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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 2: $ WORK, LWORK, INFO ) 3: * 4: * -- LAPACK routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * .. Scalar Arguments .. 10: CHARACTER SIDE, TRANS 11: INTEGER INFO, K, LDA, LDC, LWORK, M, N 12: * .. 13: * .. Array Arguments .. 14: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * DORMQR overwrites the general real M-by-N matrix C with 21: * 22: * SIDE = 'L' SIDE = 'R' 23: * TRANS = 'N': Q * C C * Q 24: * TRANS = 'T': Q**T * C C * Q**T 25: * 26: * where Q is a real orthogonal matrix defined as the product of k 27: * elementary reflectors 28: * 29: * Q = H(1) H(2) . . . H(k) 30: * 31: * as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N 32: * if SIDE = 'R'. 33: * 34: * Arguments 35: * ========= 36: * 37: * SIDE (input) CHARACTER*1 38: * = 'L': apply Q or Q**T from the Left; 39: * = 'R': apply Q or Q**T from the Right. 40: * 41: * TRANS (input) CHARACTER*1 42: * = 'N': No transpose, apply Q; 43: * = 'T': Transpose, apply Q**T. 44: * 45: * M (input) INTEGER 46: * The number of rows of the matrix C. M >= 0. 47: * 48: * N (input) INTEGER 49: * The number of columns of the matrix C. N >= 0. 50: * 51: * K (input) INTEGER 52: * The number of elementary reflectors whose product defines 53: * the matrix Q. 54: * If SIDE = 'L', M >= K >= 0; 55: * if SIDE = 'R', N >= K >= 0. 56: * 57: * A (input) DOUBLE PRECISION array, dimension (LDA,K) 58: * The i-th column must contain the vector which defines the 59: * elementary reflector H(i), for i = 1,2,...,k, as returned by 60: * DGEQRF in the first k columns of its array argument A. 61: * A is modified by the routine but restored on exit. 62: * 63: * LDA (input) INTEGER 64: * The leading dimension of the array A. 65: * If SIDE = 'L', LDA >= max(1,M); 66: * if SIDE = 'R', LDA >= max(1,N). 67: * 68: * TAU (input) DOUBLE PRECISION array, dimension (K) 69: * TAU(i) must contain the scalar factor of the elementary 70: * reflector H(i), as returned by DGEQRF. 71: * 72: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) 73: * On entry, the M-by-N matrix C. 74: * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 75: * 76: * LDC (input) INTEGER 77: * The leading dimension of the array C. LDC >= max(1,M). 78: * 79: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 80: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 81: * 82: * LWORK (input) INTEGER 83: * The dimension of the array WORK. 84: * If SIDE = 'L', LWORK >= max(1,N); 85: * if SIDE = 'R', LWORK >= max(1,M). 86: * For optimum performance LWORK >= N*NB if SIDE = 'L', and 87: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal 88: * blocksize. 89: * 90: * If LWORK = -1, then a workspace query is assumed; the routine 91: * only calculates the optimal size of the WORK array, returns 92: * this value as the first entry of the WORK array, and no error 93: * message related to LWORK is issued by XERBLA. 94: * 95: * INFO (output) INTEGER 96: * = 0: successful exit 97: * < 0: if INFO = -i, the i-th argument had an illegal value 98: * 99: * ===================================================================== 100: * 101: * .. Parameters .. 102: INTEGER NBMAX, LDT 103: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 104: * .. 105: * .. Local Scalars .. 106: LOGICAL LEFT, LQUERY, NOTRAN 107: INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, 108: $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW 109: * .. 110: * .. Local Arrays .. 111: DOUBLE PRECISION T( LDT, NBMAX ) 112: * .. 113: * .. External Functions .. 114: LOGICAL LSAME 115: INTEGER ILAENV 116: EXTERNAL LSAME, ILAENV 117: * .. 118: * .. External Subroutines .. 119: EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA 120: * .. 121: * .. Intrinsic Functions .. 122: INTRINSIC MAX, MIN 123: * .. 124: * .. Executable Statements .. 125: * 126: * Test the input arguments 127: * 128: INFO = 0 129: LEFT = LSAME( SIDE, 'L' ) 130: NOTRAN = LSAME( TRANS, 'N' ) 131: LQUERY = ( LWORK.EQ.-1 ) 132: * 133: * NQ is the order of Q and NW is the minimum dimension of WORK 134: * 135: IF( LEFT ) THEN 136: NQ = M 137: NW = N 138: ELSE 139: NQ = N 140: NW = M 141: END IF 142: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 143: INFO = -1 144: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 145: INFO = -2 146: ELSE IF( M.LT.0 ) THEN 147: INFO = -3 148: ELSE IF( N.LT.0 ) THEN 149: INFO = -4 150: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 151: INFO = -5 152: ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 153: INFO = -7 154: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 155: INFO = -10 156: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 157: INFO = -12 158: END IF 159: * 160: IF( INFO.EQ.0 ) THEN 161: * 162: * Determine the block size. NB may be at most NBMAX, where NBMAX 163: * is used to define the local array T. 164: * 165: NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, 166: $ -1 ) ) 167: LWKOPT = MAX( 1, NW )*NB 168: WORK( 1 ) = LWKOPT 169: END IF 170: * 171: IF( INFO.NE.0 ) THEN 172: CALL XERBLA( 'DORMQR', -INFO ) 173: RETURN 174: ELSE IF( LQUERY ) THEN 175: RETURN 176: END IF 177: * 178: * Quick return if possible 179: * 180: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN 181: WORK( 1 ) = 1 182: RETURN 183: END IF 184: * 185: NBMIN = 2 186: LDWORK = NW 187: IF( NB.GT.1 .AND. NB.LT.K ) THEN 188: IWS = NW*NB 189: IF( LWORK.LT.IWS ) THEN 190: NB = LWORK / LDWORK 191: NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, 192: $ -1 ) ) 193: END IF 194: ELSE 195: IWS = NW 196: END IF 197: * 198: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 199: * 200: * Use unblocked code 201: * 202: CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 203: $ IINFO ) 204: ELSE 205: * 206: * Use blocked code 207: * 208: IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 209: $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 210: I1 = 1 211: I2 = K 212: I3 = NB 213: ELSE 214: I1 = ( ( K-1 ) / NB )*NB + 1 215: I2 = 1 216: I3 = -NB 217: END IF 218: * 219: IF( LEFT ) THEN 220: NI = N 221: JC = 1 222: ELSE 223: MI = M 224: IC = 1 225: END IF 226: * 227: DO 10 I = I1, I2, I3 228: IB = MIN( NB, K-I+1 ) 229: * 230: * Form the triangular factor of the block reflector 231: * H = H(i) H(i+1) . . . H(i+ib-1) 232: * 233: CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), 234: $ LDA, TAU( I ), T, LDT ) 235: IF( LEFT ) THEN 236: * 237: * H or H' is applied to C(i:m,1:n) 238: * 239: MI = M - I + 1 240: IC = I 241: ELSE 242: * 243: * H or H' is applied to C(1:m,i:n) 244: * 245: NI = N - I + 1 246: JC = I 247: END IF 248: * 249: * Apply H or H' 250: * 251: CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, 252: $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, 253: $ WORK, LDWORK ) 254: 10 CONTINUE 255: END IF 256: WORK( 1 ) = LWKOPT 257: RETURN 258: * 259: * End of DORMQR 260: * 261: END