.TH ZPPSV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME ZPPSV - the solution to a complex system of linear equations A * X = B, .SH SYNOPSIS .TP 18 SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) .TP 18 .ti +4 CHARACTER UPLO .TP 18 .ti +4 INTEGER INFO, LDB, N, NRHS .TP 18 .ti +4 COMPLEX*16 AP( * ), B( LDB, * ) .SH PURPOSE ZPPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format 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 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. .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. .SH FURTHER DETAILS The packed storage scheme is illustrated by the following example when N = 4, UPLO = \(aqU\(aq: .br Two-dimensional storage of the Hermitian matrix A: .br a11 a12 a13 a14 .br a22 a23 a24 .br a33 a34 (aij = conjg(aji)) .br a44 .br Packed storage of the upper triangle of A: .br AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]