), DWORK(LDDWOR,*)
Arguments
Mode Parameters
RC CHARACTER*1
Indicates processing by columns or rows, as follows:
= 'R': Row transformations are applied;
= 'C': Column transformations are applied.
UL CHARACTER*1
Indicates whether A is upper or lower Hessenberg matrix,
as follows:
= 'U': A is upper Hessenberg;
= 'L': A is lower Hessenberg.
Input/Output Parameters
M (input) INTEGER
The order of the matrix A. M >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,M)
The leading M-by-M part of this array must contain a
matrix A in Hessenberg form.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,M).
LAMBD1, (input) DOUBLE PRECISION
LAMBD2, These variables must contain the 2-by-2 block to be
LAMBD3, multiplied to the elements of A.
LAMBD4
D (input/output) DOUBLE PRECISION array, dimension (2*M)
On entry, this array must contain the two right-hand
side vectors of the quasi-Hessenberg system, stored
row-wise.
On exit, if INFO = 0, this array contains the two solution
vectors of the quasi-Hessenberg system, stored row-wise.
Tolerances
TOL DOUBLE PRECISION
The tolerance to be used to test for near singularity of
the triangular factor R of the quasi-Hessenberg matrix.
A matrix whose estimated condition number is less
than 1/TOL is considered to be nonsingular.
Workspace
IWORK INTEGER array, dimension (2*M)
DWORK DOUBLE PRECISION array, dimension (LDDWOR,2*M+3)
The leading 2*M-by-2*M part of this array is used for
computing the triangular factor of the QR decomposition
of the quasi-Hessenberg matrix. The remaining 6*M elements
are used as workspace for the computation of the
reciprocal condition estimate.
LDDWOR INTEGER
The leading dimension of array DWORK.
LDDWOR >= MAX(1,2*M).
Error Indicator
INFO INTEGER
= 0: successful exit;
= 1: if the quasi-Hessenberg matrix is (numerically)
singular. That is, its estimated reciprocal
condition number is less than or equal to TOL.
Numerical Aspects
None.Further Comments
NoneExample
Program Text
NoneProgram Data
NoneProgram Results
None