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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DGERQF( 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: * DGERQF computes an RQ factorization of a real M-by-N matrix A: 19: * A = R * 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, 33: * if m <= n, the upper triangle of the subarray 34: * A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; 35: * if m >= n, the elements on and above the (m-n)-th subdiagonal 36: * contain the M-by-N upper trapezoidal matrix R; 37: * the remaining elements, with the array TAU, represent the 38: * orthogonal matrix Q as a product of min(m,n) elementary 39: * reflectors (see Further Details). 40: * 41: * LDA (input) INTEGER 42: * The leading dimension of the array A. LDA >= max(1,M). 43: * 44: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 45: * The scalar factors of the elementary reflectors (see Further 46: * Details). 47: * 48: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 49: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 50: * 51: * LWORK (input) INTEGER 52: * The dimension of the array WORK. LWORK >= max(1,M). 53: * For optimum performance LWORK >= M*NB, where NB is 54: * the optimal blocksize. 55: * 56: * If LWORK = -1, then a workspace query is assumed; the routine 57: * only calculates the optimal size of the WORK array, returns 58: * this value as the first entry of the WORK array, and no error 59: * message related to LWORK is issued by XERBLA. 60: * 61: * INFO (output) INTEGER 62: * = 0: successful exit 63: * < 0: if INFO = -i, the i-th argument had an illegal value 64: * 65: * Further Details 66: * =============== 67: * 68: * The matrix Q is represented as a product of elementary reflectors 69: * 70: * Q = H(1) H(2) . . . H(k), where k = min(m,n). 71: * 72: * Each H(i) has the form 73: * 74: * H(i) = I - tau * v * v' 75: * 76: * where tau is a real scalar, and v is a real vector with 77: * v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in 78: * A(m-k+i,1:n-k+i-1), and tau in TAU(i). 79: * 80: * ===================================================================== 81: * 82: * .. Local Scalars .. 83: LOGICAL LQUERY 84: INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT, 85: $ MU, NB, NBMIN, NU, NX 86: * .. 87: * .. External Subroutines .. 88: EXTERNAL DGERQ2, DLARFB, DLARFT, XERBLA 89: * .. 90: * .. Intrinsic Functions .. 91: INTRINSIC MAX, MIN 92: * .. 93: * .. External Functions .. 94: INTEGER ILAENV 95: EXTERNAL ILAENV 96: * .. 97: * .. Executable Statements .. 98: * 99: * Test the input arguments 100: * 101: INFO = 0 102: 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: END IF 110: * 111: IF( INFO.EQ.0 ) THEN 112: K = MIN( M, N ) 113: IF( K.EQ.0 ) THEN 114: LWKOPT = 1 115: ELSE 116: NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 ) 117: LWKOPT = M*NB 118: END IF 119: WORK( 1 ) = LWKOPT 120: * 121: IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 122: INFO = -7 123: END IF 124: END IF 125: * 126: IF( INFO.NE.0 ) THEN 127: CALL XERBLA( 'DGERQF', -INFO ) 128: RETURN 129: ELSE IF( LQUERY ) THEN 130: RETURN 131: END IF 132: * 133: * Quick return if possible 134: * 135: IF( K.EQ.0 ) THEN 136: RETURN 137: END IF 138: * 139: NBMIN = 2 140: NX = 1 141: IWS = M 142: IF( NB.GT.1 .AND. NB.LT.K ) THEN 143: * 144: * Determine when to cross over from blocked to unblocked code. 145: * 146: NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) ) 147: IF( NX.LT.K ) THEN 148: * 149: * Determine if workspace is large enough for blocked code. 150: * 151: LDWORK = M 152: IWS = LDWORK*NB 153: IF( LWORK.LT.IWS ) THEN 154: * 155: * Not enough workspace to use optimal NB: reduce NB and 156: * determine the minimum value of NB. 157: * 158: NB = LWORK / LDWORK 159: NBMIN = MAX( 2, ILAENV( 2, 'DGERQF', ' ', M, N, -1, 160: $ -1 ) ) 161: END IF 162: END IF 163: END IF 164: * 165: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 166: * 167: * Use blocked code initially. 168: * The last kk rows are handled by the block method. 169: * 170: KI = ( ( K-NX-1 ) / NB )*NB 171: KK = MIN( K, KI+NB ) 172: * 173: DO 10 I = K - KK + KI + 1, K - KK + 1, -NB 174: IB = MIN( K-I+1, NB ) 175: * 176: * Compute the RQ factorization of the current block 177: * A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) 178: * 179: CALL DGERQ2( IB, N-K+I+IB-1, A( M-K+I, 1 ), LDA, TAU( I ), 180: $ WORK, IINFO ) 181: IF( M-K+I.GT.1 ) THEN 182: * 183: * Form the triangular factor of the block reflector 184: * H = H(i+ib-1) . . . H(i+1) H(i) 185: * 186: CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, 187: $ A( M-K+I, 1 ), LDA, TAU( I ), WORK, LDWORK ) 188: * 189: * Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right 190: * 191: CALL DLARFB( 'Right', 'No transpose', 'Backward', 192: $ 'Rowwise', M-K+I-1, N-K+I+IB-1, IB, 193: $ A( M-K+I, 1 ), LDA, WORK, LDWORK, A, LDA, 194: $ WORK( IB+1 ), LDWORK ) 195: END IF 196: 10 CONTINUE 197: MU = M - K + I + NB - 1 198: NU = N - K + I + NB - 1 199: ELSE 200: MU = M 201: NU = N 202: END IF 203: * 204: * Use unblocked code to factor the last or only block 205: * 206: IF( MU.GT.0 .AND. NU.GT.0 ) 207: $ CALL DGERQ2( MU, NU, A, LDA, TAU, WORK, IINFO ) 208: * 209: WORK( 1 ) = IWS 210: RETURN 211: * 212: * End of DGERQF 213: * 214: END