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SUBROUTINE ZSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
$ WORK, RWORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * modified August 1997, a new parameter M is added to the calling * sequence. * * .. Scalar Arguments .. CHARACTER UPLO INTEGER ITYPE, LDA, LDB, LDZ, M, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), RESULT( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), $ Z( LDZ, * ) * .. * * 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 ) * * Arguments * ========= * * ITYPE (input) 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 (input) 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 (input) INTEGER * The order of the matrix A. N >= 0. * * M (input) INTEGER * The number of eigenvalues found. M >= 0. * * A (input) COMPLEX*16 array, dimension (LDA, N) * The original Hermitian matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * B (input) COMPLEX*16 array, dimension (LDB, N) * The original Hermitian positive definite matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * Z (input) COMPLEX*16 array, dimension (LDZ, M) * The computed eigenvectors of the generalized eigenproblem. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= max(1,N). * * D (input) DOUBLE PRECISION array, dimension (M) * The computed eigenvalues of the generalized eigenproblem. * * WORK (workspace) COMPLEX*16 array, dimension (N*N) * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESULT (output) DOUBLE PRECISION array, dimension (1) * The test ratio as described above. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION ANORM, ULP * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHE EXTERNAL DLAMCH, ZLANGE, ZLANHE * .. * .. External Subroutines .. EXTERNAL ZDSCAL, ZHEMM * .. * .. Executable Statements .. * RESULT( 1 ) = ZERO IF( N.LE.0 ) $ RETURN * ULP = DLAMCH( 'Epsilon' ) * * Compute product of 1-norms of A and Z. * ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )* $ ZLANGE( '1', N, M, Z, LDZ, RWORK ) IF( ANORM.EQ.ZERO ) $ ANORM = ONE * IF( ITYPE.EQ.1 ) THEN * * Norm of AZ - BZD * CALL ZHEMM( 'Left', UPLO, N, M, CONE, A, LDA, Z, LDZ, CZERO, $ WORK, N ) DO 10 I = 1, M CALL ZDSCAL( N, D( I ), Z( 1, I ), 1 ) 10 CONTINUE CALL ZHEMM( 'Left', UPLO, N, M, CONE, B, LDB, Z, LDZ, -CONE, $ WORK, N ) * RESULT( 1 ) = ( ZLANGE( '1', N, M, WORK, N, RWORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.2 ) THEN * * Norm of ABZ - ZD * CALL ZHEMM( 'Left', UPLO, N, M, CONE, B, LDB, Z, LDZ, CZERO, $ WORK, N ) DO 20 I = 1, M CALL ZDSCAL( N, D( I ), Z( 1, I ), 1 ) 20 CONTINUE CALL ZHEMM( 'Left', UPLO, N, M, CONE, A, LDA, WORK, N, -CONE, $ Z, LDZ ) * RESULT( 1 ) = ( ZLANGE( '1', N, M, Z, LDZ, RWORK ) / ANORM ) / $ ( N*ULP ) * ELSE IF( ITYPE.EQ.3 ) THEN * * Norm of BAZ - ZD * CALL ZHEMM( 'Left', UPLO, N, M, CONE, A, LDA, Z, LDZ, CZERO, $ WORK, N ) DO 30 I = 1, M CALL ZDSCAL( N, D( I ), Z( 1, I ), 1 ) 30 CONTINUE CALL ZHEMM( 'Left', UPLO, N, M, CONE, B, LDB, WORK, N, -CONE, $ Z, LDZ ) * RESULT( 1 ) = ( ZLANGE( '1', N, M, Z, LDZ, RWORK ) / ANORM ) / $ ( N*ULP ) END IF * RETURN * * End of CDGT01 * END |