.TH "SRC/dsgesv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/dsgesv.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdsgesv\fP (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info)" .br .RI "\fB DSGESV computes the solution to system of linear equations A * X = B for GE matrices\fP (mixed precision with iterative refinement) " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine dsgesv (integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * ) work, real, dimension( * ) swork, integer iter, integer info)" .PP \fB DSGESV computes the solution to system of linear equations A * X = B for GE matrices\fP (mixed precision with iterative refinement) .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DSGESV computes the solution to a real system of linear equations !> A * X = B, !> where A is an N-by-N matrix and X and B are N-by-NRHS matrices\&. !> !> DSGESV first attempts to factorize the matrix in SINGLE PRECISION !> and use this factorization within an iterative refinement procedure !> to produce a solution with DOUBLE PRECISION normwise backward error !> quality (see below)\&. If the approach fails the method switches to a !> DOUBLE PRECISION factorization and solve\&. !> !> The iterative refinement is not going to be a winning strategy if !> the ratio SINGLE PRECISION performance over DOUBLE PRECISION !> performance is too small\&. A reasonable strategy should take the !> number of right-hand sides and the size of the matrix into account\&. !> This might be done with a call to ILAENV in the future\&. Up to now, we !> always try iterative refinement\&. !> !> The iterative refinement process is stopped if !> ITER > ITERMAX !> or for all the RHS we have: !> RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX !> where !> o ITER is the number of the current iteration in the iterative !> refinement process !> o RNRM is the infinity-norm of the residual !> o XNRM is the infinity-norm of the solution !> o ANRM is the infinity-operator-norm of the matrix A !> o EPS is the machine epsilon returned by DLAMCH('Epsilon') !> The value ITERMAX and BWDMAX are fixed to 30 and 1\&.0D+00 !> respectively\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The number of linear equations, i\&.e\&., the order of the !> matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, !> dimension (LDA,N) !> On entry, the N-by-N coefficient matrix A\&. !> On exit, if iterative refinement has been successfully used !> (INFO = 0 and ITER >= 0, see description below), then A is !> unchanged, if double precision factorization has been used !> (INFO = 0 and ITER < 0, see description below), then the !> array A contains the factors L and U from the factorization !> A = P*L*U; the unit diagonal elements of L are not stored\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices that define the permutation matrix P; !> row i of the matrix was interchanged with row IPIV(i)\&. !> Corresponds either to the single precision factorization !> (if INFO = 0 and ITER >= 0) or the double precision !> factorization (if INFO = 0 and ITER < 0)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> The N-by-NRHS right hand side matrix B\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is DOUBLE PRECISION array, dimension (LDX,NRHS) !> If INFO = 0, the N-by-NRHS 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 \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (N,NRHS) !> This array is used to hold the residual vectors\&. !> .fi .PP .br \fISWORK\fP .PP .nf !> SWORK is REAL array, dimension (N*(N+NRHS)) !> This array is used to use the single precision matrix and the !> right-hand sides or solutions in single precision\&. !> .fi .PP .br \fIITER\fP .PP .nf !> ITER is INTEGER !> < 0: iterative refinement has failed, double precision !> factorization has been performed !> -1 : the routine fell back to full precision for !> implementation- or machine-specific reasons !> -2 : narrowing the precision induced an overflow, !> the routine fell back to full precision !> -3 : failure of SGETRF !> -31: stop the iterative refinement after the 30th !> iterations !> > 0: iterative refinement has been successfully used\&. !> Returns the number of iterations !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is !> exactly zero\&. The factorization has been completed, !> but the factor U is exactly singular, so the solution !> could not be computed\&. !> .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 .PP Definition at line \fB193\fP of file \fBdsgesv\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.