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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, 2: $ 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: INTEGER INFO, LDA, LWORK, M, N 11: * .. 12: * .. Array Arguments .. 13: INTEGER JPVT( * ) 14: DOUBLE PRECISION RWORK( * ) 15: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * ZGEQP3 computes a QR factorization with column pivoting of a 22: * matrix A: A*P = Q*R using Level 3 BLAS. 23: * 24: * Arguments 25: * ========= 26: * 27: * M (input) INTEGER 28: * The number of rows of the matrix A. M >= 0. 29: * 30: * N (input) INTEGER 31: * The number of columns of the matrix A. N >= 0. 32: * 33: * A (input/output) COMPLEX*16 array, dimension (LDA,N) 34: * On entry, the M-by-N matrix A. 35: * On exit, the upper triangle of the array contains the 36: * min(M,N)-by-N upper trapezoidal matrix R; the elements below 37: * the diagonal, together with the array TAU, represent the 38: * unitary matrix Q as a product of min(M,N) elementary 39: * reflectors. 40: * 41: * LDA (input) INTEGER 42: * The leading dimension of the array A. LDA >= max(1,M). 43: * 44: * JPVT (input/output) INTEGER array, dimension (N) 45: * On entry, if JPVT(J).ne.0, the J-th column of A is permuted 46: * to the front of A*P (a leading column); if JPVT(J)=0, 47: * the J-th column of A is a free column. 48: * On exit, if JPVT(J)=K, then the J-th column of A*P was the 49: * the K-th column of A. 50: * 51: * TAU (output) COMPLEX*16 array, dimension (min(M,N)) 52: * The scalar factors of the elementary reflectors. 53: * 54: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 55: * On exit, if INFO=0, WORK(1) returns the optimal LWORK. 56: * 57: * LWORK (input) INTEGER 58: * The dimension of the array WORK. LWORK >= N+1. 59: * For optimal performance LWORK >= ( N+1 )*NB, where NB 60: * is the optimal blocksize. 61: * 62: * If LWORK = -1, then a workspace query is assumed; the routine 63: * only calculates the optimal size of the WORK array, returns 64: * this value as the first entry of the WORK array, and no error 65: * message related to LWORK is issued by XERBLA. 66: * 67: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) 68: * 69: * INFO (output) INTEGER 70: * = 0: successful exit. 71: * < 0: if INFO = -i, the i-th argument had an illegal value. 72: * 73: * Further Details 74: * =============== 75: * 76: * The matrix Q is represented as a product of elementary reflectors 77: * 78: * Q = H(1) H(2) . . . H(k), where k = min(m,n). 79: * 80: * Each H(i) has the form 81: * 82: * H(i) = I - tau * v * v' 83: * 84: * where tau is a real/complex scalar, and v is a real/complex vector 85: * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in 86: * A(i+1:m,i), and tau in TAU(i). 87: * 88: * Based on contributions by 89: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain 90: * X. Sun, Computer Science Dept., Duke University, USA 91: * 92: * ===================================================================== 93: * 94: * .. Parameters .. 95: INTEGER INB, INBMIN, IXOVER 96: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 ) 97: * .. 98: * .. Local Scalars .. 99: LOGICAL LQUERY 100: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB, 101: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN 102: * .. 103: * .. External Subroutines .. 104: EXTERNAL XERBLA, ZGEQRF, ZLAQP2, ZLAQPS, ZSWAP, ZUNMQR 105: * .. 106: * .. External Functions .. 107: INTEGER ILAENV 108: DOUBLE PRECISION DZNRM2 109: EXTERNAL ILAENV, DZNRM2 110: * .. 111: * .. Intrinsic Functions .. 112: INTRINSIC INT, MAX, MIN 113: * .. 114: * .. Executable Statements .. 115: * 116: * Test input arguments 117: * ==================== 118: * 119: INFO = 0 120: LQUERY = ( LWORK.EQ.-1 ) 121: IF( M.LT.0 ) THEN 122: INFO = -1 123: ELSE IF( N.LT.0 ) THEN 124: INFO = -2 125: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 126: INFO = -4 127: END IF 128: * 129: IF( INFO.EQ.0 ) THEN 130: MINMN = MIN( M, N ) 131: IF( MINMN.EQ.0 ) THEN 132: IWS = 1 133: LWKOPT = 1 134: ELSE 135: IWS = N + 1 136: NB = ILAENV( INB, 'ZGEQRF', ' ', M, N, -1, -1 ) 137: LWKOPT = ( N + 1 )*NB 138: END IF 139: WORK( 1 ) = LWKOPT 140: * 141: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN 142: INFO = -8 143: END IF 144: END IF 145: * 146: IF( INFO.NE.0 ) THEN 147: CALL XERBLA( 'ZGEQP3', -INFO ) 148: RETURN 149: ELSE IF( LQUERY ) THEN 150: RETURN 151: END IF 152: * 153: * Quick return if possible. 154: * 155: IF( MINMN.EQ.0 ) THEN 156: RETURN 157: END IF 158: * 159: * Move initial columns up front. 160: * 161: NFXD = 1 162: DO 10 J = 1, N 163: IF( JPVT( J ).NE.0 ) THEN 164: IF( J.NE.NFXD ) THEN 165: CALL ZSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 ) 166: JPVT( J ) = JPVT( NFXD ) 167: JPVT( NFXD ) = J 168: ELSE 169: JPVT( J ) = J 170: END IF 171: NFXD = NFXD + 1 172: ELSE 173: JPVT( J ) = J 174: END IF 175: 10 CONTINUE 176: NFXD = NFXD - 1 177: * 178: * Factorize fixed columns 179: * ======================= 180: * 181: * Compute the QR factorization of fixed columns and update 182: * remaining columns. 183: * 184: IF( NFXD.GT.0 ) THEN 185: NA = MIN( M, NFXD ) 186: *CC CALL ZGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) 187: CALL ZGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) 188: IWS = MAX( IWS, INT( WORK( 1 ) ) ) 189: IF( NA.LT.N ) THEN 190: *CC CALL ZUNM2R( 'Left', 'Conjugate Transpose', M, N-NA, 191: *CC $ NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK, 192: *CC $ INFO ) 193: CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, N-NA, NA, A, 194: $ LDA, TAU, A( 1, NA+1 ), LDA, WORK, LWORK, 195: $ INFO ) 196: IWS = MAX( IWS, INT( WORK( 1 ) ) ) 197: END IF 198: END IF 199: * 200: * Factorize free columns 201: * ====================== 202: * 203: IF( NFXD.LT.MINMN ) THEN 204: * 205: SM = M - NFXD 206: SN = N - NFXD 207: SMINMN = MINMN - NFXD 208: * 209: * Determine the block size. 210: * 211: NB = ILAENV( INB, 'ZGEQRF', ' ', SM, SN, -1, -1 ) 212: NBMIN = 2 213: NX = 0 214: * 215: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN 216: * 217: * Determine when to cross over from blocked to unblocked code. 218: * 219: NX = MAX( 0, ILAENV( IXOVER, 'ZGEQRF', ' ', SM, SN, -1, 220: $ -1 ) ) 221: * 222: * 223: IF( NX.LT.SMINMN ) THEN 224: * 225: * Determine if workspace is large enough for blocked code. 226: * 227: MINWS = ( SN+1 )*NB 228: IWS = MAX( IWS, MINWS ) 229: IF( LWORK.LT.MINWS ) THEN 230: * 231: * Not enough workspace to use optimal NB: Reduce NB and 232: * determine the minimum value of NB. 233: * 234: NB = LWORK / ( SN+1 ) 235: NBMIN = MAX( 2, ILAENV( INBMIN, 'ZGEQRF', ' ', SM, SN, 236: $ -1, -1 ) ) 237: * 238: * 239: END IF 240: END IF 241: END IF 242: * 243: * Initialize partial column norms. The first N elements of work 244: * store the exact column norms. 245: * 246: DO 20 J = NFXD + 1, N 247: RWORK( J ) = DZNRM2( SM, A( NFXD+1, J ), 1 ) 248: RWORK( N+J ) = RWORK( J ) 249: 20 CONTINUE 250: * 251: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND. 252: $ ( NX.LT.SMINMN ) ) THEN 253: * 254: * Use blocked code initially. 255: * 256: J = NFXD + 1 257: * 258: * Compute factorization: while loop. 259: * 260: * 261: TOPBMN = MINMN - NX 262: 30 CONTINUE 263: IF( J.LE.TOPBMN ) THEN 264: JB = MIN( NB, TOPBMN-J+1 ) 265: * 266: * Factorize JB columns among columns J:N. 267: * 268: CALL ZLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, 269: $ JPVT( J ), TAU( J ), RWORK( J ), 270: $ RWORK( N+J ), WORK( 1 ), WORK( JB+1 ), 271: $ N-J+1 ) 272: * 273: J = J + FJB 274: GO TO 30 275: END IF 276: ELSE 277: J = NFXD + 1 278: END IF 279: * 280: * Use unblocked code to factor the last or only block. 281: * 282: * 283: IF( J.LE.MINMN ) 284: $ CALL ZLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), 285: $ TAU( J ), RWORK( J ), RWORK( N+J ), WORK( 1 ) ) 286: * 287: END IF 288: * 289: WORK( 1 ) = IWS 290: RETURN 291: * 292: * End of ZGEQP3 293: * 294: END