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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 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: INTEGER INFO, LDA, LWORK, M, N 10: * .. 11: * .. Array Arguments .. 12: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 13: * .. 14: * 15: * Purpose 16: * ======= 17: * 18: * ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A 19: * to upper triangular form by means of unitary transformations. 20: * 21: * The upper trapezoidal matrix A is factored as 22: * 23: * A = ( R 0 ) * Z, 24: * 25: * where Z is an N-by-N unitary matrix and R is an M-by-M upper 26: * triangular matrix. 27: * 28: * Arguments 29: * ========= 30: * 31: * M (input) INTEGER 32: * The number of rows of the matrix A. M >= 0. 33: * 34: * N (input) INTEGER 35: * The number of columns of the matrix A. N >= M. 36: * 37: * A (input/output) COMPLEX*16 array, dimension (LDA,N) 38: * On entry, the leading M-by-N upper trapezoidal part of the 39: * array A must contain the matrix to be factorized. 40: * On exit, the leading M-by-M upper triangular part of A 41: * contains the upper triangular matrix R, and elements M+1 to 42: * N of the first M rows of A, with the array TAU, represent the 43: * unitary matrix Z as a product of M elementary reflectors. 44: * 45: * LDA (input) INTEGER 46: * The leading dimension of the array A. LDA >= max(1,M). 47: * 48: * TAU (output) COMPLEX*16 array, dimension (M) 49: * The scalar factors of the elementary reflectors. 50: * 51: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 52: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 53: * 54: * LWORK (input) INTEGER 55: * The dimension of the array WORK. LWORK >= max(1,M). 56: * For optimum performance LWORK >= M*NB, where NB is 57: * the optimal blocksize. 58: * 59: * If LWORK = -1, then a workspace query is assumed; the routine 60: * only calculates the optimal size of the WORK array, returns 61: * this value as the first entry of the WORK array, and no error 62: * message related to LWORK is issued by XERBLA. 63: * 64: * INFO (output) INTEGER 65: * = 0: successful exit 66: * < 0: if INFO = -i, the i-th argument had an illegal value 67: * 68: * Further Details 69: * =============== 70: * 71: * Based on contributions by 72: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 73: * 74: * The factorization is obtained by Householder's method. The kth 75: * transformation matrix, Z( k ), which is used to introduce zeros into 76: * the ( m - k + 1 )th row of A, is given in the form 77: * 78: * Z( k ) = ( I 0 ), 79: * ( 0 T( k ) ) 80: * 81: * where 82: * 83: * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), 84: * ( 0 ) 85: * ( z( k ) ) 86: * 87: * tau is a scalar and z( k ) is an ( n - m ) element vector. 88: * tau and z( k ) are chosen to annihilate the elements of the kth row 89: * of X. 90: * 91: * The scalar tau is returned in the kth element of TAU and the vector 92: * u( k ) in the kth row of A, such that the elements of z( k ) are 93: * in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in 94: * the upper triangular part of A. 95: * 96: * Z is given by 97: * 98: * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). 99: * 100: * ===================================================================== 101: * 102: * .. Parameters .. 103: COMPLEX*16 ZERO 104: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 105: * .. 106: * .. Local Scalars .. 107: LOGICAL LQUERY 108: INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB, 109: $ NBMIN, NX 110: * .. 111: * .. External Subroutines .. 112: EXTERNAL XERBLA, ZLARZB, ZLARZT, ZLATRZ 113: * .. 114: * .. Intrinsic Functions .. 115: INTRINSIC MAX, MIN 116: * .. 117: * .. External Functions .. 118: INTEGER ILAENV 119: EXTERNAL ILAENV 120: * .. 121: * .. Executable Statements .. 122: * 123: * Test the input arguments 124: * 125: INFO = 0 126: LQUERY = ( LWORK.EQ.-1 ) 127: IF( M.LT.0 ) THEN 128: INFO = -1 129: ELSE IF( N.LT.M ) THEN 130: INFO = -2 131: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 132: INFO = -4 133: END IF 134: * 135: IF( INFO.EQ.0 ) THEN 136: IF( M.EQ.0 .OR. M.EQ.N ) THEN 137: LWKOPT = 1 138: ELSE 139: * 140: * Determine the block size. 141: * 142: NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 ) 143: LWKOPT = M*NB 144: END IF 145: WORK( 1 ) = LWKOPT 146: * 147: IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 148: INFO = -7 149: END IF 150: END IF 151: * 152: IF( INFO.NE.0 ) THEN 153: CALL XERBLA( 'ZTZRZF', -INFO ) 154: RETURN 155: ELSE IF( LQUERY ) THEN 156: RETURN 157: END IF 158: * 159: * Quick return if possible 160: * 161: IF( M.EQ.0 ) THEN 162: RETURN 163: ELSE IF( M.EQ.N ) THEN 164: DO 10 I = 1, N 165: TAU( I ) = ZERO 166: 10 CONTINUE 167: RETURN 168: END IF 169: * 170: NBMIN = 2 171: NX = 1 172: IWS = M 173: IF( NB.GT.1 .AND. NB.LT.M ) THEN 174: * 175: * Determine when to cross over from blocked to unblocked code. 176: * 177: NX = MAX( 0, ILAENV( 3, 'ZGERQF', ' ', M, N, -1, -1 ) ) 178: IF( NX.LT.M ) THEN 179: * 180: * Determine if workspace is large enough for blocked code. 181: * 182: LDWORK = M 183: IWS = LDWORK*NB 184: IF( LWORK.LT.IWS ) THEN 185: * 186: * Not enough workspace to use optimal NB: reduce NB and 187: * determine the minimum value of NB. 188: * 189: NB = LWORK / LDWORK 190: NBMIN = MAX( 2, ILAENV( 2, 'ZGERQF', ' ', M, N, -1, 191: $ -1 ) ) 192: END IF 193: END IF 194: END IF 195: * 196: IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN 197: * 198: * Use blocked code initially. 199: * The last kk rows are handled by the block method. 200: * 201: M1 = MIN( M+1, N ) 202: KI = ( ( M-NX-1 ) / NB )*NB 203: KK = MIN( M, KI+NB ) 204: * 205: DO 20 I = M - KK + KI + 1, M - KK + 1, -NB 206: IB = MIN( M-I+1, NB ) 207: * 208: * Compute the TZ factorization of the current block 209: * A(i:i+ib-1,i:n) 210: * 211: CALL ZLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ), 212: $ WORK ) 213: IF( I.GT.1 ) THEN 214: * 215: * Form the triangular factor of the block reflector 216: * H = H(i+ib-1) . . . H(i+1) H(i) 217: * 218: CALL ZLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ), 219: $ LDA, TAU( I ), WORK, LDWORK ) 220: * 221: * Apply H to A(1:i-1,i:n) from the right 222: * 223: CALL ZLARZB( 'Right', 'No transpose', 'Backward', 224: $ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ), 225: $ LDA, WORK, LDWORK, A( 1, I ), LDA, 226: $ WORK( IB+1 ), LDWORK ) 227: END IF 228: 20 CONTINUE 229: MU = I + NB - 1 230: ELSE 231: MU = M 232: END IF 233: * 234: * Use unblocked code to factor the last or only block 235: * 236: IF( MU.GT.0 ) 237: $ CALL ZLATRZ( MU, N, N-M, A, LDA, TAU, WORK ) 238: * 239: WORK( 1 ) = LWKOPT 240: * 241: RETURN 242: * 243: * End of ZTZRZF 244: * 245: END