.TH "SRC/clatrs3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/clatrs3.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBclatrs3\fP (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)" .br .RI "\fBCLATRS3\fP solves a triangular system of equations with the scale factors set to prevent overflow\&. " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine clatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) scale, real, dimension( * ) cnorm, real, dimension( * ) work, integer lwork, integer info)" .PP \fBCLATRS3\fP solves a triangular system of equations with the scale factors set to prevent overflow\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CLATRS3 solves one of the triangular systems !> !> A * X = B * diag(scale), A**T * X = B * diag(scale), or !> A**H * X = B * diag(scale) !> !> with scaling to prevent overflow\&. Here A is an upper or lower !> triangular matrix, A**T denotes the transpose of A, A**H denotes the !> conjugate transpose of A\&. X and B are n-by-nrhs matrices and scale !> is an nrhs-element vector of scaling factors\&. A scaling factor scale(j) !> is usually less than or equal to 1, chosen such that X(:,j) is less !> than the overflow threshold\&. If the matrix A is singular (A(j,j) = 0 !> for some j), then a non-trivial solution to A*X = 0 is returned\&. If !> the system is so badly scaled that the solution cannot be represented !> as (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned\&. !> !> This is a BLAS-3 version of LATRS for solving several right !> hand sides simultaneously\&. !> !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the matrix A is upper or lower triangular\&. !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fITRANS\fP .PP .nf !> TRANS is CHARACTER*1 !> Specifies the operation applied to A\&. !> = 'N': Solve A * x = s*b (No transpose) !> = 'T': Solve A**T* x = s*b (Transpose) !> = 'C': Solve A**T* x = s*b (Conjugate transpose) !> .fi .PP .br \fIDIAG\fP .PP .nf !> DIAG is CHARACTER*1 !> Specifies whether or not the matrix A is unit triangular\&. !> = 'N': Non-unit triangular !> = 'U': Unit triangular !> .fi .PP .br \fINORMIN\fP .PP .nf !> NORMIN is CHARACTER*1 !> Specifies whether CNORM has been set or not\&. !> = 'Y': CNORM contains the column norms on entry !> = 'N': CNORM is not set on entry\&. On exit, the norms will !> be computed and stored in CNORM\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of columns of X\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> The triangular matrix A\&. If UPLO = 'U', the leading n by n !> upper triangular part of the array A contains the upper !> triangular matrix, and the strictly lower triangular part of !> A is not referenced\&. If UPLO = 'L', the leading n by n lower !> triangular part of the array A contains the lower triangular !> matrix, and the strictly upper triangular part of A is not !> referenced\&. If DIAG = 'U', the diagonal elements of A are !> also not referenced and are assumed to be 1\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max (1,N)\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is COMPLEX array, dimension (LDX,NRHS) !> On entry, the right hand side B of the triangular system\&. !> On exit, X is overwritten by the solution matrix X\&. !> .fi .PP .br \fILDX\fP .PP .nf !> LDX is INTEGER !> The leading dimension of the array X\&. LDX >= max (1,N)\&. !> .fi .PP .br \fISCALE\fP .PP .nf !> SCALE is REAL array, dimension (NRHS) !> The scaling factor s(k) is for the triangular system !> A * x(:,k) = s(k)*b(:,k) or A**T* x(:,k) = s(k)*b(:,k)\&. !> If SCALE = 0, the matrix A is singular or badly scaled\&. !> If A(j,j) = 0 is encountered, a non-trivial vector x(:,k) !> that is an exact or approximate solution to A*x(:,k) = 0 !> is returned\&. If the system so badly scaled that solution !> cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0 !> is returned\&. !> .fi .PP .br \fICNORM\fP .PP .nf !> CNORM is REAL array, dimension (N) !> !> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) !> contains the norm of the off-diagonal part of the j-th column !> of A\&. If TRANS = 'N', CNORM(j) must be greater than or equal !> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) !> must be greater than or equal to the 1-norm\&. !> !> If NORMIN = 'N', CNORM is an output argument and CNORM(j) !> returns the 1-norm of the offdiagonal part of the j-th column !> of A\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal size of !> WORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The dimension of the array WORK\&. !> !> If MIN(N,NRHS) = 0, LWORK >= 1, else !> LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where !> NBA = (N + NB - 1)/NB and NB is the optimal block size\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal dimensions of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> .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 \fBFurther Details:\fP .RS 4 .RE .PP .PP Definition at line \fB233\fP of file \fBclatrs3\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.