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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, 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: INTEGER JPVT( * ) 13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * DGEQP3 computes a QR factorization with column pivoting of a 20: * matrix A: A*P = Q*R using Level 3 BLAS. 21: * 22: * Arguments 23: * ========= 24: * 25: * M (input) INTEGER 26: * The number of rows of the matrix A. M >= 0. 27: * 28: * N (input) INTEGER 29: * The number of columns of the matrix A. N >= 0. 30: * 31: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 32: * On entry, the M-by-N matrix A. 33: * On exit, the upper triangle of the array contains the 34: * min(M,N)-by-N upper trapezoidal matrix R; the elements below 35: * the diagonal, together with the array TAU, represent the 36: * orthogonal matrix Q as a product of min(M,N) elementary 37: * reflectors. 38: * 39: * LDA (input) INTEGER 40: * The leading dimension of the array A. LDA >= max(1,M). 41: * 42: * JPVT (input/output) INTEGER array, dimension (N) 43: * On entry, if JPVT(J).ne.0, the J-th column of A is permuted 44: * to the front of A*P (a leading column); if JPVT(J)=0, 45: * the J-th column of A is a free column. 46: * On exit, if JPVT(J)=K, then the J-th column of A*P was the 47: * the K-th column of A. 48: * 49: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 50: * The scalar factors of the elementary reflectors. 51: * 52: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 53: * On exit, if INFO=0, WORK(1) returns the optimal LWORK. 54: * 55: * LWORK (input) INTEGER 56: * The dimension of the array WORK. LWORK >= 3*N+1. 57: * For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB 58: * is the optimal blocksize. 59: * 60: * If LWORK = -1, then a workspace query is assumed; the routine 61: * only calculates the optimal size of the WORK array, returns 62: * this value as the first entry of the WORK array, and no error 63: * message related to LWORK is issued by XERBLA. 64: * 65: * INFO (output) INTEGER 66: * = 0: successful exit. 67: * < 0: if INFO = -i, the i-th argument had an illegal value. 68: * 69: * Further Details 70: * =============== 71: * 72: * The matrix Q is represented as a product of elementary reflectors 73: * 74: * Q = H(1) H(2) . . . H(k), where k = min(m,n). 75: * 76: * Each H(i) has the form 77: * 78: * H(i) = I - tau * v * v' 79: * 80: * where tau is a real/complex scalar, and v is a real/complex vector 81: * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in 82: * A(i+1:m,i), and tau in TAU(i). 83: * 84: * Based on contributions by 85: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain 86: * X. Sun, Computer Science Dept., Duke University, USA 87: * 88: * ===================================================================== 89: * 90: * .. Parameters .. 91: INTEGER INB, INBMIN, IXOVER 92: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 ) 93: * .. 94: * .. Local Scalars .. 95: LOGICAL LQUERY 96: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB, 97: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN 98: * .. 99: * .. External Subroutines .. 100: EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA 101: * .. 102: * .. External Functions .. 103: INTEGER ILAENV 104: DOUBLE PRECISION DNRM2 105: EXTERNAL ILAENV, DNRM2 106: * .. 107: * .. Intrinsic Functions .. 108: INTRINSIC INT, MAX, MIN 109: * .. 110: * .. Executable Statements .. 111: * 112: * Test input arguments 113: * ==================== 114: * 115: INFO = 0 116: LQUERY = ( LWORK.EQ.