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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DGELQF( 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: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 13: * .. 14: * 15: * Purpose 16: * ======= 17: * 18: * DGELQF computes an LQ factorization of a real M-by-N matrix A: 19: * A = L * Q. 20: * 21: * Arguments 22: * ========= 23: * 24: * M (input) INTEGER 25: * The number of rows of the matrix A. M >= 0. 26: * 27: * N (input) INTEGER 28: * The number of columns of the matrix A. N >= 0. 29: * 30: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 31: * On entry, the M-by-N matrix A. 32: * On exit, the elements on and below the diagonal of the array 33: * contain the m-by-min(m,n) lower trapezoidal matrix L (L is 34: * lower triangular if m <= n); the elements above the diagonal, 35: * with the array TAU, represent the orthogonal matrix Q as a 36: * product of elementary reflectors (see Further Details). 37: * 38: * LDA (input) INTEGER 39: * The leading dimension of the array A. LDA >= max(1,M). 40: * 41: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 42: * The scalar factors of the elementary reflectors (see Further 43: * Details). 44: * 45: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 46: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 47: * 48: * LWORK (input) INTEGER 49: * The dimension of the array WORK. LWORK >= max(1,M). 50: * For optimum performance LWORK >= M*NB, where NB is the 51: * optimal blocksize. 52: * 53: * If LWORK = -1, then a workspace query is assumed; the routine 54: * only calculates the optimal size of the WORK array, returns 55: * this value as the first entry of the WORK array, and no error 56: * message related to LWORK is issued by XERBLA. 57: * 58: * INFO (output) INTEGER 59: * = 0: successful exit 60: * < 0: if INFO = -i, the i-th argument had an illegal value 61: * 62: * Further Details 63: * =============== 64: * 65: * The matrix Q is represented as a product of elementary reflectors 66: * 67: * Q = H(k) . . . H(2) H(1), where k = min(m,n). 68: * 69: * Each H(i) has the form 70: * 71: * H(i) = I - tau * v * v' 72: * 73: * where tau is a real scalar, and v is a real vector with 74: * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), 75: * and tau in TAU(i). 76: * 77: * ===================================================================== 78: * 79: * .. Local Scalars .. 80: LOGICAL LQUERY 81: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, 82: $ NBMIN, NX 83: * .. 84: * .. External Subroutines .. 85: EXTERNAL DGELQ2, DLARFB, DLARFT, XERBLA 86: * .. 87: * .. Intrinsic Functions .. 88: INTRINSIC MAX, MIN 89: * .. 90: * .. External Functions .. 91: INTEGER ILAENV 92: EXTERNAL ILAENV 93: * .. 94: * .. Executable Statements .. 95: * 96: * Test the input arguments 97: * 98: INFO = 0 99: NB = ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) 100: LWKOPT = M*NB 101: WORK( 1 ) = LWKOPT 102: LQUERY = ( LWORK.EQ.-1 ) 103: IF( M.LT.0 ) THEN 104: INFO = -1 105: ELSE IF( N.LT.0 ) THEN 106: INFO = -2 107: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 108: INFO = -4 109: ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 110: INFO = -7 111: END IF 112: IF( INFO.NE.0 ) THEN 113: CALL XERBLA( 'DGELQF', -INFO ) 114: RETURN 115: ELSE IF( LQUERY ) THEN 116: RETURN 117: END IF 118: * 119: * Quick return if possible 120: * 121: K = MIN( M, N ) 122: IF( K.EQ.0 ) THEN 123: WORK( 1 ) = 1 124: RETURN 125: END IF 126: * 127: NBMIN = 2 128: NX = 0 129: IWS = M 130: IF( NB.GT.1 .AND. NB.LT.K ) THEN 131: * 132: * Determine when to cross over from blocked to unblocked code. 133: * 134: NX = MAX( 0, ILAENV( 3, 'DGELQF', ' ', M, N, -1, -1 ) ) 135: IF( NX.LT.K ) THEN 136: * 137: * Determine if workspace is large enough for blocked code. 138: * 139: LDWORK = M 140: IWS = LDWORK*NB 141: IF( LWORK.LT.IWS ) THEN 142: * 143: * Not enough workspace to use optimal NB: reduce NB and 144: * determine the minimum value of NB. 145: * 146: NB = LWORK / LDWORK 147: NBMIN = MAX( 2, ILAENV( 2, 'DGELQF', ' ', M, N, -1, 148: $ -1 ) ) 149: END IF 150: END IF 151: END IF 152: * 153: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 154: * 155: * Use blocked code initially 156: * 157: DO 10 I = 1, K - NX, NB 158: IB = MIN( K-I+1, NB ) 159: * 160: * Compute the LQ factorization of the current block 161: * A(i:i+ib-1,i:n) 162: * 163: CALL DGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 164: $ IINFO ) 165: IF( I+IB.LE.M ) THEN 166: * 167: * Form the triangular factor of the block reflector 168: * H = H(i) H(i+1) . . . H(i+ib-1) 169: * 170: CALL DLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), 171: $ LDA, TAU( I ), WORK, LDWORK ) 172: * 173: * Apply H to A(i+ib:m,i:n) from the right 174: * 175: CALL DLARFB( 'Right', 'No transpose', 'Forward', 176: $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), 177: $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, 178: $ WORK( IB+1 ), LDWORK ) 179: END IF 180: 10 CONTINUE 181: ELSE 182: I = 1 183: END IF 184: * 185: * Use unblocked code to factor the last or only block. 186: * 187: IF( I.LE.K ) 188: $ CALL DGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 189: $ IINFO ) 190: * 191: WORK( 1 ) = IWS 192: RETURN 193: * 194: * End of DGELQF 195: * 196: END