.TH "SRC/ssysv_rk.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/ssysv_rk.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBssysv_rk\fP (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, work, lwork, info)" .br .RI "\fB SSYSV_RK 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_rk (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)" .PP \fB SSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> SSYSV_RK 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 bounded Bunch-Kaufman (rook) diagonal pivoting method is used !> to factor A as !> A = P*U*D*(U**T)*(P**T), if UPLO = 'U', or !> A = P*L*D*(L**T)*(P**T), if UPLO = 'L', !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> SSYTRF_RK is called to compute the factorization of a real !> symmetric matrix\&. The factored form of A is then used to solve !> the system of equations A * X = B by calling BLAS3 routine SSYTRS_3\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = '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, diagonal of the block diagonal !> matrix D and factors U or L as computed by SSYTRF_RK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> are stored on exit in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> For more info see the description of DSYTRF_RK routine\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is REAL array, dimension (N) !> On exit, contains the output computed by the factorization !> routine DSYTRF_RK, i\&.e\&. the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; !> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is set to 0 in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> !> For more info see the description of DSYTRF_RK routine\&. !> .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_RK\&. !> !> For more info see the description of DSYTRF_RK routine\&. !> .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) )\&. !> Work array used in the factorization stage\&. !> 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\&. For best performance !> of factorization stage LWORK >= max(1,N*NB), where NB is !> the optimal blocksize for DSYTRF_RK\&. !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the WORK !> array for factorization stage, 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 !> !> > 0: If INFO = k, the matrix A is singular, because: !> If UPLO = 'U': column k in the upper !> triangular part of A contains all zeros\&. !> If UPLO = 'L': column k in the lower !> triangular part of A contains all zeros\&. !> !> Therefore D(k,k) is exactly zero, and superdiagonal !> elements of column k of U (or subdiagonal elements of !> column k of L ) are all zeros\&. The factorization has !> been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if !> it is used to solve a system of equations\&. !> !> NOTE: INFO only stores the first occurrence of !> a singularity, any subsequent occurrence of singularity !> is not stored in INFO even though the factorization !> always completes\&. !> .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 !> !> December 2016, 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 \fB226\fP of file \fBssysv_rk\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.