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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, 2: $ WORK ) 3: * 4: * -- LAPACK auxiliary routine (version 3.2.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * June 2010 8: * 9: * .. Scalar Arguments .. 10: INTEGER LDA, M, N, OFFSET 11: * .. 12: * .. Array Arguments .. 13: INTEGER JPVT( * ) 14: DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), 15: $ WORK( * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * DLAQP2 computes a QR factorization with column pivoting of 22: * the block A(OFFSET+1:M,1:N). 23: * The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. 24: * 25: * Arguments 26: * ========= 27: * 28: * M (input) INTEGER 29: * The number of rows of the matrix A. M >= 0. 30: * 31: * N (input) INTEGER 32: * The number of columns of the matrix A. N >= 0. 33: * 34: * OFFSET (input) INTEGER 35: * The number of rows of the matrix A that must be pivoted 36: * but no factorized. OFFSET >= 0. 37: * 38: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 39: * On entry, the M-by-N matrix A. 40: * On exit, the upper triangle of block A(OFFSET+1:M,1:N) is 41: * the triangular factor obtained; the elements in block 42: * A(OFFSET+1:M,1:N) below the diagonal, together with the 43: * array TAU, represent the orthogonal matrix Q as a product of 44: * elementary reflectors. Block A(1:OFFSET,1:N) has been 45: * accordingly pivoted, but no factorized. 46: * 47: * LDA (input) INTEGER 48: * The leading dimension of the array A. LDA >= max(1,M). 49: * 50: * JPVT (input/output) INTEGER array, dimension (N) 51: * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted 52: * to the front of A*P (a leading column); if JPVT(i) = 0, 53: * the i-th column of A is a free column. 54: * On exit, if JPVT(i) = k, then the i-th column of A*P 55: * was the k-th column of A. 56: * 57: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 58: * The scalar factors of the elementary reflectors. 59: * 60: * VN1 (input/output) DOUBLE PRECISION array, dimension (N) 61: * The vector with the partial column norms. 62: * 63: * VN2 (input/output) DOUBLE PRECISION array, dimension (N) 64: * The vector with the exact column norms. 65: * 66: * WORK (workspace) DOUBLE PRECISION array, dimension (N) 67: * 68: * Further Details 69: * =============== 70: * 71: * Based on contributions by 72: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain 73: * X. Sun, Computer Science Dept., Duke University, USA 74: * 75: * Partial column norm updating strategy modified by 76: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics, 77: * University of Zagreb, Croatia. 78: * June 2010 79: * For more details see LAPACK Working Note 176. 80: * ===================================================================== 81: * 82: * .. Parameters .. 83: DOUBLE PRECISION ZERO, ONE 84: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 85: * .. 86: * .. Local Scalars .. 87: INTEGER I, ITEMP, J, MN, OFFPI, PVT 88: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z 89: * .. 90: * .. External Subroutines .. 91: EXTERNAL DLARF, DLARFG, DSWAP 92: * .. 93: * .. Intrinsic Functions .. 94: INTRINSIC ABS, MAX, MIN, SQRT 95: * .. 96: * .. External Functions .. 97: INTEGER IDAMAX 98: DOUBLE PRECISION DLAMCH, DNRM2 99: EXTERNAL IDAMAX, DLAMCH, DNRM2 100: * .. 101: * .. Executable Statements .. 102: * 103: MN = MIN( M-OFFSET, N ) 104: TOL3Z = SQRT(DLAMCH('Epsilon')) 105: * 106: * Compute factorization. 107: * 108: DO 20 I = 1, MN 109: * 110: OFFPI = OFFSET + I 111: * 112: * Determine ith pivot column and swap if necessary. 113: * 114: PVT = ( I-1 ) + IDAMAX( N-I+1, VN1( I ), 1 ) 115: * 116: IF( PVT.NE.I ) THEN 117: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) 118: ITEMP = JPVT( PVT ) 119: JPVT( PVT ) = JPVT( I ) 120: JPVT( I ) = ITEMP 121: VN1( PVT ) = VN1( I ) 122: VN2( PVT ) = VN2( I ) 123: END IF 124: * 125: * Generate elementary reflector H(i). 126: * 127: IF( OFFPI.LT.M ) THEN 128: CALL DLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1, 129: $ TAU( I ) ) 130: ELSE 131: CALL DLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) ) 132: END IF 133: * 134: IF( I.LE.N ) THEN 135: * 136: * Apply H(i)' to A(offset+i:m,i+1:n) from the left. 137: * 138: AII = A( OFFPI, I ) 139: A( OFFPI, I ) = ONE 140: CALL DLARF( 'Left', M-OFFPI+1, N-I, A( OFFPI, I ), 1, 141: $ TAU( I ), A( OFFPI, I+1 ), LDA, WORK( 1 ) ) 142: A( OFFPI, I ) = AII 143: END IF 144: * 145: * Update partial column norms. 146: * 147: DO 10 J = I + 1, N 148: IF( VN1( J ).NE.ZERO ) THEN 149: * 150: * NOTE: The following 4 lines follow from the analysis in 151: * Lapack Working Note 176. 152: * 153: TEMP = ONE - ( ABS( A( OFFPI, J ) ) / VN1( J ) )**2 154: TEMP = MAX( TEMP, ZERO ) 155: TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2 156: IF( TEMP2 .LE. TOL3Z ) THEN 157: IF( OFFPI.LT.M ) THEN 158: VN1( J ) = DNRM2( M-OFFPI, A( OFFPI+1, J ), 1 ) 159: VN2( J ) = VN1( J ) 160: ELSE 161: VN1( J ) = ZERO 162: VN2( J ) = ZERO 163: END IF 164: ELSE 165: VN1( J ) = VN1( J )*SQRT( TEMP ) 166: END IF 167: END IF 168: 10 CONTINUE 169: * 170: 20 CONTINUE 171: * 172: RETURN 173: * 174: * End of DLAQP2 175: * 176: END