# zhet22.f - Man Page

TESTING/EIG/zhet22.f

## Synopsis

### Functions/Subroutines

subroutine **zhet22** (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, rwork, result)**ZHET22**

## Function/Subroutine Documentation

### subroutine zhet22 (integer itype, character uplo, integer n, integer m, integer kband, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result)

**ZHET22**

**Purpose:**

ZHET22 generally checks a decomposition of the form A U = U S where A is complex Hermitian, the columns of U are orthonormal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as a dense matrix, otherwise the U is expressed as a product of Householder transformations, whose vectors are stored in the array 'V' and whose scaling constants are in 'TAU'; we shall use the letter 'V' to refer to the product of Householder transformations (which should be equal to U). Specifically, if ITYPE=1, then: RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and RESULT(2) = | I - U**H U | / ( m ulp )

ITYPE INTEGER Specifies the type of tests to be performed. 1: U expressed as a dense orthogonal matrix: RESULT(1) = | A - U S U**H | / ( |A| n ulp ) *and RESULT(2) = | I - U U**H | / ( n ulp ) UPLO CHARACTER If UPLO='U', the upper triangle of A will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A will be used and the (strictly) upper triangle will not be referenced. Not modified. N INTEGER The size of the matrix. If it is zero, ZHET22 does nothing. It must be at least zero. Not modified. M INTEGER The number of columns of U. If it is zero, ZHET22 does nothing. It must be at least zero. Not modified. KBAND INTEGER The bandwidth of the matrix. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal. Not modified. A COMPLEX*16 array, dimension (LDA , N) The original (unfactored) matrix. It is assumed to be symmetric, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced. Not modified. LDA INTEGER The leading dimension of A. It must be at least 1 and at least N. Not modified. D DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix. Not modified. E DOUBLE PRECISION array, dimension (N) The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. Not referenced if KBAND=0. Not modified. U COMPLEX*16 array, dimension (LDU, N) If ITYPE=1, this contains the orthogonal matrix in the decomposition, expressed as a dense matrix. Not modified. LDU INTEGER The leading dimension of U. LDU must be at least N and at least 1. Not modified. V COMPLEX*16 array, dimension (LDV, N) If ITYPE=2 or 3, the lower triangle of this array contains the Householder vectors used to describe the orthogonal matrix in the decomposition. If ITYPE=1, then it is not referenced. Not modified. LDV INTEGER The leading dimension of V. LDV must be at least N and at least 1. Not modified. TAU COMPLEX*16 array, dimension (N) If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)**H in the Householder transformation H(j) of the product U = H(1)...H(n-2) If ITYPE < 2, then TAU is not referenced. Not modified. WORK COMPLEX*16 array, dimension (2*N**2) Workspace. Modified. RWORK DOUBLE PRECISION array, dimension (N) Workspace. Modified. RESULT DOUBLE PRECISION array, dimension (2) The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified. RESULT(2) is modified only if LDU is at least N. Modified.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **159** of file **zhet22.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhet22(3) is an alias of zhet22.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK