.TH DLAQTR 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLAQTR - the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE .SH SYNOPSIS .TP 19 SUBROUTINE DLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO ) .TP 19 .ti +4 LOGICAL LREAL, LTRAN .TP 19 .ti +4 INTEGER INFO, LDT, N .TP 19 .ti +4 DOUBLE PRECISION SCALE, W .TP 19 .ti +4 DOUBLE PRECISION B( * ), T( LDT, * ), WORK( * ), X( * ) .SH PURPOSE DLAQTR solves the real quasi-triangular system or the complex quasi-triangular systems .br op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE. in real arithmetic, where T is upper quasi-triangular. .br If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1, B is the specially structured matrix .br B = [ b(1) b(2) ... b(n) ] .br [ w ] .br [ w ] .br [ . ] .br [ w ] .br op(A) = A or A\(aq, A\(aq denotes the conjugate transpose of .br matrix A. .br On input, X = [ c ]. On output, X = [ p ]. .br [ d ] [ q ] .br This subroutine is designed for the condition number estimation in routine DTRSNA. .br .SH ARGUMENTS .TP 8 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)\(aq. .TP 8 LREAL (input) LOGICAL On entry, LREAL specifies the input matrix structure: = .FALSE., the input is complex = .TRUE., the input is real .TP 8 N (input) INTEGER On entry, N specifies the order of T+i*B. N >= 0. .TP 8 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. .TP 8 LDT (input) INTEGER The leading dimension of the matrix T. LDT >= max(1,N). .TP 8 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. .TP 8 W (input) DOUBLE PRECISION On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced. .TP 8 SCALE (output) DOUBLE PRECISION On exit, SCALE is the scale factor. .TP 8 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. .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER On exit, INFO is set to 0: successful exit. .br 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.