- SUBROUTINE SLAQTR(
- LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )
- LOGICAL LREAL, LTRAN
- INTEGER INFO, LDT, N
- REAL SCALE, W
- REAL B( * ), T( LDT, * ), WORK( * ), X( * )
PURPOSESLAQTR solves the real quasi-triangular system 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', A' denotes the conjugate transpose of
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
This subroutine is designed for the condition number estimation in routine STRSNA.
- 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)'.
- 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.