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annotate libcruft/lapack/clarfg.f @ 8596:8833c0b18eb2

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enable default settings queries in optim funcs
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 27 Jan 2009 08:15:08 +0100
parents 82be108cc558
children
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1 SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )
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2 *
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3 * -- LAPACK auxiliary routine (version 3.1) --
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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5 * November 2006
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6 *
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7 * .. Scalar Arguments ..
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8 INTEGER INCX, N
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9 COMPLEX ALPHA, TAU
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10 * ..
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11 * .. Array Arguments ..
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12 COMPLEX X( * )
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13 * ..
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14 *
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15 * Purpose
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16 * =======
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17 *
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18 * CLARFG generates a complex elementary reflector H of order n, such
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19 * that
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20 *
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21 * H' * ( alpha ) = ( beta ), H' * H = I.
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22 * ( x ) ( 0 )
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23 *
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24 * where alpha and beta are scalars, with beta real, and x is an
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25 * (n-1)-element complex vector. H is represented in the form
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26 *
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27 * H = I - tau * ( 1 ) * ( 1 v' ) ,
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28 * ( v )
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29 *
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30 * where tau is a complex scalar and v is a complex (n-1)-element
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31 * vector. Note that H is not hermitian.
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32 *
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33 * If the elements of x are all zero and alpha is real, then tau = 0
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34 * and H is taken to be the unit matrix.
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35 *
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36 * Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .
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37 *
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38 * Arguments
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39 * =========
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40 *
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41 * N (input) INTEGER
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42 * The order of the elementary reflector.
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43 *
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44 * ALPHA (input/output) COMPLEX
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45 * On entry, the value alpha.
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46 * On exit, it is overwritten with the value beta.
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47 *
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48 * X (input/output) COMPLEX array, dimension
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49 * (1+(N-2)*abs(INCX))
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50 * On entry, the vector x.
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51 * On exit, it is overwritten with the vector v.
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52 *
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53 * INCX (input) INTEGER
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54 * The increment between elements of X. INCX > 0.
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55 *
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56 * TAU (output) COMPLEX
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57 * The value tau.
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58 *
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59 * =====================================================================
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60 *
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61 * .. Parameters ..
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62 REAL ONE, ZERO
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63 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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64 * ..
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65 * .. Local Scalars ..
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66 INTEGER J, KNT
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67 REAL ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM
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68 * ..
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69 * .. External Functions ..
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70 REAL SCNRM2, SLAMCH, SLAPY3
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71 COMPLEX CLADIV
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72 EXTERNAL SCNRM2, SLAMCH, SLAPY3, CLADIV
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73 * ..
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74 * .. Intrinsic Functions ..
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75 INTRINSIC ABS, AIMAG, CMPLX, REAL, SIGN
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76 * ..
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77 * .. External Subroutines ..
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78 EXTERNAL CSCAL, CSSCAL
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79 * ..
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80 * .. Executable Statements ..
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81 *
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82 IF( N.LE.0 ) THEN
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83 TAU = ZERO
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84 RETURN
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85 END IF
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86 *
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87 XNORM = SCNRM2( N-1, X, INCX )
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88 ALPHR = REAL( ALPHA )
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89 ALPHI = AIMAG( ALPHA )
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90 *
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91 IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN
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92 *
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93 * H = I
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94 *
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95 TAU = ZERO
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96 ELSE
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97 *
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98 * general case
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99 *
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100 BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
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101 SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' )
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102 RSAFMN = ONE / SAFMIN
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103 *
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104 IF( ABS( BETA ).LT.SAFMIN ) THEN
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105 *
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106 * XNORM, BETA may be inaccurate; scale X and recompute them
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107 *
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108 KNT = 0
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109 10 CONTINUE
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110 KNT = KNT + 1
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111 CALL CSSCAL( N-1, RSAFMN, X, INCX )
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112 BETA = BETA*RSAFMN
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113 ALPHI = ALPHI*RSAFMN
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114 ALPHR = ALPHR*RSAFMN
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115 IF( ABS( BETA ).LT.SAFMIN )
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116 $ GO TO 10
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117 *
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118 * New BETA is at most 1, at least SAFMIN
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119 *
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120 XNORM = SCNRM2( N-1, X, INCX )
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121 ALPHA = CMPLX( ALPHR, ALPHI )
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122 BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
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123 TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )
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124 ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA )
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125 CALL CSCAL( N-1, ALPHA, X, INCX )
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126 *
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127 * If ALPHA is subnormal, it may lose relative accuracy
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128 *
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129 ALPHA = BETA
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130 DO 20 J = 1, KNT
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131 ALPHA = ALPHA*SAFMIN
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132 20 CONTINUE
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133 ELSE
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134 TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )
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135 ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA )
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136 CALL CSCAL( N-1, ALPHA, X, INCX )
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137 ALPHA = BETA
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138 END IF
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139 END IF
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140 *
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141 RETURN
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142 *
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143 * End of CLARFG
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144 *
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145 END