root / src / lapack / double / dlarf.f @ 1
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| 1 | 1 | equemene | SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
|---|---|---|---|
| 2 | 1 | equemene | IMPLICIT NONE |
| 3 | 1 | equemene | * |
| 4 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2) -- |
| 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 | * November 2006 |
| 8 | 1 | equemene | * |
| 9 | 1 | equemene | * .. Scalar Arguments .. |
| 10 | 1 | equemene | CHARACTER SIDE |
| 11 | 1 | equemene | INTEGER INCV, LDC, M, N |
| 12 | 1 | equemene | DOUBLE PRECISION TAU |
| 13 | 1 | equemene | * .. |
| 14 | 1 | equemene | * .. Array Arguments .. |
| 15 | 1 | equemene | DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) |
| 16 | 1 | equemene | * .. |
| 17 | 1 | equemene | * |
| 18 | 1 | equemene | * Purpose |
| 19 | 1 | equemene | * ======= |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * DLARF applies a real elementary reflector H to a real m by n matrix |
| 22 | 1 | equemene | * C, from either the left or the right. H is represented in the form |
| 23 | 1 | equemene | * |
| 24 | 1 | equemene | * H = I - tau * v * v' |
| 25 | 1 | equemene | * |
| 26 | 1 | equemene | * where tau is a real scalar and v is a real vector. |
| 27 | 1 | equemene | * |
| 28 | 1 | equemene | * If tau = 0, then H is taken to be the unit matrix. |
| 29 | 1 | equemene | * |
| 30 | 1 | equemene | * Arguments |
| 31 | 1 | equemene | * ========= |
| 32 | 1 | equemene | * |
| 33 | 1 | equemene | * SIDE (input) CHARACTER*1 |
| 34 | 1 | equemene | * = 'L': form H * C |
| 35 | 1 | equemene | * = 'R': form C * H |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * M (input) INTEGER |
| 38 | 1 | equemene | * The number of rows of the matrix C. |
| 39 | 1 | equemene | * |
| 40 | 1 | equemene | * N (input) INTEGER |
| 41 | 1 | equemene | * The number of columns of the matrix C. |
| 42 | 1 | equemene | * |
| 43 | 1 | equemene | * V (input) DOUBLE PRECISION array, dimension |
| 44 | 1 | equemene | * (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
| 45 | 1 | equemene | * or (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
| 46 | 1 | equemene | * The vector v in the representation of H. V is not used if |
| 47 | 1 | equemene | * TAU = 0. |
| 48 | 1 | equemene | * |
| 49 | 1 | equemene | * INCV (input) INTEGER |
| 50 | 1 | equemene | * The increment between elements of v. INCV <> 0. |
| 51 | 1 | equemene | * |
| 52 | 1 | equemene | * TAU (input) DOUBLE PRECISION |
| 53 | 1 | equemene | * The value tau in the representation of H. |
| 54 | 1 | equemene | * |
| 55 | 1 | equemene | * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
| 56 | 1 | equemene | * On entry, the m by n matrix C. |
| 57 | 1 | equemene | * On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
| 58 | 1 | equemene | * or C * H if SIDE = 'R'. |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * LDC (input) INTEGER |
| 61 | 1 | equemene | * The leading dimension of the array C. LDC >= max(1,M). |
| 62 | 1 | equemene | * |
| 63 | 1 | equemene | * WORK (workspace) DOUBLE PRECISION array, dimension |
| 64 | 1 | equemene | * (N) if SIDE = 'L' |
| 65 | 1 | equemene | * or (M) if SIDE = 'R' |
| 66 | 1 | equemene | * |
| 67 | 1 | equemene | * ===================================================================== |
| 68 | 1 | equemene | * |
| 69 | 1 | equemene | * .. Parameters .. |
| 70 | 1 | equemene | DOUBLE PRECISION ONE, ZERO |
| 71 | 1 | equemene | PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
| 72 | 1 | equemene | * .. |
| 73 | 1 | equemene | * .. Local Scalars .. |
