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Mise à jour de lapack vers la version 3.2.2.
1: SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO ) 2: * 3: * -- LAPACK deprecated computational routine (version 3.2.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * June 2010 7: * 8: * .. Scalar Arguments .. 9: INTEGER INFO, LDA, M, N 10: * .. 11: * .. Array Arguments .. 12: INTEGER JPVT( * ) 13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * This routine is deprecated and has been replaced by routine DGEQP3. 20: * 21: * DGEQPF computes a QR factorization with column pivoting of a 22: * real M-by-N matrix A: A*P = Q*R. 23: * 24: * Arguments 25: *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) DOUBLE PRECISION 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 triangular matrix R; the elements 37: * below the diagonal, together with the array TAU, 38: * represent the orthogonal matrix Q as a product of 39: * min(m,n) elementary 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(i) .ne. 0, the i-th column of A is permuted 46: * to the front of A*P (a leading column); if JPVT(i) = 0, 47: * the i-th column of A is a free column. 48: * On exit, if JPVT(i) = k, then the i-th column of A*P 49: * was the k-th column of A. 50: * 51: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 52: * The scalar factors of the elementary reflectors. 53: * 54: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N) 55: * 56: * INFO (output) INTEGER 57: * = 0: successful exit 58: * < 0: if INFO = -i, the i-th argument had an illegal value 59: * 60: * Further Details 61: * =============== 62: * 63: * The matrix Q is represented as a product of elementary reflectors 64: * 65: * Q = H(1) H(2) . . . H(n) 66: * 67: * Each H(i) has the form 68: * 69: * H = I - tau * v * v' 70: * 71: * where tau is a real scalar, and v is a real vector with 72: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i). 73: * 74: * The matrix P is represented in jpvt as follows: If 75: * jpvt(j) = i 76: * then the jth column of P is the ith canonical unit vector. 77: * 78: * Partial column norm updating strategy modified by 79: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics, 80: * University of Zagreb, Croatia. 81: * June 2010 82: * For more details see LAPACK Working Note 176. 83: * 84: * ===================================================================== 85: * 86: * .. Parameters .. 87: DOUBLE PRECISION ZERO, ONE 88: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 89: * .. 90: * .. Local Scalars .. 91: INTEGER I, ITEMP, J, MA, MN, PVT 92: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z 93: * .. 94: * .. External Subroutines .. 95: EXTERNAL DGEQR2, DLARF, DLARFG, DORM2R, DSWAP, XERBLA 96: * .. 97: * .. Intrinsic Functions .. 98: INTRINSIC ABS, MAX, MIN, SQRT 99: * .. 100: * .. External Functions .. 101: INTEGER IDAMAX 102: DOUBLE PRECISION DLAMCH, DNRM2 103: EXTERNAL IDAMAX, DLAMCH, DNRM2 104: * .. 105: * .. Executable Statements .. 106: * 107: * Test the input arguments 108: * 109: INFO = 0 110: IF( M.LT.0 ) THEN 111: INFO = -1 112: ELSE IF( N.LT.0 ) THEN 113: INFO = -2 114: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 115: INFO = -4 116: END IF 117: IF( INFO.NE.0 ) THEN 118: CALL XERBLA( 'DGEQPF', -INFO ) 119: RETURN 120: END IF 121: * 122: MN = MIN( M, N ) 123: TOL3Z = SQRT(DLAMCH('Epsilon')) 124: * 125: * Move initial columns up front 126: * 127: ITEMP = 1 128: DO 10 I = 1, N 129: IF( JPVT( I ).NE.0 ) THEN 130: IF( I.NE.ITEMP ) THEN 131: CALL DSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 ) 132: JPVT( I ) = JPVT( ITEMP ) 133: JPVT( ITEMP ) = I 134: ELSE 135: JPVT( I ) = I 136: END IF 137: ITEMP = ITEMP + 1 138: ELSE 139: JPVT( I ) = I 140: END IF 141: 10 CONTINUE 142: ITEMP = ITEMP - 1 143: * 144: * Compute the QR factorization and update remaining columns 145: * 146: IF( ITEMP.GT.0 ) THEN 147: MA = MIN( ITEMP, M ) 148: CALL DGEQR2( M, MA, A, LDA, TAU, WORK, INFO ) 149: IF( MA.LT.N ) THEN 150: CALL DORM2R( 'Left', 'Transpose', M, N-MA, MA, A, LDA, TAU, 151: $ A( 1, MA+1 ), LDA, WORK, INFO ) 152: END IF 153: END IF 154: * 155: IF( ITEMP.LT.MN ) THEN 156: * 157: * Initialize partial column norms. The first n elements of 158: * work store the exact column norms. 159: * 160: DO 20 I = ITEMP + 1, N 161: WORK( I ) = DNRM2( M-ITEMP, A( ITEMP+1, I ), 1 ) 162: WORK( N+I ) = WORK( I ) 163: 20 CONTINUE 164: * 165: * Compute factorization 166: * 167: DO 40 I = ITEMP + 1, MN 168: * 169: * Determine ith pivot column and swap if necessary 170: * 171: PVT = ( I-1 ) + IDAMAX( N-I+1, WORK( I ), 1 ) 172: * 173: IF( PVT.NE.I ) THEN 174: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) 175: ITEMP = JPVT( PVT ) 176: JPVT( PVT ) = JPVT( I ) 177: JPVT( I ) = ITEMP 178: WORK( PVT ) = WORK( I ) 179: WORK( N+PVT ) = WORK( N+I ) 180: END IF 181: * 182: * Generate elementary reflector H(i) 183: * 184: IF( I.LT.M ) THEN 185: CALL DLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) ) 186: ELSE 187: CALL DLARFG( 1, A( M, M ), A( M, M ), 1, TAU( M ) ) 188: END IF 189: * 190: IF( I.LT.N ) THEN 191: * 192: * Apply H(i) to A(i:m,i+1:n) from the left 193: * 194: AII = A( I, I ) 195: A( I, I ) = ONE 196: CALL DLARF( 'LEFT', M-I+1, N-I, A( I, I ), 1, TAU( I ), 197: $ A( I, I+1 ), LDA, WORK( 2*N+1 ) ) 198: A( I, I ) = AII 199: END IF 200: * 201: * Update partial column norms 202: * 203: DO 30 J = I + 1, N 204: IF( WORK( J ).NE.ZERO ) THEN 205: * 206: * NOTE: The following 4 lines follow from the analysis in 207: * Lapack Working Note 176. 208: * 209: TEMP = ABS( A( I, J ) ) / WORK( J ) 210: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) ) 211: TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2 212: IF( TEMP2 .LE. TOL3Z ) THEN 213: IF( M-I.GT.0 ) THEN 214: WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 ) 215: WORK( N+J ) = WORK( J ) 216: ELSE 217: WORK( J ) = ZERO 218: WORK( N+J ) = ZERO 219: END IF 220: ELSE 221: WORK( J ) = WORK( J )*SQRT( TEMP ) 222: END IF 223: END IF 224: 30 CONTINUE 225: * 226: 40 CONTINUE 227: END IF 228: RETURN 229: * 230: * End of DGEQPF 231: * 232: END