# 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

Univ. of Colorado Denver

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