|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 |
SUBROUTINE CUNT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK,
$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER ROWCOL INTEGER LDU, LWORK, M, N REAL RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX U( LDU, * ), WORK( * ) * .. * * Purpose * ======= * * CUNT01 checks that the matrix U is unitary by computing the ratio * * RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R', * or * RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'. * * Alternatively, if there isn't sufficient workspace to form * I - U*U' or I - U'*U, the ratio is computed as * * RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R', * or * RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'. * * where EPS is the machine precision. ROWCOL is used only if m = n; * if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is * assumed to be 'R'. * * Arguments * ========= * * ROWCOL (input) CHARACTER * Specifies whether the rows or columns of U should be checked * for orthogonality. Used only if M = N. * = 'R': Check for orthogonal rows of U * = 'C': Check for orthogonal columns of U * * M (input) INTEGER * The number of rows of the matrix U. * * N (input) INTEGER * The number of columns of the matrix U. * * U (input) COMPLEX array, dimension (LDU,N) * The unitary matrix U. U is checked for orthogonal columns * if m > n or if m = n and ROWCOL = 'C'. U is checked for * orthogonal rows if m < n or if m = n and ROWCOL = 'R'. * * LDU (input) INTEGER * The leading dimension of the array U. LDU >= max(1,M). * * WORK (workspace) COMPLEX array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. For best performance, LWORK * should be at least N*N if ROWCOL = 'C' or M*M if * ROWCOL = 'R', but the test will be done even if LWORK is 0. * * RWORK (workspace) REAL array, dimension (min(M,N)) * Used only if LWORK is large enough to use the Level 3 BLAS * code. * * RESID (output) REAL * RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or * RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. CHARACTER TRANSU INTEGER I, J, K, LDWORK, MNMIN REAL EPS COMPLEX TMP, ZDUM * .. * .. External Functions .. LOGICAL LSAME REAL CLANSY, SLAMCH COMPLEX CDOTC EXTERNAL LSAME, CLANSY, SLAMCH, CDOTC * .. * .. External Subroutines .. EXTERNAL CHERK, CLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, CMPLX, MAX, MIN, REAL * .. * .. Statement Functions .. REAL CABS1 * .. * .. Statement Function definitions .. CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) * .. * .. Executable Statements .. * RESID = ZERO * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * EPS = SLAMCH( 'Precision' ) IF( M.LT.N .OR. ( M.EQ.N .AND. LSAME( ROWCOL, 'R' ) ) ) THEN TRANSU = 'N' K = N ELSE TRANSU = 'C' K = M END IF MNMIN = MIN( M, N ) * IF( ( MNMIN+1 )*MNMIN.LE.LWORK ) THEN LDWORK = MNMIN ELSE LDWORK = 0 END IF IF( LDWORK.GT.0 ) THEN * * Compute I - U*U' or I - U'*U. * CALL CLASET( 'Upper', MNMIN, MNMIN, CMPLX( ZERO ), $ CMPLX( ONE ), WORK, LDWORK ) CALL CHERK( 'Upper', TRANSU, MNMIN, K, -ONE, U, LDU, ONE, WORK, $ LDWORK ) * * Compute norm( I - U*U' ) / ( K * EPS ) . * RESID = CLANSY( '1', 'Upper', MNMIN, WORK, LDWORK, RWORK ) RESID = ( RESID / REAL( K ) ) / EPS ELSE IF( TRANSU.EQ.'C' ) THEN * * Find the maximum element in abs( I - U'*U ) / ( m * EPS ) * DO 20 J = 1, N DO 10 I = 1, J IF( I.NE.J ) THEN TMP = ZERO ELSE TMP = ONE END IF TMP = TMP - CDOTC( M, U( 1, I ), 1, U( 1, J ), 1 ) RESID = MAX( RESID, CABS1( TMP ) ) 10 CONTINUE 20 CONTINUE RESID = ( RESID / REAL( M ) ) / EPS ELSE * * Find the maximum element in abs( I - U*U' ) / ( n * EPS ) * DO 40 J = 1, M DO 30 I = 1, J IF( I.NE.J ) THEN TMP = ZERO ELSE TMP = ONE END IF TMP = TMP - CDOTC( N, U( J, 1 ), LDU, U( I, 1 ), LDU ) RESID = MAX( RESID, CABS1( TMP ) ) 30 CONTINUE 40 CONTINUE RESID = ( RESID / REAL( N ) ) / EPS END IF RETURN * * End of CUNT01 * END |