zsgt01.f - Man Page

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

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 150 of file zsgt01.f.