root / src / lapack / double / dlarfg.f @ 1
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| 1 | 1 | equemene | SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | INTEGER INCX, N |
| 10 | 1 | equemene | DOUBLE PRECISION ALPHA, TAU |
| 11 | 1 | equemene | * .. |
| 12 | 1 | equemene | * .. Array Arguments .. |
| 13 | 1 | equemene | DOUBLE PRECISION X( * ) |
| 14 | 1 | equemene | * .. |
| 15 | 1 | equemene | * |
| 16 | 1 | equemene | * Purpose |
| 17 | 1 | equemene | * ======= |
| 18 | 1 | equemene | * |
| 19 | 1 | equemene | * DLARFG generates a real elementary reflector H of order n, such |
| 20 | 1 | equemene | * that |
| 21 | 1 | equemene | * |
| 22 | 1 | equemene | * H * ( alpha ) = ( beta ), H' * H = I. |
| 23 | 1 | equemene | * ( x ) ( 0 ) |
| 24 | 1 | equemene | * |
| 25 | 1 | equemene | * where alpha and beta are scalars, and x is an (n-1)-element real |
| 26 | 1 | equemene | * vector. H is represented in the form |
| 27 | 1 | equemene | * |
| 28 | 1 | equemene | * H = I - tau * ( 1 ) * ( 1 v' ) , |
| 29 | 1 | equemene | * ( v ) |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * where tau is a real scalar and v is a real (n-1)-element |
| 32 | 1 | equemene | * vector. |
| 33 | 1 | equemene | * |
| 34 | 1 | equemene | * If the elements of x are all zero, then tau = 0 and H is taken to be |
| 35 | 1 | equemene | * the unit matrix. |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * Otherwise 1 <= tau <= 2. |
| 38 | 1 | equemene | * |
| 39 | 1 | equemene | * Arguments |
| 40 | 1 | equemene | * ========= |
| 41 | 1 | equemene | * |
| 42 | 1 | equemene | * N (input) INTEGER |
| 43 | 1 | equemene | * The order of the elementary reflector. |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * ALPHA (input/output) DOUBLE PRECISION |
| 46 | 1 | equemene | * On entry, the value alpha. |
| 47 | 1 | equemene | * On exit, it is overwritten with the value beta. |
| 48 | 1 | equemene | * |
| 49 | 1 | equemene | * X (input/output) DOUBLE PRECISION array, dimension |
| 50 | 1 | equemene | * (1+(N-2)*abs(INCX)) |
| 51 | 1 | equemene | * On entry, the vector x. |
| 52 | 1 | equemene | * On exit, it is overwritten with the vector v. |
| 53 | 1 | equemene | * |
| 54 | 1 | equemene | * INCX (input) INTEGER |
| 55 | 1 | equemene | * The increment between elements of X. INCX > 0. |
| 56 | 1 | equemene | * |
| 57 | 1 | equemene | * TAU (output) DOUBLE PRECISION |
| 58 | 1 | equemene | * The value tau. |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * ===================================================================== |
| 61 | 1 | equemene | * |
| 62 | 1 | equemene | * .. Parameters .. |
| 63 | 1 | equemene | DOUBLE PRECISION ONE, ZERO |
| 64 | 1 | equemene | PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
| 65 | 1 | equemene | * .. |
| 66 | 1 | equemene | * .. Local Scalars .. |
| 67 | 1 | equemene | INTEGER J, KNT |
| 68 | 1 | equemene | DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM |
| 69 | 1 | equemene | * .. |
| 70 | 1 | equemene | * .. External Functions .. |
| 71 | 1 | equemene | DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 |
| 72 | 1 | equemene | EXTERNAL DLAMCH, DLAPY2, DNRM2 |
| 73 | 1 | equemene | * .. |
| 74 | 1 | equemene | * .. Intrinsic Functions .. |
| 75 | 1 | equemene | INTRINSIC ABS, SIGN |
| 76 | 1 | equemene | * .. |
| 77 | 1 | equemene | * .. External Subroutines .. |
| 78 | 1 | equemene | EXTERNAL DSCAL |
| 79 | 1 | equemene | * .. |
| 80 | 1 | equemene | * .. Executable Statements .. |
| 81 | 1 | equemene | * |
| 82 | 1 | equemene | IF( N.LE.1 ) THEN |
| 83 | 1 | equemene | TAU = ZERO |
| 84 | 1 | equemene | RETURN |
| 85 | 1 | equemene | END IF |
| 86 | 1 | equemene | * |
| 87 | 1 | equemene | XNORM = DNRM2( N-1, X, INCX ) |
| 88 | 1 | equemene | * |
| 89 | 1 | equemene | IF( XNORM.EQ.ZERO ) THEN |
| 90 | 1 | equemene | * |
| 91 | 1 | equemene | * H = I |
| 92 | 1 | equemene | * |
| 93 | 1 | equemene | TAU = ZERO |
| 94 | 1 | equemene | ELSE |
| 95 | 1 | equemene | * |
| 96 | 1 | equemene | * general case |
| 97 | 1 | equemene | * |
| 98 | 1 | equemene | BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) |
| 99 | 1 | equemene | SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) |
| 100 | 1 | equemene | KNT = 0 |
| 101 | 1 | equemene | IF( ABS( BETA ).LT.SAFMIN ) THEN |
| 102 | 1 | equemene | * |
| 103 | 1 | equemene | * XNORM, BETA may be inaccurate; scale X and recompute them |
| 104 | 1 | equemene | * |
| 105 | 1 | equemene | RSAFMN = ONE / SAFMIN |
| 106 | 1 | equemene | 10 CONTINUE |
| 107 | 1 | equemene | KNT = KNT + 1 |
| 108 | 1 | equemene | CALL DSCAL( N-1, RSAFMN, X, INCX ) |
| 109 | 1 | equemene | BETA = BETA*RSAFMN |
| 110 | 1 | equemene | ALPHA = ALPHA*RSAFMN |
| 111 | 1 | equemene | IF( ABS( BETA ).LT.SAFMIN ) |
| 112 | 1 | equemene | $ GO TO 10 |
| 113 | 1 | equemene | * |
| 114 | 1 | equemene | * New BETA is at most 1, at least SAFMIN |
| 115 | 1 | equemene | * |
| 116 | 1 | equemene | XNORM = DNRM2( N-1, X, INCX ) |
| 117 | 1 | equemene | BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) |
| 118 | 1 | equemene | END IF |
| 119 | 1 | equemene | TAU = ( BETA-ALPHA ) / BETA |
| 120 | 1 | equemene | CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | * If ALPHA is subnormal, it may lose relative accuracy |
| 123 | 1 | equemene | * |
| 124 | 1 | equemene | DO 20 J = 1, KNT |
| 125 | 1 | equemene | BETA = BETA*SAFMIN |
| 126 | 1 | equemene | 20 CONTINUE |
| 127 | 1 | equemene | ALPHA = BETA |
| 128 | 1 | equemene | END IF |
| 129 | 1 | equemene | * |
| 130 | 1 | equemene | RETURN |
| 131 | 1 | equemene | * |
| 132 | 1 | equemene | * End of DLARFG |
| 133 | 1 | equemene | * |
| 134 | 1 | equemene | END |