Annotation of rpl/lapack/lapack/zlarft.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER DIRECT, STOREV
! 10: INTEGER K, LDT, LDV, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZLARFT forms the triangular factor T of a complex block reflector H
! 20: * of order n, which is defined as a product of k elementary reflectors.
! 21: *
! 22: * If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
! 23: *
! 24: * If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
! 25: *
! 26: * If STOREV = 'C', the vector which defines the elementary reflector
! 27: * H(i) is stored in the i-th column of the array V, and
! 28: *
! 29: * H = I - V * T * V'
! 30: *
! 31: * If STOREV = 'R', the vector which defines the elementary reflector
! 32: * H(i) is stored in the i-th row of the array V, and
! 33: *
! 34: * H = I - V' * T * V
! 35: *
! 36: * Arguments
! 37: * =========
! 38: *
! 39: * DIRECT (input) CHARACTER*1
! 40: * Specifies the order in which the elementary reflectors are
! 41: * multiplied to form the block reflector:
! 42: * = 'F': H = H(1) H(2) . . . H(k) (Forward)
! 43: * = 'B': H = H(k) . . . H(2) H(1) (Backward)
! 44: *
! 45: * STOREV (input) CHARACTER*1
! 46: * Specifies how the vectors which define the elementary
! 47: * reflectors are stored (see also Further Details):
! 48: * = 'C': columnwise
! 49: * = 'R': rowwise
! 50: *
! 51: * N (input) INTEGER
! 52: * The order of the block reflector H. N >= 0.
! 53: *
! 54: * K (input) INTEGER
! 55: * The order of the triangular factor T (= the number of
! 56: * elementary reflectors). K >= 1.
! 57: *
! 58: * V (input/output) COMPLEX*16 array, dimension
! 59: * (LDV,K) if STOREV = 'C'
! 60: * (LDV,N) if STOREV = 'R'
! 61: * The matrix V. See further details.
! 62: *
! 63: * LDV (input) INTEGER
! 64: * The leading dimension of the array V.
! 65: * If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
! 66: *
! 67: * TAU (input) COMPLEX*16 array, dimension (K)
! 68: * TAU(i) must contain the scalar factor of the elementary
! 69: * reflector H(i).
! 70: *
! 71: * T (output) COMPLEX*16 array, dimension (LDT,K)
! 72: * The k by k triangular factor T of the block reflector.
! 73: * If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
! 74: * lower triangular. The rest of the array is not used.
! 75: *
! 76: * LDT (input) INTEGER
! 77: * The leading dimension of the array T. LDT >= K.
! 78: *
! 79: * Further Details
! 80: * ===============
! 81: *
! 82: * The shape of the matrix V and the storage of the vectors which define
! 83: * the H(i) is best illustrated by the following example with n = 5 and
! 84: * k = 3. The elements equal to 1 are not stored; the corresponding
! 85: * array elements are modified but restored on exit. The rest of the
! 86: * array is not used.
! 87: *
! 88: * DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
! 89: *
! 90: * V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
! 91: * ( v1 1 ) ( 1 v2 v2 v2 )
! 92: * ( v1 v2 1 ) ( 1 v3 v3 )
! 93: * ( v1 v2 v3 )
! 94: * ( v1 v2 v3 )
! 95: *
! 96: * DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
! 97: *
! 98: * V = ( v1 v2 v3 ) V = ( v1 v1 1 )
! 99: * ( v1 v2 v3 ) ( v2 v2 v2 1 )
! 100: * ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
! 101: * ( 1 v3 )
! 102: * ( 1 )
! 103: *
! 104: * =====================================================================
! 105: *
! 106: * .. Parameters ..
! 107: COMPLEX*16 ONE, ZERO
! 108: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
! 109: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
! 110: * ..
! 111: * .. Local Scalars ..
! 112: INTEGER I, J, PREVLASTV, LASTV
! 113: COMPLEX*16 VII
! 114: * ..
! 115: * .. External Subroutines ..
! 116: EXTERNAL ZGEMV, ZLACGV, ZTRMV
! 117: * ..
! 118: * .. External Functions ..
! 119: LOGICAL LSAME
! 120: EXTERNAL LSAME
! 121: * ..
! 122: * .. Executable Statements ..
! 123: *
! 124: * Quick return if possible
! 125: *
! 126: IF( N.EQ.0 )
! 127: $ RETURN
! 128: *
! 129: IF( LSAME( DIRECT, 'F' ) ) THEN
! 130: PREVLASTV = N
! 131: DO 20 I = 1, K
! 132: PREVLASTV = MAX( PREVLASTV, I )
! 133: IF( TAU( I ).EQ.ZERO ) THEN
! 134: *
! 135: * H(i) = I
! 136: *
! 137: DO 10 J = 1, I
! 138: T( J, I ) = ZERO
! 139: 10 CONTINUE
! 140: ELSE
! 141: *
! 142: * general case
! 143: *
! 144: VII = V( I, I )
! 145: V( I, I ) = ONE
! 146: IF( LSAME( STOREV, 'C' ) ) THEN
! 147: ! Skip any trailing zeros.