-1 ) 117: IF( M.LT.0 ) THEN 118: INFO = -1 119: ELSE IF( N.LT.0 ) THEN 120: INFO = -2 121: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 122: INFO = -4 123: END IF 124: * 125: IF( INFO.EQ.0 ) THEN 126: MINMN = MIN( M, N ) 127: IF( MINMN.EQ.0 ) THEN 128: IWS = 1 129: LWKOPT = 1 130: ELSE 131: IWS = 3*N + 1 132: NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 ) 133: LWKOPT = 2*N + ( N + 1 )*NB 134: END IF 135: WORK( 1 ) = LWKOPT 136: * 137: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN 138: INFO = -8 139: END IF 140: END IF 141: * 142: IF( INFO.NE.0 ) THEN 143: CALL XERBLA( 'DGEQP3', -INFO ) 144: RETURN 145: ELSE IF( LQUERY ) THEN 146: RETURN 147: END IF 148: * 149: * Quick return if possible. 150: * 151: IF( MINMN.EQ.0 ) THEN 152: RETURN 153: END IF 154: * 155: * Move initial columns up front. 156: * 157: NFXD = 1 158: DO 10 J = 1, N 159: IF( JPVT( J ).NE.0 ) THEN 160: IF( J.NE.NFXD ) THEN 161: CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 ) 162: JPVT( J ) = JPVT( NFXD ) 163: JPVT( NFXD ) = J 164: ELSE 165: JPVT( J ) = J 166: END IF 167: NFXD = NFXD + 1 168: ELSE 169: JPVT( J ) = J 170: END IF 171: 10 CONTINUE 172: NFXD = NFXD - 1 173: * 174: * Factorize fixed columns 175: * ======================= 176: * 177: * Compute the QR factorization of fixed columns and update 178: * remaining columns. 179: * 180: IF( NFXD.GT.0 ) THEN 181: NA = MIN( M, NFXD ) 182: *CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) 183: CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) 184: IWS = MAX( IWS, INT( WORK( 1 ) ) ) 185: IF( NA.LT.N ) THEN 186: *CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, 187: *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) 188: CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU, 189: $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO ) 190: IWS = MAX( IWS, INT( WORK( 1 ) ) ) 191: END IF 192: END IF 193: * 194: * Factorize free columns 195: * ====================== 196: * 197: IF( NFXD.LT.MINMN ) THEN 198: * 199: SM = M - NFXD 200: SN = N - NFXD 201: SMINMN = MINMN - NFXD 202: * 203: * Determine the block size. 204: * 205: NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 ) 206: NBMIN = 2 207: NX = 0 208: * 209: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN 210: * 211: * Determine when to cross over from blocked to unblocked code. 212: * 213: NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1, 214: $ -1 ) ) 215: * 216: * 217: IF( NX.LT.SMINMN ) THEN 218: * 219: * Determine if workspace is large enough for blocked code. 220: * 221: MINWS = 2*SN + ( SN+1 )*NB 222: IWS = MAX( IWS, MINWS ) 223: IF( LWORK.LT.MINWS ) THEN 224: * 225: * Not enough workspace to use optimal NB: Reduce NB and 226: * determine the minimum value of NB. 227: * 228: NB = ( LWORK-2*SN ) / ( SN+1 ) 229: NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN, 230: $ -1, -1 ) ) 231: * 232: * 233: END IF 234: END IF 235: END IF 236: * 237: * Initialize partial column norms. The first N elements of work 238: * store the exact column norms. 239: * 240: DO 20 J = NFXD + 1, N 241: WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 ) 242: WORK( N+J ) = WORK( J ) 243: 20 CONTINUE 244: * 245: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND. 246: $ ( NX.LT.SMINMN ) ) THEN 247: * 248: * Use blocked code initially. 249: * 250: J = NFXD + 1 251: * 252: * Compute factorization: while loop. 253: * 254: * 255: TOPBMN = MINMN - NX 256: 30 CONTINUE 257: IF( J.LE.TOPBMN ) THEN 258: JB = MIN( NB, TOPBMN-J+1 ) 259: * 260: * Factorize JB columns among columns J:N. 261: * 262: CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, 263: $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ), 264: $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 ) 265: * 266: J = J + FJB 267: GO TO 30 268: END IF 269: ELSE 270: J = NFXD + 1 271: END IF 272: * 273: * Use unblocked code to factor the last or only block. 274: * 275: * 276: IF( J.LE.MINMN ) 277: $ CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), 278: $ TAU( J ), WORK( J ), WORK( N+J ), 279: $ WORK( 2*N+1 ) ) 280: * 281: END IF 282: * 283: WORK( 1 ) = IWS 284: RETURN 285: * 286: * End of DGEQP3 287: * 288: END