# zsgt01.f - Man Page

TESTING/EIG/zsgt01.f

## Synopsis

### Functions/Subroutines

subroutine zsgt01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work, rwork, result)
ZSGT01

## Function/Subroutine Documentation

### subroutine zsgt01 (integer itype, character uplo, integer n, integer m, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) d, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZSGT01

Purpose:

``` CDGT01 checks a decomposition of the form

A Z   =  B Z D or
A B Z =  Z D or
B A Z =  Z D

where A is a Hermitian matrix, B is Hermitian positive definite,
Z is unitary, and D is diagonal.

One of the following test ratios is computed:

ITYPE = 1:  RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )

ITYPE = 2:  RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )

ITYPE = 3:  RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )```
Parameters

ITYPE

```          ITYPE is INTEGER
The form of the Hermitian generalized eigenproblem.
= 1:  A*z = (lambda)*B*z
= 2:  A*B*z = (lambda)*z
= 3:  B*A*z = (lambda)*z```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrices A and B is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

M

```          M is INTEGER
The number of eigenvalues found.  M >= 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).```

B

```          B is COMPLEX*16 array, dimension (LDB, N)
The original Hermitian positive definite matrix B.```

LDB

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

Z

```          Z is COMPLEX*16 array, dimension (LDZ, M)
The computed eigenvectors of the generalized eigenproblem.```

LDZ

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

D

```          D is DOUBLE PRECISION array, dimension (M)
The computed eigenvalues of the generalized eigenproblem.```

WORK

`          WORK is COMPLEX*16 array, dimension (N*N)`

RWORK

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

RESULT

```          RESULT is DOUBLE PRECISION array, dimension (1)
The test ratio as described above.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 150 of file zsgt01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zsgt01(3) is an alias of zsgt01.f(3).

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