---
name: "zpst01.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zpst01.f"
---

# zpst01.f(3)

## NAME

TESTING/LIN/zpst01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zpst01** (uplo, n, a, lda, afac, ldafac, perm, ldperm, piv, rwork, resid, rank)\
 **ZPST01**

## Function/Subroutine Documentation

### subroutine zpst01 (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldafac, \* ) afac, integer ldafac, complex\*16, dimension( ldperm, \* ) perm, integer ldperm, integer, dimension( \* ) piv, double precision, dimension( \* ) rwork, double precision resid, integer rank)

**ZPST01**

**Purpose:**

```
!>
!> ZPST01 reconstructs an Hermitian positive semidefinite matrix A
!> from its L or U factors and the permutation matrix P and computes
!> the residual
!>    norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
!>    norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
!> where EPS is the machine epsilon, L' is the conjugate transpose of L,
!> and U' is the conjugate transpose of U.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The number of rows and columns of the matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The original Hermitian matrix A.
!>
```

*LDA*

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

*AFAC*

```
!>          AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
!>          The factor L or U from the L*L' or U'*U
!>          factorization of A.
!>
```

*LDAFAC*

```
!>          LDAFAC is INTEGER
!>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
!>
```

*PERM*

```
!>          PERM is COMPLEX*16 array, dimension (LDPERM,N)
!>          Overwritten with the reconstructed matrix, and then with the
!>          difference P*L*L'*P' - A (or P*U'*U*P' - A)
!>
```

*LDPERM*

```
!>          LDPERM is INTEGER
!>          The leading dimension of the array PERM.
!>          LDAPERM >= max(1,N).
!>
```

*PIV*

```
!>          PIV is INTEGER array, dimension (N)
!>          PIV is such that the nonzero entries are
!>          P( PIV( K ), K ) = 1.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>
```

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
!>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
!>
```

*RANK*

```
!>          RANK is INTEGER
!>          number of nonzero singular values of A.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **zpst01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.