# zposv.f - Man Page

SRC/zposv.f

## Synopsis

### Functions/Subroutines

subroutine **zposv** (uplo, n, nrhs, a, lda, b, ldb, info)

**ZPOSV computes the solution to system of linear equations A * X = B for PO matrices**

## Function/Subroutine Documentation

### subroutine zposv (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

**ZPOSV computes the solution to system of linear equations A * X = B for PO matrices**

**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. The Cholesky decomposition is used to factor A as A = U**H* U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', 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.

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian 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 factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*B*B is 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.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **129** of file **zposv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zposv(3) is an alias of zposv.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK