---
name: "chpsv"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/chpsv/3lapack"
---

# chpsv(3lapack)

computes the solution to a complex system of linear equations A \* X = B,

## NAME

CHPSV - computes the solution to a complex system of linear equations  A \* X = B,

## SYNOPSIS

- SUBROUTINE CHPSV(

  UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDB, N, NRHS

- INTEGER

  IPIV( \* )

- COMPLEX

  AP( \* ), B( LDB, \* )

## PURPOSE

CHPSV computes the solution to a complex system of linear equations\
    A \* X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices.\
 The diagonal pivoting method is used to factor A as\
\
    A = U \* D \* U\*\*H,  if UPLO = 'U', or\
\
    A = L \* D \* L\*\*H,  if UPLO = 'L',\
 where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian 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.\

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

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

- NRHS (input) INTEGER

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

- AP (input/output) COMPLEX 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 = 'U', AP(i + (j-1)\*j/2) = A(i,j) for 1\<=i\<=j; if UPLO = 'L', AP(i + (j-1)\*(2n-j)/2) = A(i,j) for j\<=i\<=n. See below for further details. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U\*D\*U\*\*H or A = L\*D\*L\*\*H as computed by CHPTRF, stored as a packed triangular matrix in the same storage format as A.

- IPIV (output) INTEGER array, dimension (N)

  Details of the interchanges and the block structure of D, as determined by CHPTRF.  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 = 'U' 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 = 'L' 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.

- B (input/output) COMPLEX 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 (input) INTEGER

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

- INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 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.

## FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':\
 Two-dimensional storage of the Hermitian matrix A:\
\
    a11 a12 a13 a14\
\
        a22 a23 a24\
\
            a33 a34     (aij = conjg(aji))\
\
                a44\
 Packed storage of the upper triangle of A:\
 AP = \[ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 \]