# chpsv.f man page

chpsv.f

## Synopsis

### Functions/Subroutines

subroutine chpsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices

## Function/Subroutine Documentation

### subroutine chpsv (character UPLO, integer N, integer NRHS, complex, dimension( * ) AP, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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.```
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.```

AP

```          AP is 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

```          IPIV is 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

```          B is 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

```          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, 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.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

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 ]```

Definition at line 164 of file chpsv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK