SLAQTR
Purpose
SLAQTR solves the real quasi-triangular system
op(T)*p = scale*c, if LREAL = .TRUE.
or the complex quasi-triangular systems
op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE.
in real arithmetic, where T is upper quasi-triangular.
If LREAL = .FALSE., then the first diagonal block of T must be
1 by 1, B is the specially structured matrix
B = [ b(1) b(2) ... b(n) ]
[ w ]
[ w ]
[ . ]
[ w ]
op(A) = A or A**T, A**T denotes the transpose of
matrix A.
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
This subroutine is designed for the condition number estimation
in routine STRSNA.
op(T)*p = scale*c, if LREAL = .TRUE.
or the complex quasi-triangular systems
op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE.
in real arithmetic, where T is upper quasi-triangular.
If LREAL = .FALSE., then the first diagonal block of T must be
1 by 1, B is the specially structured matrix
B = [ b(1) b(2) ... b(n) ]
[ w ]
[ w ]
[ . ]
[ w ]
op(A) = A or A**T, A**T denotes the transpose of
matrix A.
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
This subroutine is designed for the condition number estimation
in routine STRSNA.
Arguments
| LTRAN |
(input) LOGICAL
On entry, LTRAN specifies the option of conjugate transpose:
= .FALSE., op(T+i*B) = T+i*B, = .TRUE., op(T+i*B) = (T+i*B)**T. |
| LREAL |
(input) LOGICAL
On entry, LREAL specifies the input matrix structure:
= .FALSE., the input is complex = .TRUE., the input is real |
| N |
(input) INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
|
| T |
(input) REAL array, dimension (LDT,N)
On entry, T contains a matrix in Schur canonical form.
If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1. |
| LDT |
(input) INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
|
| B |
(input) REAL array, dimension (N)
On entry, B contains the elements to form the matrix
B as described above. If LREAL = .TRUE., B is not referenced. |
| W |
(input) REAL
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced. |
| SCALE |
(output) REAL
On exit, SCALE is the scale factor.
|
| X |
(input/output) REAL array, dimension (2*N)
On entry, X contains the right hand side of the system.
On exit, X is overwritten by the solution. |
| WORK |
(workspace) REAL array, dimension (N)
|
| INFO |
(output) INTEGER
On exit, INFO is set to
0: successful exit. 1: the some diagonal 1 by 1 block has been perturbed by a small number SMIN to keep nonsingularity. 2: the some diagonal 2 by 2 block has been perturbed by a small number in SLALN2 to keep nonsingularity. NOTE: In the interests of speed, this routine does not check the inputs for errors. |