Man page - laqtr(3)

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laqtr

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlaqtr (logical ltran, logical lreal, integer n, doubleprecision, dimension( ldt, * ) t, integer ldt, double precision,dimension( * ) b, double precision w, double precision scale, doubleprecision, dimension( * ) x, double precision, dimension( * ) work,integer info)
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, integerinfo)
Author

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, doubleprecision, dimension( ldt, * ) t, integer ldt, double precision,dimension( * ) b, double precision w, double precision scale, doubleprecision, 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, integerinfo)

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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