! 148: DO LASTV = N, I+1, -1
! 149: IF( V( LASTV, I ).NE.ZERO ) EXIT
! 150: END DO
! 151: J = MIN( LASTV, PREVLASTV )
! 152: *
! 153: * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i)
! 154: *
! 155: CALL ZGEMV( 'Conjugate transpose', J-I+1, I-1,
! 156: $ -TAU( I ), V( I, 1 ), LDV, V( I, I ), 1,
! 157: $ ZERO, T( 1, I ), 1 )
! 158: ELSE
! 159: ! Skip any trailing zeros.
! 160: DO LASTV = N, I+1, -1
! 161: IF( V( I, LASTV ).NE.ZERO ) EXIT
! 162: END DO
! 163: J = MIN( LASTV, PREVLASTV )
! 164: *
! 165: * T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)'
! 166: *
! 167: IF( I.LT.J )
! 168: $ CALL ZLACGV( J-I, V( I, I+1 ), LDV )
! 169: CALL ZGEMV( 'No transpose', I-1, J-I+1, -TAU( I ),
! 170: $ V( 1, I ), LDV, V( I, I ), LDV, ZERO,
! 171: $ T( 1, I ), 1 )
! 172: IF( I.LT.J )
! 173: $ CALL ZLACGV( J-I, V( I, I+1 ), LDV )
! 174: END IF
! 175: V( I, I ) = VII
! 176: *
! 177: * T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
! 178: *
! 179: CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
! 180: $ LDT, T( 1, I ), 1 )
! 181: T( I, I ) = TAU( I )
! 182: IF( I.GT.1 ) THEN
! 183: PREVLASTV = MAX( PREVLASTV, LASTV )
! 184: ELSE
! 185: PREVLASTV = LASTV
! 186: END IF
! 187: END IF
! 188: 20 CONTINUE
! 189: ELSE
! 190: PREVLASTV = 1
! 191: DO 40 I = K, 1, -1
! 192: IF( TAU( I ).EQ.ZERO ) THEN
! 193: *
! 194: * H(i) = I
! 195: *
! 196: DO 30 J = I, K
! 197: T( J, I ) = ZERO
! 198: 30 CONTINUE
! 199: ELSE
! 200: *
! 201: * general case
! 202: *
! 203: IF( I.LT.K ) THEN
! 204: IF( LSAME( STOREV, 'C' ) ) THEN
! 205: VII = V( N-K+I, I )
! 206: V( N-K+I, I ) = ONE
! 207: ! Skip any leading zeros.
! 208: DO LASTV = 1, I-1
! 209: IF( V( LASTV, I ).NE.ZERO ) EXIT
! 210: END DO
! 211: J = MAX( LASTV, PREVLASTV )
! 212: *
! 213: * T(i+1:k,i) :=
! 214: * - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i)
! 215: *
! 216: CALL ZGEMV( 'Conjugate transpose', N-K+I-J+1, K-I,
! 217: $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ),
! 218: $ 1, ZERO, T( I+1, I ), 1 )
! 219: V( N-K+I, I ) = VII
! 220: ELSE
! 221: VII = V( I, N-K+I )
! 222: V( I, N-K+I ) = ONE
! 223: ! Skip any leading zeros.
! 224: DO LASTV = 1, I-1
! 225: IF( V( I, LASTV ).NE.ZERO ) EXIT
! 226: END DO
! 227: J = MAX( LASTV, PREVLASTV )
! 228: *
! 229: * T(i+1:k,i) :=
! 230: * - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)'
! 231: *
! 232: CALL ZLACGV( N-K+I-1-J+1, V( I, J ), LDV )
! 233: CALL ZGEMV( 'No transpose', K-I, N-K+I-J+1,
! 234: $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
! 235: $ ZERO, T( I+1, I ), 1 )
! 236: CALL ZLACGV( N-K+I-1-J+1, V( I, J ), LDV )
! 237: V( I, N-K+I ) = VII
! 238: END IF
! 239: *
! 240: * T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
! 241: *
! 242: CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
! 243: $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
! 244: IF( I.GT.1 ) THEN
! 245: PREVLASTV = MIN( PREVLASTV, LASTV )
! 246: ELSE
! 247: PREVLASTV = LASTV
! 248: END IF
! 249: END IF
! 250: T( I, I ) = TAU( I )
! 251: END IF
! 252: 40 CONTINUE
! 253: END IF
! 254: RETURN
! 255: *
! 256: * End of ZLARFT
! 257: *
! 258: END
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