Provided by: liblapack-doc_3.12.0-3build1.1_all 
NAME
laqtr - laqtr: quasi-triangular solve
SYNOPSIS
Functions
subroutine dlaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of
special form, in real arithmetic.
subroutine slaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of
special form, in real arithmetic.
Detailed Description
Function Documentation
subroutine dlaqtr (logical ltran, logical lreal, integer n, double precision, dimension( ldt, * ) t, integer
ldt, double precision, dimension( * ) b, double precision w, double precision scale, double precision,
dimension( * ) x, double precision, dimension( * ) work, integer info)
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of
special form, in real arithmetic.
Purpose:
DLAQTR 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 DTRSNA.
Parameters
LTRAN
LTRAN is 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
LREAL is LOGICAL
On entry, LREAL specifies the input matrix structure:
= .FALSE., the input is complex
= .TRUE., the input is real
N
N is INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
T
T is DOUBLE PRECISION array, dimension (LDT,N)
On entry, T contains a matrix in Schur canonical form.
If LREAL = .FALSE., then the first diagonal block of T mu
be 1 by 1.
LDT
LDT is INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
B
B is DOUBLE PRECISION 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
W is DOUBLE PRECISION
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced.
SCALE
SCALE is DOUBLE PRECISION
On exit, SCALE is the scale factor.
X
X is DOUBLE PRECISION array, dimension (2*N)
On entry, X contains the right hand side of the system.
On exit, X is overwritten by the solution.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is 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 DLALN2 to keep nonsingularity.
NOTE: In the interests of speed, this routine does not
check the inputs for errors.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine slaqtr (logical ltran, logical lreal, integer n, real, dimension( ldt, * ) t, integer ldt, real,
dimension( * ) b, real w, real scale, real, dimension( * ) x, real, dimension( * ) work, integer info)
SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of
special form, in real arithmetic.
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.
Parameters
LTRAN
LTRAN is 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
LREAL is LOGICAL
On entry, LREAL specifies the input matrix structure:
= .FALSE., the input is complex
= .TRUE., the input is real
N
N is INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
T
T is 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
LDT is INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
B
B is 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
W is REAL
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced.
SCALE
SCALE is REAL
On exit, SCALE is the scale factor.
X
X is 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
WORK is REAL array, dimension (N)
INFO
INFO is 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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Version 3.12.0 Fri Aug 9 2024 02:33:22 laqtr(3)