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.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 167 of file dlaqtr.f.
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