dlaqtr-f(3)

dlaqtr.f –

Synopsis

Functions/Subroutines

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.

Function/Subroutine Documentation

subroutine dlaqtr (logicalLTRAN, logicalLREAL, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( * )B, double precisionW, double precisionSCALE, double precision, dimension( * )X, double precision, dimension( * )WORK, integerINFO)

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 is INTEGER
 On entry, N specifies the order of T+i*B. N >= 0.

 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 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 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 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.

Date:

September 2012

Definition at line 165 of file dlaqtr.f.

Author

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