|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 |
SUBROUTINE CLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
$ LDV, T, LDT, C, LDC, WORK, LDWORK ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * ) * .. * * Purpose * ======= * * CLARZB applies a complex block reflector H or its transpose H**H * to a complex distributed M-by-N C from the left or the right. * * Currently, only STOREV = 'R' and DIRECT = 'B' are supported. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': apply H or H**H from the Left * = 'R': apply H or H**H from the Right * * TRANS (input) CHARACTER*1 * = 'N': apply H (No transpose) * = 'C': apply H**H (Conjugate transpose) * * DIRECT (input) CHARACTER*1 * Indicates how H is formed from a product of elementary * reflectors * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) * = 'B': H = H(k) . . . H(2) H(1) (Backward) * * STOREV (input) CHARACTER*1 * Indicates how the vectors which define the elementary * reflectors are stored: * = 'C': Columnwise (not supported yet) * = 'R': Rowwise * * M (input) INTEGER * The number of rows of the matrix C. * * N (input) INTEGER * The number of columns of the matrix C. * * K (input) INTEGER * The order of the matrix T (= the number of elementary * reflectors whose product defines the block reflector). * * L (input) INTEGER * The number of columns of the matrix V containing the * meaningful part of the Householder reflectors. * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. * * V (input) COMPLEX array, dimension (LDV,NV). * If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. * * LDV (input) INTEGER * The leading dimension of the array V. * If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K. * * T (input) COMPLEX array, dimension (LDT,K) * The triangular K-by-K matrix T in the representation of the * block reflector. * * LDT (input) INTEGER * The leading dimension of the array T. LDT >= K. * * C (input/output) COMPLEX array, dimension (LDC,N) * On entry, the M-by-N matrix C. * On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * WORK (workspace) COMPLEX array, dimension (LDWORK,K) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. * If SIDE = 'L', LDWORK >= max(1,N); * if SIDE = 'R', LDWORK >= max(1,M). * * Further Details * =============== * * Based on contributions by * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. CHARACTER TRANST INTEGER I, INFO, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CCOPY, CGEMM, CLACGV, CTRMM, XERBLA * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * * Check for currently supported options * INFO = 0 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN INFO = -3 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CLARZB', -INFO ) RETURN END IF * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**H * C * * W( 1:n, 1:k ) = C( 1:k, 1:n )**H * DO 10 J = 1, K CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE * * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ... * C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T * IF( L.GT.0 ) $ CALL CGEMM( 'Transpose', 'Conjugate transpose', N, K, L, $ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, $ LDWORK ) * * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T * CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T, $ LDT, WORK, LDWORK ) * * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H * DO 30 J = 1, N DO 20 I = 1, K C( I, J ) = C( I, J ) - WORK( J, I ) 20 CONTINUE 30 CONTINUE * * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... * V( 1:k, 1:l )**H * W( 1:n, 1:k )**H * IF( L.GT.0 ) $ CALL CGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV, $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC ) * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**H * * W( 1:m, 1:k ) = C( 1:m, 1:k ) * DO 40 J = 1, K CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE * * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ... * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H * IF( L.GT.0 ) $ CALL CGEMM( 'No transpose', 'Transpose', M, K, L, ONE, $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK ) * * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or * W( 1:m, 1:k ) * T**H * DO 50 J = 1, K CALL CLACGV( K-J+1, T( J, J ), 1 ) 50 CONTINUE CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T, $ LDT, WORK, LDWORK ) DO 60 J = 1, K CALL CLACGV( K-J+1, T( J, J ), 1 ) 60 CONTINUE * * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k ) * DO 80 J = 1, K DO 70 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 70 CONTINUE 80 CONTINUE * * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... * W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) ) * DO 90 J = 1, L CALL CLACGV( K, V( 1, J ), 1 ) 90 CONTINUE IF( L.GT.0 ) $ CALL CGEMM( 'No transpose', 'No transpose', M, L, K, -ONE, $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC ) DO 100 J = 1, L CALL CLACGV( K, V( 1, J ), 1 ) 100 CONTINUE * END IF * RETURN * * End of CLARZB * END |