root / src / lapack / double / dlaqp2.f @ 2
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| 1 | 1 | equemene | SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, |
|---|---|---|---|
| 2 | 1 | equemene | $ WORK ) |
| 3 | 1 | equemene | * |
| 4 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2.2) -- |
| 5 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 6 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 7 | 1 | equemene | * June 2010 |
| 8 | 1 | equemene | * |
| 9 | 1 | equemene | * .. Scalar Arguments .. |
| 10 | 1 | equemene | INTEGER LDA, M, N, OFFSET |
| 11 | 1 | equemene | * .. |
| 12 | 1 | equemene | * .. Array Arguments .. |
| 13 | 1 | equemene | INTEGER JPVT( * ) |
| 14 | 1 | equemene | DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), |
| 15 | 1 | equemene | $ WORK( * ) |
| 16 | 1 | equemene | * .. |
| 17 | 1 | equemene | * |
| 18 | 1 | equemene | * Purpose |
| 19 | 1 | equemene | * ======= |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * DLAQP2 computes a QR factorization with column pivoting of |
| 22 | 1 | equemene | * the block A(OFFSET+1:M,1:N). |
| 23 | 1 | equemene | * The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. |
| 24 | 1 | equemene | * |
| 25 | 1 | equemene | * Arguments |
| 26 | 1 | equemene | * ========= |
| 27 | 1 | equemene | * |
| 28 | 1 | equemene | * M (input) INTEGER |
| 29 | 1 | equemene | * The number of rows of the matrix A. M >= 0. |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * N (input) INTEGER |
| 32 | 1 | equemene | * The number of columns of the matrix A. N >= 0. |
| 33 | 1 | equemene | * |
| 34 | 1 | equemene | * OFFSET (input) INTEGER |
| 35 | 1 | equemene | * The number of rows of the matrix A that must be pivoted |
| 36 | 1 | equemene | * but no factorized. OFFSET >= 0. |
| 37 | 1 | equemene | * |
| 38 | 1 | equemene | * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
| 39 | 1 | equemene | * On entry, the M-by-N matrix A. |
| 40 | 1 | equemene | * On exit, the upper triangle of block A(OFFSET+1:M,1:N) is |
| 41 | 1 | equemene | * the triangular factor obtained; the elements in block |
| 42 | 1 | equemene | * A(OFFSET+1:M,1:N) below the diagonal, together with the |
| 43 | 1 | equemene | * array TAU, represent the orthogonal matrix Q as a product of |
| 44 | 1 | equemene | * elementary reflectors. Block A(1:OFFSET,1:N) has been |
| 45 | 1 | equemene | * accordingly pivoted, but no factorized. |
| 46 | 1 | equemene | * |
| 47 | 1 | equemene | * LDA (input) INTEGER |
| 48 | 1 | equemene | * The leading dimension of the array A. LDA >= max(1,M). |
| 49 | 1 | equemene | * |
| 50 | 1 | equemene | * JPVT (input/output) INTEGER array, dimension (N) |
| 51 | 1 | equemene | * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted |
| 52 | 1 | equemene | * to the front of A*P (a leading column); if JPVT(i) = 0, |
| 53 | 1 | equemene | * the i-th column of A is a free column. |
| 54 | 1 | equemene | * On exit, if JPVT(i) = k, then the i-th column of A*P |
| 55 | 1 | equemene | * was the k-th column of A. |
| 56 | 1 | equemene | * |
| 57 | 1 | equemene | * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) |
| 58 | 1 | equemene | * The scalar factors of the elementary reflectors. |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * VN1 (input/output) DOUBLE PRECISION array, dimension (N) |
| 61 | 1 | equemene | * The vector with the partial column norms. |
| 62 | 1 | equemene | * |
| 63 | 1 | equemene | * VN2 (input/output) DOUBLE PRECISION array, dimension (N) |
| 64 | 1 | equemene | * The vector with the exact column norms. |
| 65 | 1 | equemene | * |
| 66 | 1 | equemene | * WORK (workspace) DOUBLE PRECISION array, dimension (N) |
| 67 | 1 | equemene | * |
| 68 | 1 | equemene | * Further Details |
| 69 | 1 | equemene | * =============== |
| 70 | 1 | equemene | * |
| 71 | 1 | equemene | * Based on contributions by |
| 72 | 1 | equemene | * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain |
| 73 | 1 | equemene | * X. Sun, Computer Science Dept., Duke University, USA |
| 74 | 1 | equemene | * |
| 75 | 1 | equemene | * Partial column norm updating strategy modified by |
| 76 | 1 | equemene | * Z. Drmac and Z. Bujanovic, Dept. of Mathematics, |
| 77 | 1 | equemene | * University of Zagreb, Croatia. |
| 78 | 1 | equemene | * June 2010 |
| 79 | 1 | equemene | * For more details see LAPACK Working Note 176. |
