Annotation of rpl/lapack/lapack/zlarzb.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
! 2: $ LDV, T, LDT, C, LDC, WORK, LDWORK )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER DIRECT, SIDE, STOREV, TRANS
! 11: INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
! 15: $ WORK( LDWORK, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZLARZB applies a complex block reflector H or its transpose H**H
! 22: * to a complex distributed M-by-N C from the left or the right.
! 23: *
! 24: * Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * SIDE (input) CHARACTER*1
! 30: * = 'L': apply H or H' from the Left
! 31: * = 'R': apply H or H' from the Right
! 32: *
! 33: * TRANS (input) CHARACTER*1
! 34: * = 'N': apply H (No transpose)
! 35: * = 'C': apply H' (Conjugate transpose)
! 36: *
! 37: * DIRECT (input) CHARACTER*1
! 38: * Indicates how H is formed from a product of elementary
! 39: * reflectors
! 40: * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
! 41: * = 'B': H = H(k) . . . H(2) H(1) (Backward)
! 42: *
! 43: * STOREV (input) CHARACTER*1
! 44: * Indicates how the vectors which define the elementary
! 45: * reflectors are stored:
! 46: * = 'C': Columnwise (not supported yet)
! 47: * = 'R': Rowwise
! 48: *
! 49: * M (input) INTEGER
! 50: * The number of rows of the matrix C.
! 51: *
! 52: * N (input) INTEGER
! 53: * The number of columns of the matrix C.
! 54: *
! 55: * K (input) INTEGER
! 56: * The order of the matrix T (= the number of elementary
! 57: * reflectors whose product defines the block reflector).
! 58: *
! 59: * L (input) INTEGER
! 60: * The number of columns of the matrix V containing the
! 61: * meaningful part of the Householder reflectors.
! 62: * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
! 63: *
! 64: * V (input) COMPLEX*16 array, dimension (LDV,NV).
! 65: * If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
! 66: *
! 67: * LDV (input) INTEGER
! 68: * The leading dimension of the array V.
! 69: * If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
! 70: *
! 71: * T (input) COMPLEX*16 array, dimension (LDT,K)
! 72: * The triangular K-by-K matrix T in the representation of the
! 73: * block reflector.
! 74: *
! 75: * LDT (input) INTEGER
! 76: * The leading dimension of the array T. LDT >= K.
! 77: *
! 78: * C (input/output) COMPLEX*16 array, dimension (LDC,N)
! 79: * On entry, the M-by-N matrix C.
! 80: * On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
! 81: *
! 82: * LDC (input) INTEGER
! 83: * The leading dimension of the array C. LDC >= max(1,M).
! 84: *
! 85: * WORK (workspace) COMPLEX*16 array, dimension (LDWORK,K)
! 86: *
! 87: * LDWORK (input) INTEGER
! 88: * The leading dimension of the array WORK.
! 89: * If SIDE = 'L', LDWORK >= max(1,N);
! 90: * if SIDE = 'R', LDWORK >= max(1,M).
! 91: *
! 92: * Further Details
! 93: * ===============
! 94: *
! 95: * Based on contributions by
! 96: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 97: *
! 98: * =====================================================================
! 99: *
! 100: * .. Parameters ..
! 101: COMPLEX*16 ONE
! 102: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 103: * ..
! 104: * .. Local Scalars ..
! 105: CHARACTER TRANST
! 106: INTEGER I, INFO, J
! 107: * ..
! 108: * .. External Functions ..
! 109: LOGICAL LSAME
! 110: EXTERNAL LSAME
! 111: * ..
! 112: * .. External Subroutines ..
! 113: EXTERNAL XERBLA, ZCOPY, ZGEMM, ZLACGV, ZTRMM
! 114: * ..
! 115: * .. Executable Statements ..
! 116: *
! 117: * Quick return if possible
! 118: *
! 119: IF( M.LE.0 .OR. N.LE.0 )
! 120: $ RETURN
! 121: *
! 122: * Check for currently supported options
! 123: *
! 124: INFO = 0
! 125: IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
! 126: INFO = -3
! 127: ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
! 128: INFO = -4
! 129: END IF
! 130: IF( INFO.NE.0 ) THEN
! 131: CALL XERBLA( 'ZLARZB', -INFO )
! 132: RETURN
! 133: END IF
! 134: *
! 135: IF( LSAME( TRANS, 'N' ) ) THEN
! 136: TRANST = 'C'
! 137: ELSE
! 138: TRANST = 'N'
! 139: END IF
! 140: *
! 141: IF( LSAME( SIDE, 'L' ) ) THEN
! 142: *
! 143: * Form H * C or H' * C
! 144: *
! 145: * W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
! 146: *
! 147: DO 10 J = 1, K
! 148: CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
! 149: 10 CONTINUE
! 150: *
! 151: * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
! 152: * conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
! 153: *
! 154: IF( L.GT.0 )
! 155: $ CALL ZGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
! 156: $ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
! 157: $ LDWORK )
! 158: *
! 159: * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T' or W( 1:m, 1:k ) * T
! 160: *
! 161: CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
! 162: $ LDT, WORK, LDWORK )
! 163: *
! 164: * C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
! 165: *
! 166: DO 30 J = 1, N
! 167: DO 20 I = 1, K
! 168: C( I, J ) = C( I, J ) - WORK( J, I )
! 169: 20 CONTINUE
! 170: 30 CONTINUE
! 171: *
! 172: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
! 173: * conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
! 174: *
! 175: IF( L.GT.0 )
! 176: $ CALL ZGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
! 177: $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
! 178: *
! 179: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
! 180: *
! 181: * Form C * H or C * H'
! 182: *
! 183: * W( 1:m, 1:k ) = C( 1:m, 1:k )
! 184: *
! 185: DO 40 J = 1, K
! 186: CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
! 187: 40 CONTINUE
! 188: *
! 189: * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
! 190: * C( 1:m, n-l+1:n ) * conjg( V( 1:k, 1:l )' )
! 191: *
! 192: IF( L.GT.0 )
! 193: $ CALL ZGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
! 194: $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
! 195: *
! 196: * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
! 197: * W( 1:m, 1:k ) * conjg( T' )
! 198: *
! 199: DO 50 J = 1, K
! 200: CALL ZLACGV( K-J+1, T( J, J ), 1 )
! 201: 50 CONTINUE
! 202: CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
! 203: $ LDT, WORK, LDWORK )
! 204: DO 60 J = 1, K
! 205: CALL ZLACGV( K-J+1, T( J, J ), 1 )
! 206: 60 CONTINUE
! 207: *
! 208: * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
! 209: *
! 210: DO 80 J = 1, K
! 211: DO 70 I = 1, M
! 212: C( I, J ) = C( I, J ) - WORK( I, J )
! 213: 70 CONTINUE
! 214: 80 CONTINUE
! 215: *
! 216: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
! 217: * W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
! 218: *
! 219: DO 90 J = 1, L
! 220: CALL ZLACGV( K, V( 1, J ), 1 )
! 221: 90 CONTINUE
! 222: IF( L.GT.0 )
! 223: $ CALL ZGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
! 224: $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
! 225: DO 100 J = 1, L
! 226: CALL ZLACGV( K, V( 1, J ), 1 )
! 227: 100 CONTINUE
! 228: *
! 229: END IF
! 230: *
! 231: RETURN
! 232: *
! 233: * End of ZLARZB
! 234: *
! 235: END
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