.TH ZPOSV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME ZPOSV - the solution to a complex system of linear equations A * X = B, .SH SYNOPSIS .TP 18 SUBROUTINE ZPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) .TP 18 .ti +4 CHARACTER UPLO .TP 18 .ti +4 INTEGER INFO, LDA, LDB, N, NRHS .TP 18 .ti +4 COMPLEX*16 A( LDA, * ), B( LDB, * ) .SH PURPOSE ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. .br The Cholesky decomposition is used to factor A as .br A = U**H* U, if UPLO = \(aqU\(aq, or .br A = L * L**H, if UPLO = \(aqL\(aq, .br where U is an upper triangular matrix and L is a lower triangular matrix. 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) COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian 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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 B (input/output) COMPLEX*16 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 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.