| 80 | 1 | equemene | * ===================================================================== |
| 81 | 1 | equemene | * |
| 82 | 1 | equemene | * .. Parameters .. |
| 83 | 1 | equemene | DOUBLE PRECISION ZERO, ONE |
| 84 | 1 | equemene | PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) |
| 85 | 1 | equemene | * .. |
| 86 | 1 | equemene | * .. Local Scalars .. |
| 87 | 1 | equemene | INTEGER I, ITEMP, J, MN, OFFPI, PVT |
| 88 | 1 | equemene | DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z |
| 89 | 1 | equemene | * .. |
| 90 | 1 | equemene | * .. External Subroutines .. |
| 91 | 1 | equemene | EXTERNAL DLARF, DLARFG, DSWAP |
| 92 | 1 | equemene | * .. |
| 93 | 1 | equemene | * .. Intrinsic Functions .. |
| 94 | 1 | equemene | INTRINSIC ABS, MAX, MIN, SQRT |
| 95 | 1 | equemene | * .. |
| 96 | 1 | equemene | * .. External Functions .. |
| 97 | 1 | equemene | INTEGER IDAMAX |
| 98 | 1 | equemene | DOUBLE PRECISION DLAMCH, DNRM2 |
| 99 | 1 | equemene | EXTERNAL IDAMAX, DLAMCH, DNRM2 |
| 100 | 1 | equemene | * .. |
| 101 | 1 | equemene | * .. Executable Statements .. |
| 102 | 1 | equemene | * |
| 103 | 1 | equemene | MN = MIN( M-OFFSET, N ) |
| 104 | 1 | equemene | TOL3Z = SQRT(DLAMCH('Epsilon'))
|
| 105 | 1 | equemene | * |
| 106 | 1 | equemene | * Compute factorization. |
| 107 | 1 | equemene | * |
| 108 | 1 | equemene | DO 20 I = 1, MN |
| 109 | 1 | equemene | * |
| 110 | 1 | equemene | OFFPI = OFFSET + I |
| 111 | 1 | equemene | * |
| 112 | 1 | equemene | * Determine ith pivot column and swap if necessary. |
| 113 | 1 | equemene | * |
| 114 | 1 | equemene | PVT = ( I-1 ) + IDAMAX( N-I+1, VN1( I ), 1 ) |
| 115 | 1 | equemene | * |
| 116 | 1 | equemene | IF( PVT.NE.I ) THEN |
| 117 | 1 | equemene | CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) |
| 118 | 1 | equemene | ITEMP = JPVT( PVT ) |
| 119 | 1 | equemene | JPVT( PVT ) = JPVT( I ) |
| 120 | 1 | equemene | JPVT( I ) = ITEMP |
| 121 | 1 | equemene | VN1( PVT ) = VN1( I ) |
| 122 | 1 | equemene | VN2( PVT ) = VN2( I ) |
| 123 | 1 | equemene | END IF |
| 124 | 1 | equemene | * |
| 125 | 1 | equemene | * Generate elementary reflector H(i). |
| 126 | 1 | equemene | * |
| 127 | 1 | equemene | IF( OFFPI.LT.M ) THEN |
| 128 | 1 | equemene | CALL DLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1, |
| 129 | 1 | equemene | $ TAU( I ) ) |
| 130 | 1 | equemene | ELSE |
| 131 | 1 | equemene | CALL DLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) ) |
| 132 | 1 | equemene | END IF |
| 133 | 1 | equemene | * |
| 134 | 1 | equemene | IF( I.LE.N ) THEN |
| 135 | 1 | equemene | * |
| 136 | 1 | equemene | * Apply H(i)' to A(offset+i:m,i+1:n) from the left. |
| 137 | 1 | equemene | * |
| 138 | 1 | equemene | AII = A( OFFPI, I ) |
| 139 | 1 | equemene | A( OFFPI, I ) = ONE |
| 140 | 1 | equemene | CALL DLARF( 'Left', M-OFFPI+1, N-I, A( OFFPI, I ), 1, |
| 141 | 1 | equemene | $ TAU( I ), A( OFFPI, I+1 ), LDA, WORK( 1 ) ) |
| 142 | 1 | equemene | A( OFFPI, I ) = AII |
| 143 | 1 | equemene | END IF |
| 144 | 1 | equemene | * |
| 145 | 1 | equemene | * Update partial column norms. |
| 146 | 1 | equemene | * |
| 147 | 1 | equemene | DO 10 J = I + 1, N |
| 148 | 1 | equemene | IF( VN1( J ).NE.ZERO ) THEN |
| 149 | 1 | equemene | * |
| 150 | 1 | equemene | * NOTE: The following 4 lines follow from the analysis in |
| 151 | 1 | equemene | * Lapack Working Note 176. |
| 152 | 1 | equemene | * |
| 153 | 1 | equemene | TEMP = ONE - ( ABS( A( OFFPI, J ) ) / VN1( J ) )**2 |
| 154 | 1 | equemene | TEMP = MAX( TEMP, ZERO ) |
| 155 | 1 | equemene | TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2 |
| 156 | 1 | equemene | IF( TEMP2 .LE. TOL3Z ) THEN |
| 157 | 1 | equemene | IF( OFFPI.LT.M ) THEN |
| 158 | 1 | equemene | VN1( J ) = DNRM2( M-OFFPI, A( OFFPI+1, J ), 1 ) |
| 159 | 1 | equemene | VN2( J ) = VN1( J ) |
| 160 | 1 | equemene | ELSE |
| 161 | 1 | equemene | VN1( J ) = ZERO |
| 162 | 1 | equemene | VN2( J ) = ZERO |
| 163 | 1 | equemene | END IF |
| 164 | 1 | equemene | ELSE |
| 165 | 1 | equemene | VN1( J ) = VN1( J )*SQRT( TEMP ) |
| 166 | 1 | equemene | END IF |
| 167 | 1 | equemene | END IF |
| 168 | 1 | equemene | 10 CONTINUE |
| 169 | 1 | equemene | * |
| 170 | 1 | equemene | 20 CONTINUE |
| 171 | 1 | equemene | * |
| 172 | 1 | equemene | RETURN |
| 173 | 1 | equemene | * |
| 174 | 1 | equemene | * End of DLAQP2 |
| 175 | 1 | equemene | * |
| 176 | 1 | equemene | END |