# zhet01_3.f - Man Page

TESTING/LIN/zhet01_3.f

## Synopsis

### Functions/Subroutines

subroutine zhet01_3 (uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc, rwork, resid)
ZHET01_3

## Function/Subroutine Documentation

### subroutine zhet01_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldafac, * ) afac, integer ldafac, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) rwork, double precision resid)

ZHET01_3

Purpose:

``` ZHET01_3 reconstructs a Hermitian indefinite matrix A from its
block L*D*L' or U*D*U' factorization computed by ZHETRF_RK
(or ZHETRF_BK) and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.```
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)
Diagonal of the block diagonal matrix D and factors U or L
as computed by ZHETRF_RK and ZHETRF_BK:
a) ONLY diagonal elements of the Hermitian block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = 'U': factor U in the superdiagonal part of A.
If UPLO = 'L': factor L in the subdiagonal part of A.```

LDAFAC

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

E

```          E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the Hermitian block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices from ZHETRF_RK (or ZHETRF_BK).```

C

`          C is COMPLEX*16 array, dimension (LDC,N)`

LDC

```          LDC is INTEGER
The leading dimension of the array C.  LDC >= max(1,N).```

RWORK

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

RESID

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 139 of file zhet01_3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhet01_3(3) is an alias of zhet01_3.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK