SUBROUTINE ZGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, \$ RWORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER ITYPE, LDA, LDB, LDU, LDV, N DOUBLE PRECISION RESULT * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), U( LDU, * ), \$ V( LDV, * ), WORK( * ) * .. * * Purpose * ======= * * ZGET51 generally checks a decomposition of the form * * A = U B V* * * 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 ) * * Arguments * ========= * * ITYPE (input) 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 ) * * N (input) INTEGER * The size of the matrix. If it is zero, ZGET51 does nothing. * It must be at least zero. * * A (input) COMPLEX*16 array, dimension (LDA, N) * The original (unfactored) matrix. * * LDA (input) INTEGER * The leading dimension of A. It must be at least 1 * and at least N. * * B (input) COMPLEX*16 array, dimension (LDB, N) * The factored matrix. * * LDB (input) INTEGER * The leading dimension of B. It must be at least 1 * and at least N. * * U (input) COMPLEX*16 array, dimension (LDU, N) * The unitary matrix on the left-hand side in the * decomposition. * Not referenced if ITYPE=2 * * LDU (input) INTEGER * The leading dimension of U. LDU must be at least N and * at least 1. * * V (input) COMPLEX*16 array, dimension (LDV, N) * The unitary matrix on the left-hand side in the * decomposition. * Not referenced if ITYPE=2 * * LDV (input) INTEGER * The leading dimension of V. LDV must be at least N and * at least 1. * * WORK (workspace) COMPLEX*16 array, dimension (2*N**2) * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESULT (output) DOUBLE PRECISION * 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. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TEN PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 10.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), \$ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER JCOL, JDIAG, JROW DOUBLE PRECISION ANORM, ULP, UNFL, WNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE EXTERNAL DLAMCH, ZLANGE * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZLACPY * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * RESULT = ZERO IF( N.LE.0 ) \$ RETURN * * Constants * UNFL = DLAMCH( 'Safe minimum' ) ULP = DLAMCH( 'Epsilon' )*DLAMCH( '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( ZLANGE( '1', N, N, A, LDA, RWORK ), UNFL ) * IF( ITYPE.EQ.1 ) THEN * * ITYPE=1: Compute W = A - UBV' * CALL ZLACPY( ' ', N, N, A, LDA, WORK, N ) CALL ZGEMM( 'N', 'N', N, N, N, CONE, U, LDU, B, LDB, CZERO, \$ WORK( N**2+1 ), N ) * CALL ZGEMM( 'N', 'C', N, N, N, -CONE, WORK( N**2+1 ), N, V, \$ LDV, CONE, WORK, N ) * ELSE * * ITYPE=2: Compute W = A - B * CALL ZLACPY( ' ', 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 = ZLANGE( '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, DBLE( N ) ) / ( N*ULP ) END IF END IF * ELSE * * Tests not scaled by norm(A) * * ITYPE=3: Compute UU' - I * CALL ZGEMM( '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( ZLANGE( '1', N, N, WORK, N, RWORK ), \$ DBLE( N ) ) / ( N*ULP ) END IF * RETURN * * End of ZGET51 * END