SSGT01 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 symmetric matrix, B is


 symmetric positive definite, Z is orthogonal, 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 )

ITYPE

          ITYPE is INTEGER


          The form of the symmetric 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


          symmetric 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.  0 <= M <= N.

A

          A is REAL array, dimension (LDA, N)


          The original symmetric matrix A.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

B

          B is REAL array, dimension (LDB, N)


          The original symmetric positive definite matrix B.

LDB

          LDB is INTEGER


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

Z

          Z is REAL 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 REAL array, dimension (M)


          The computed eigenvalues of the generalized eigenproblem.

WORK

          WORK is REAL array, dimension (N*N)

RESULT

          RESULT is REAL array, dimension (1)


          The test ratio as described above.

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