.TH "SRC/ssysv_rook.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/ssysv_rook.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBssysv_rook\fP (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)" .br .RI "\fB SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine ssysv_rook (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)" .PP \fB SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SSYSV_ROOK computes the solution to a real system of linear !> equations !> A * X = B, !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS !> matrices\&. !> !> The diagonal pivoting method is used to factor A as !> A = U * D * U**T, if UPLO = 'U', or !> A = L * D * L**T, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> SSYTRF_ROOK is called to compute the factorization of a real !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal !> pivoting method\&. !> !> The factored form of A is then used to solve the system !> of equations A * X = B by calling SSYTRS_ROOK\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \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 REAL array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> !> On exit, if INFO = 0, the block diagonal matrix D and the !> multipliers used to obtain the factor U or L from the !> factorization A = U*D*U**T or A = L*D*L**T as computed by !> SSYTRF_ROOK\&. !> .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) !> Details of the interchanges and the block structure of D, !> as determined by SSYTRF_ROOK\&. !> !> If UPLO = 'U': !> If IPIV(k) > 0, then rows and columns k and IPIV(k) !> were interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and !> columns k and -IPIV(k) were interchanged and rows and !> columns k-1 and -IPIV(k-1) were inerchaged, !> D(k-1:k,k-1:k) is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> If IPIV(k) > 0, then rows and columns k and IPIV(k) !> were interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and !> columns k and -IPIV(k) were interchanged and rows and !> columns k+1 and -IPIV(k+1) were inerchaged, !> D(k:k+1,k:k+1) is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is REAL array, dimension (LDB,NRHS) !> On entry, the N-by-NRHS right hand side matrix B\&. !> On exit, if INFO = 0, the N-by-NRHS solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .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 LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= 1, and for best performance !> LWORK >= max(1,N*NB), where NB is the optimal blocksize for !> SSYTRF_ROOK\&. !> !> TRS will be done with Level 2 BLAS !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size 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 = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D 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 \fBContributors:\fP .RS 4 .PP .nf !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> .fi .PP .RE .PP .PP Definition at line \fB202\fP of file \fBssysv_rook\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.