# dlaqtr.f(3) [centos man page]

dlaqtr.f(3) LAPACK dlaqtr.f(3)NAME

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.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dlaqtr.f(3)

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DLAQTR(l)) DLAQTR(l)NAME

DLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUESYNOPSIS

SUBROUTINE DLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO ) LOGICAL LREAL, LTRAN INTEGER INFO, LDT, N DOUBLE PRECISION SCALE, W DOUBLE PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )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', A' denotes the conjugate 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.ARGUMENTS

LTRAN (input) 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)'. LREAL (input) LOGICAL On entry, LREAL specifies the input matrix structure: = .FALSE., the input is complex = .TRUE., the input is real N (input) INTEGER On entry, N specifies the order of T+i*B. N >= 0. T (input) 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 (input) INTEGER The leading dimension of the matrix T. LDT >= max(1,N). B (input) 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 (input) DOUBLE PRECISION On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced. SCALE (output) DOUBLE PRECISION On exit, SCALE is the scale factor. X (input/output) 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 (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) 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.LAPACK version 3.015 June 2000 DLAQTR(l)