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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) 2: * 3: * -- LAPACK 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: * ZLARZT forms the triangular factor T of a complex block reflector 20: * H of order > n, which is defined as a product of k elementary 21: * reflectors. 22: * 23: * If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; 24: * 25: * If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. 26: * 27: * If STOREV = 'C', the vector which defines the elementary reflector 28: * H(i) is stored in the i-th column of the array V, and 29: * 30: * H = I - V * T * V' 31: * 32: * If STOREV = 'R', the vector which defines the elementary reflector 33: * H(i) is stored in the i-th row of the array V, and 34: * 35: * H = I - V' * T * V 36: * 37: * Currently, only STOREV = 'R' and DIRECT = 'B' are supported. 38: * 39: * Arguments 40: * ========= 41: * 42: * DIRECT (input) CHARACTER*1 43: * Specifies the order in which the elementary reflectors are 44: * multiplied to form the block reflector: 45: * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) 46: * = 'B': H = H(k) . . . H(2) H(1) (Backward) 47: * 48: * STOREV (input) CHARACTER*1 49: * Specifies how the vectors which define the elementary 50: * reflectors are stored (see also Further Details): 51: * = 'C': columnwise (not supported yet) 52: * = 'R': rowwise 53: * 54: * N (input) INTEGER 55: * The order of the block reflector H. N >= 0. 56: * 57: * K (input) INTEGER 58: * The order of the triangular factor T (= the number of 59: * elementary reflectors). K >= 1. 60: * 61: * V (input/output) COMPLEX*16 array, dimension 62: * (LDV,K) if STOREV = 'C' 63: * (LDV,N) if STOREV = 'R' 64: * The matrix V. See further details. 65: * 66: * LDV (input) INTEGER 67: * The leading dimension of the array V. 68: * If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. 69: * 70: * TAU (input) COMPLEX*16 array, dimension (K) 71: * TAU(i) must contain the scalar factor of the elementary 72: * reflector H(i). 73: * 74: * T (output) COMPLEX*16 array, dimension (LDT,K) 75: * The k by k triangular factor T of the block reflector. 76: * If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is 77: * lower triangular. The rest of the array is not used. 78: * 79: * LDT (input) INTEGER 80: * The leading dimension of the array T. LDT >= K. 81: * 82: * Further Details 83: * =============== 84: * 85: * Based on contributions by 86: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 87: * 88: * The shape of the matrix V and the storage of the vectors which define 89: * the H(i) is best illustrated by the following example with n = 5 and 90: * k = 3. The elements equal to 1 are not stored; the corresponding 91: * array elements are modified but restored on exit. The rest of the 92: * array is not used. 93: * 94: * DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': 95: * 96: * ______V_____ 97: * ( v1 v2 v3 ) / \ 98: * ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) 99: * V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) 100: * ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) 101: * ( v1 v2 v3 ) 102: * . . . 103: * . . . 104: * 1 . . 105: * 1 . 106: * 1 107: * 108: * DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': 109: * 110: * ______V_____ 111: * 1 / \ 112: * . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) 113: * . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) 114: * . . . ( . . 1 . . v3 v3 v3 v3 v3 ) 115: * . . . 116: * ( v1 v2 v3 ) 117: * ( v1 v2 v3 ) 118: * V = ( v1 v2 v3 ) 119: * ( v1 v2 v3 ) 120: * ( v1 v2 v3 ) 121: * 122: * ===================================================================== 123: * 124: * .. Parameters .. 125: COMPLEX*16 ZERO 126: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 127: * .. 128: * .. Local Scalars .. 129: INTEGER I, INFO, J 130: * .. 131: * .. External Subroutines .. 132: EXTERNAL XERBLA, ZGEMV, ZLACGV, ZTRMV 133: * .. 134: * .. External Functions .. 135: LOGICAL LSAME 136: EXTERNAL LSAME 137: * .. 138: * .. Executable Statements .. 139: * 140: * Check for currently supported options 141: * 142: INFO = 0 143: IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN 144: INFO = -1 145: ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN 146: INFO = -2 147: END IF 148: IF( INFO.NE.0 ) THEN 149: CALL XERBLA( 'ZLARZT', -INFO ) 150: RETURN 151: END IF 152: * 153: DO 20 I = K, 1, -1 154: IF( TAU( I ).EQ.ZERO ) THEN 155: * 156: * H(i) = I 157: * 158: DO 10 J = I, K 159: T( J, I ) = ZERO 160: 10 CONTINUE 161: ELSE 162: * 163: * general case 164: * 165: IF( I.LT.K ) THEN 166: * 167: * T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)' 168: * 169: CALL ZLACGV( N, V( I, 1 ), LDV ) 170: CALL ZGEMV( 'No transpose', K-I, N, -TAU( I ), 171: $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO, 172: $ T( I+1, I ), 1 ) 173: CALL ZLACGV( N, V( I, 1 ), LDV ) 174: * 175: * T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i) 176: * 177: CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, 178: $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) 179: END IF 180: T( I, I ) = TAU( I ) 181: END IF 182: 20 CONTINUE 183: RETURN 184: * 185: * End of ZLARZT 186: * 187: END