| 74 | 1 | equemene | LOGICAL APPLYLEFT |
| 75 | 1 | equemene | INTEGER I, LASTV, LASTC |
| 76 | 1 | equemene | * .. |
| 77 | 1 | equemene | * .. External Subroutines .. |
| 78 | 1 | equemene | EXTERNAL DGEMV, DGER |
| 79 | 1 | equemene | * .. |
| 80 | 1 | equemene | * .. External Functions .. |
| 81 | 1 | equemene | LOGICAL LSAME |
| 82 | 1 | equemene | INTEGER ILADLR, ILADLC |
| 83 | 1 | equemene | EXTERNAL LSAME, ILADLR, ILADLC |
| 84 | 1 | equemene | * .. |
| 85 | 1 | equemene | * .. Executable Statements .. |
| 86 | 1 | equemene | * |
| 87 | 1 | equemene | APPLYLEFT = LSAME( SIDE, 'L' ) |
| 88 | 1 | equemene | LASTV = 0 |
| 89 | 1 | equemene | LASTC = 0 |
| 90 | 1 | equemene | IF( TAU.NE.ZERO ) THEN |
| 91 | 1 | equemene | ! Set up variables for scanning V. LASTV begins pointing to the end |
| 92 | 1 | equemene | ! of V. |
| 93 | 1 | equemene | IF( APPLYLEFT ) THEN |
| 94 | 1 | equemene | LASTV = M |
| 95 | 1 | equemene | ELSE |
| 96 | 1 | equemene | LASTV = N |
| 97 | 1 | equemene | END IF |
| 98 | 1 | equemene | IF( INCV.GT.0 ) THEN |
| 99 | 1 | equemene | I = 1 + (LASTV-1) * INCV |
| 100 | 1 | equemene | ELSE |
| 101 | 1 | equemene | I = 1 |
| 102 | 1 | equemene | END IF |
| 103 | 1 | equemene | ! Look for the last non-zero row in V. |
| 104 | 1 | equemene | DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) |
| 105 | 1 | equemene | LASTV = LASTV - 1 |
| 106 | 1 | equemene | I = I - INCV |
| 107 | 1 | equemene | END DO |
| 108 | 1 | equemene | IF( APPLYLEFT ) THEN |
| 109 | 1 | equemene | ! Scan for the last non-zero column in C(1:lastv,:). |
| 110 | 1 | equemene | LASTC = ILADLC(LASTV, N, C, LDC) |
| 111 | 1 | equemene | ELSE |
| 112 | 1 | equemene | ! Scan for the last non-zero row in C(:,1:lastv). |
| 113 | 1 | equemene | LASTC = ILADLR(M, LASTV, C, LDC) |
| 114 | 1 | equemene | END IF |
| 115 | 1 | equemene | END IF |
| 116 | 1 | equemene | ! Note that lastc.eq.0 renders the BLAS operations null; no special |
| 117 | 1 | equemene | ! case is needed at this level. |
| 118 | 1 | equemene | IF( APPLYLEFT ) THEN |
| 119 | 1 | equemene | * |
| 120 | 1 | equemene | * Form H * C |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | IF( LASTV.GT.0 ) THEN |
| 123 | 1 | equemene | * |
| 124 | 1 | equemene | * w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) |
| 125 | 1 | equemene | * |
| 126 | 1 | equemene | CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, |
| 127 | 1 | equemene | $ ZERO, WORK, 1 ) |
| 128 | 1 | equemene | * |
| 129 | 1 | equemene | * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' |
| 130 | 1 | equemene | * |
| 131 | 1 | equemene | CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) |
| 132 | 1 | equemene | END IF |
| 133 | 1 | equemene | ELSE |
| 134 | 1 | equemene | * |
| 135 | 1 | equemene | * Form C * H |
| 136 | 1 | equemene | * |
| 137 | 1 | equemene | IF( LASTV.GT.0 ) THEN |
| 138 | 1 | equemene | * |
| 139 | 1 | equemene | * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) |
| 140 | 1 | equemene | * |
| 141 | 1 | equemene | CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, |
| 142 | 1 | equemene | $ V, INCV, ZERO, WORK, 1 ) |
| 143 | 1 | equemene | * |
| 144 | 1 | equemene | * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' |
| 145 | 1 | equemene | * |
| 146 | 1 | equemene | CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) |
| 147 | 1 | equemene | END IF |
| 148 | 1 | equemene | END IF |
| 149 | 1 | equemene | RETURN |
| 150 | 1 | equemene | * |
| 151 | 1 | equemene | * End of DLARF |
| 152 | 1 | equemene | * |
| 153 | 1 | equemene | END |