.TH SSYSV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME SSYSV - the solution to a real system of linear equations A * X = B, .SH SYNOPSIS .TP 18 SUBROUTINE SSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO ) .TP 18 .ti +4 CHARACTER UPLO .TP 18 .ti +4 INTEGER INFO, LDA, LDB, LWORK, N, NRHS .TP 18 .ti +4 INTEGER IPIV( * ) .TP 18 .ti +4 REAL A( LDA, * ), B( LDB, * ), WORK( * ) .SH PURPOSE SSYSV 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. .br The diagonal pivoting method is used to factor A as .br A = U * D * U**T, if UPLO = \(aqU\(aq, or .br A = L * D * L**T, if UPLO = \(aqL\(aq, .br 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. The factored form of A is then used to solve the system of equations A * X = B. .br .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. .TP 8 NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. .TP 8 A (input/output) REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = \(aqU\(aq, 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 = \(aqL\(aq, 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 IPIV (output) INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by SSYTRF. 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 UPLO = \(aqU\(aq and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = \(aqL\(aq and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. .TP 8 B (input/output) 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. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. .TP 8 LWORK (input) INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for SSYTRF. 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 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.