SLAQTR(3F) SLAQTR(3F)
SLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if
LREAL = .TRUE
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( * )
SLAQTR 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
matrix A.
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
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SLAQTR(3F) SLAQTR(3F)
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.
SLAQTR(3F) SLAQTR(3F)
SLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if
LREAL = .TRUE
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( * )
SLAQTR 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
matrix A.
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
Page 1
SLAQTR(3F) SLAQTR(3F)
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.
PPPPaaaaggggeeee 2222 [ Back ]
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