DLAQTR (3) Linux Manual Page

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

 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.

Date:

September 2012

Definition at line 165 of file dlaqtr.f.

Author

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