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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DGEQRF( 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: * DGEQRF computes a QR factorization of a real M-by-N matrix A: 19: * A = Q * R. 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 above the diagonal of the array 33: * contain the min(M,N)-by-N upper trapezoidal matrix R (R is 34: * upper triangular if m >= n); the elements below the diagonal, 35: * with the array TAU, represent the orthogonal matrix Q as a 36: * product of min(m,n) elementary reflectors (see Further 37: * Details). 38: * 39: * LDA (input) INTEGER 40: * The leading dimension of the array A. LDA >= max(1,M). 41: * 42: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 43: * The scalar factors of the elementary reflectors (see Further 44: * Details). 45: * 46: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 47: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 48: * 49: * LWORK (input) INTEGER 50: * The dimension of the array WORK. LWORK >= max(1,N). 51: * For optimum performance LWORK >= N*NB, where NB is 52: * the optimal blocksize. 53: * 54: * If LWORK = -1, then a workspace query is assumed; the routine 55: * only calculates the optimal size of the WORK array, returns 56: * this value as the first entry of the WORK array, and no error 57: * message related to LWORK is issued by XERBLA. 58: * 59: * INFO (output) INTEGER 60: * = 0: successful exit 61: * < 0: if INFO = -i, the i-th argument had an illegal value 62: * 63: * Further Details 64: * =============== 65: * 66: * The matrix Q is represented as a product of elementary reflectors 67: * 68: * Q = H(1) H(2) . . . H(k), where k = min(m,n). 69: * 70: * Each H(i) has the form 71: * 72: * H(i) = I - tau * v * v' 73: * 74: * where tau is a real scalar, and v is a real vector with 75: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), 76: * and tau in TAU(i). 77: * 78: * ===================================================================== 79: * 80: * .. Local Scalars .. 81: LOGICAL LQUERY 82: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, 83: $ NBMIN, NX 84: * .. 85: * .. External Subroutines .. 86: EXTERNAL DGEQR2, DLARFB, DLARFT, XERBLA 87: * .. 88: * .. Intrinsic Functions .. 89: INTRINSIC MAX, MIN 90: * .. 91: * .. External Functions .. 92: INTEGER ILAENV 93: EXTERNAL ILAENV 94: * .. 95: * .. Executable Statements .. 96: * 97: * Test the input arguments 98: * 99: INFO = 0 100: NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) 101: LWKOPT = N*NB 102: WORK( 1 ) = LWKOPT 103: LQUERY = ( LWORK.EQ.-1 ) 104: IF( M.LT.0 ) THEN 105: INFO = -1 106: ELSE IF( N.LT.0 ) THEN 107: INFO = -2 108: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 109: INFO = -4 110: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN 111: INFO = -7 112: END IF 113: IF( INFO.NE.0 ) THEN 114: CALL XERBLA( 'DGEQRF', -INFO ) 115: RETURN 116: ELSE IF( LQUERY ) THEN 117: RETURN 118: END IF 119: * 120: * Quick return if possible 121: * 122: K = MIN( M, N ) 123: IF( K.EQ.0 ) THEN 124: WORK( 1 ) = 1 125: RETURN 126: END IF 127: * 128: NBMIN = 2 129: NX = 0 130: IWS = N 131: IF( NB.GT.1 .AND. NB.LT.K ) THEN 132: * 133: * Determine when to cross over from blocked to unblocked code. 134: * 135: NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) ) 136: IF( NX.LT.K ) THEN 137: * 138: * Determine if workspace is large enough for blocked code. 139: * 140: LDWORK = N 141: IWS = LDWORK*NB 142: IF( LWORK.LT.IWS ) THEN 143: * 144: * Not enough workspace to use optimal NB: reduce NB and 145: * determine the minimum value of NB. 146: * 147: NB = LWORK / LDWORK 148: NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1, 149: $ -1 ) ) 150: END IF 151: END IF 152: END IF 153: * 154: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 155: * 156: * Use blocked code initially 157: * 158: DO 10 I = 1, K - NX, NB 159: IB = MIN( K-I+1, NB ) 160: * 161: * Compute the QR factorization of the current block 162: * A(i:m,i:i+ib-1) 163: * 164: CALL DGEQR2( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, 165: $ IINFO ) 166: IF( I+IB.LE.N ) THEN 167: * 168: * Form the triangular factor of the block reflector 169: * H = H(i) H(i+1) . . . H(i+ib-1) 170: * 171: CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB, 172: $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) 173: * 174: * Apply H' to A(i:m,i+ib:n) from the left 175: * 176: CALL DLARFB( 'Left', 'Transpose', 'Forward', 177: $ 'Columnwise', M-I+1, N-I-IB+1, IB, 178: $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), 179: $ LDA, WORK( IB+1 ), LDWORK ) 180: END IF 181: 10 CONTINUE 182: ELSE 183: I = 1 184: END IF 185: * 186: * Use unblocked code to factor the last or only block. 187: * 188: IF( I.LE.K ) 189: $ CALL DGEQR2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 190: $ IINFO ) 191: * 192: WORK( 1 ) = IWS 193: RETURN 194: * 195: * End of DGEQRF 196: * 197: END