.TH "laqtr" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqtr \- laqtr: quasi-triangular solve .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdlaqtr\fP (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)" .br .RI "\fBDLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&. " .ti -1c .RI "subroutine \fBslaqtr\fP (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)" .br .RI "\fBSLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dlaqtr (logical ltran, logical lreal, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) b, double precision w, double precision scale, double precision, dimension( * ) x, double precision, dimension( * ) work, integer info)" .PP \fBDLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fILTRAN\fP .PP .nf 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\&. .fi .PP .br \fILREAL\fP .PP .nf LREAL is LOGICAL On entry, LREAL specifies the input matrix structure: = \&.FALSE\&., the input is complex = \&.TRUE\&., the input is real .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of T+i*B\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf 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\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the matrix T\&. LDT >= max(1,N)\&. .fi .PP .br \fIB\fP .PP .nf 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\&. .fi .PP .br \fIW\fP .PP .nf W is DOUBLE PRECISION On entry, W is the diagonal element of the matrix B\&. If LREAL = \&.TRUE\&., W is not referenced\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is DOUBLE PRECISION On exit, SCALE is the scale factor\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine slaqtr (logical ltran, logical lreal, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) b, real w, real scale, real, dimension( * ) x, real, dimension( * ) work, integer info)" .PP \fBSLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQTR 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 STRSNA\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fILTRAN\fP .PP .nf 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\&. .fi .PP .br \fILREAL\fP .PP .nf LREAL is LOGICAL On entry, LREAL specifies the input matrix structure: = \&.FALSE\&., the input is complex = \&.TRUE\&., the input is real .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of T+i*B\&. N >= 0\&. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,N) On entry, T contains a matrix in Schur canonical form\&. If LREAL = \&.FALSE\&., then the first diagonal block of T must be 1 by 1\&. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the matrix T\&. LDT >= max(1,N)\&. .fi .PP .br \fIB\fP .PP .nf B is REAL array, dimension (N) On entry, B contains the elements to form the matrix B as described above\&. If LREAL = \&.TRUE\&., B is not referenced\&. .fi .PP .br \fIW\fP .PP .nf W is REAL On entry, W is the diagonal element of the matrix B\&. If LREAL = \&.TRUE\&., W is not referenced\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is REAL On exit, SCALE is the scale factor\&. .fi .PP .br \fIX\fP .PP .nf X is REAL array, dimension (2*N) On entry, X contains the right hand side of the system\&. On exit, X is overwritten by the solution\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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 SLALN2 to keep nonsingularity\&. NOTE: In the interests of speed, this routine does not check the inputs for errors\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.