*> \brief \b CGET51 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER ITYPE, LDA, LDB, LDU, LDV, N * REAL RESULT * .. * .. Array Arguments .. * REAL RWORK( * ) * COMPLEX A( LDA, * ), B( LDB, * ), U( LDU, * ), * $ V( LDV, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGET51 generally checks a decomposition of the form *> *> A = U B VC> *> where * means conjugate transpose and U and V are unitary. *> *> Specifically, if ITYPE=1 *> *> RESULT = | A - U B V* | / ( |A| n ulp ) *> *> If ITYPE=2, then: *> *> RESULT = | A - B | / ( |A| n ulp ) *> *> If ITYPE=3, then: *> *> RESULT = | I - UU* | / ( n ulp ) *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> Specifies the type of tests to be performed. *> =1: RESULT = | A - U B V* | / ( |A| n ulp ) *> =2: RESULT = | A - B | / ( |A| n ulp ) *> =3: RESULT = | I - UU* | / ( n ulp ) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The size of the matrix. If it is zero, CGET51 does nothing. *> It must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA, N) *> The original (unfactored) matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of A. It must be at least 1 *> and at least N. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX array, dimension (LDB, N) *> The factored matrix. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of B. It must be at least 1 *> and at least N. *> \endverbatim *> *> \param[in] U *> \verbatim *> U is COMPLEX array, dimension (LDU, N) *> The unitary matrix on the left-hand side in the *> decomposition. *> Not referenced if ITYPE=2 *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of U. LDU must be at least N and *> at least 1. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is COMPLEX array, dimension (LDV, N) *> The unitary matrix on the left-hand side in the *> decomposition. *> Not referenced if ITYPE=2 *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of V. LDV must be at least N and *> at least 1. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (2*N**2) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL *> The values computed by the test specified by ITYPE. The *> value is currently limited to 1/ulp, to avoid overflow. *> Errors are flagged by RESULT=10/ulp. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2011 * *> \ingroup complex_eig * * ===================================================================== SUBROUTINE CGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, $ RWORK, RESULT ) * * -- LAPACK test routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. Scalar Arguments .. INTEGER ITYPE, LDA, LDB, LDU, LDV, N REAL RESULT * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX A( LDA, * ), B( LDB, * ), U( LDU, * ), $ V( LDV, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, TEN PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 10.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER JCOL, JDIAG, JROW REAL ANORM, ULP, UNFL, WNORM * .. * .. External Functions .. REAL CLANGE, SLAMCH EXTERNAL CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM, CLACPY * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Executable Statements .. * RESULT = ZERO IF( N.LE.0 ) $ RETURN * * Constants * UNFL = SLAMCH( 'Safe minimum' ) ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) * * Some Error Checks * IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN RESULT = TEN / ULP RETURN END IF * IF( ITYPE.LE.2 ) THEN * * Tests scaled by the norm(A) * ANORM = MAX( CLANGE( '1', N, N, A, LDA, RWORK ), UNFL ) * IF( ITYPE.EQ.1 ) THEN * * ITYPE=1: Compute W = A - UBV' * CALL CLACPY( ' ', N, N, A, LDA, WORK, N ) CALL CGEMM( 'N', 'N', N, N, N, CONE, U, LDU, B, LDB, CZERO, $ WORK( N**2+1 ), N ) * CALL CGEMM( 'N', 'C', N, N, N, -CONE, WORK( N**2+1 ), N, V, $ LDV, CONE, WORK, N ) * ELSE * * ITYPE=2: Compute W = A - B * CALL CLACPY( ' ', N, N, B, LDB, WORK, N ) * DO 20 JCOL = 1, N DO 10 JROW = 1, N WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) ) $ - A( JROW, JCOL ) 10 CONTINUE 20 CONTINUE END IF * * Compute norm(W)/ ( ulp*norm(A) ) * WNORM = CLANGE( '1', N, N, WORK, N, RWORK ) * IF( ANORM.GT.WNORM ) THEN RESULT = ( WNORM / ANORM ) / ( N*ULP ) ELSE IF( ANORM.LT.ONE ) THEN RESULT = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP ) ELSE RESULT = MIN( WNORM / ANORM, REAL( N ) ) / ( N*ULP ) END IF END IF * ELSE * * Tests not scaled by norm(A) * * ITYPE=3: Compute UU' - I * CALL CGEMM( 'N', 'C', N, N, N, CONE, U, LDU, U, LDU, CZERO, $ WORK, N ) * DO 30 JDIAG = 1, N WORK( ( N+1 )*( JDIAG-1 )+1 ) = WORK( ( N+1 )*( JDIAG-1 )+ $ 1 ) - CONE 30 CONTINUE * RESULT = MIN( CLANGE( '1', N, N, WORK, N, RWORK ), $ REAL( N ) ) / ( N*ULP ) END IF * RETURN * * End of CGET51 * END