csgt01()

subroutine csgt01	(	integer	ITYPE,
		character	UPLO,
		integer	N,
		integer	M,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldz, * )	Z,
		integer	LDZ,
		real, dimension( * )	D,
		complex, dimension( * )	WORK,
		real, dimension( * )	RWORK,
		real, dimension( * )	RESULT
	)

CSGT01

Purpose:

 CSGT01 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

[in]	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
[in]	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
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	M	M is INTEGER The number of eigenvalues found. M >= 0.
[in]	A	A is COMPLEX array, dimension (LDA, N) The original Hermitian matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	B	B is COMPLEX array, dimension (LDB, N) The original Hermitian positive definite matrix B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]	Z	Z is COMPLEX array, dimension (LDZ, M) The computed eigenvectors of the generalized eigenproblem.
[in]	LDZ	LDZ is INTEGER The leading dimension of the array Z. LDZ >= max(1,N).
[in]	D	D is REAL array, dimension (M) The computed eigenvalues of the generalized eigenproblem.
[out]	WORK	WORK is COMPLEX array, dimension (N*N)
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESULT	RESULT is REAL array, dimension (1) The test ratio as described above.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.