1 | *> \brief \b SLASSQ |
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2 | * |
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3 | * =========== DOCUMENTATION =========== |
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4 | * |
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5 | * Online html documentation available at |
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6 | * http://www.netlib.org/lapack/explore-html/ |
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7 | * |
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8 | *> \htmlonly |
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9 | *> Download SLASSQ + dependencies |
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10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slassq.f"> |
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11 | *> [TGZ]</a> |
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12 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slassq.f"> |
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13 | *> [ZIP]</a> |
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14 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slassq.f"> |
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15 | *> [TXT]</a> |
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16 | *> \endhtmlonly |
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17 | * |
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18 | * Definition: |
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19 | * =========== |
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20 | * |
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21 | * SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ ) |
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22 | * |
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23 | * .. Scalar Arguments .. |
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24 | * INTEGER INCX, N |
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25 | * REAL SCALE, SUMSQ |
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26 | * .. |
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27 | * .. Array Arguments .. |
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28 | * REAL X( * ) |
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29 | * .. |
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30 | * |
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31 | * |
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32 | *> \par Purpose: |
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33 | * ============= |
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34 | *> |
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35 | *> \verbatim |
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36 | *> |
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37 | *> SLASSQ returns the values scl and smsq such that |
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38 | *> |
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39 | *> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, |
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40 | *> |
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41 | *> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is |
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42 | *> assumed to be non-negative and scl returns the value |
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43 | *> |
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44 | *> scl = max( scale, abs( x( i ) ) ). |
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45 | *> |
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46 | *> scale and sumsq must be supplied in SCALE and SUMSQ and |
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47 | *> scl and smsq are overwritten on SCALE and SUMSQ respectively. |
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48 | *> |
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49 | *> The routine makes only one pass through the vector x. |
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50 | *> \endverbatim |
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51 | * |
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52 | * Arguments: |
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53 | * ========== |
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54 | * |
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55 | *> \param[in] N |
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56 | *> \verbatim |
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57 | *> N is INTEGER |
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58 | *> The number of elements to be used from the vector X. |
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59 | *> \endverbatim |
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60 | *> |
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61 | *> \param[in] X |
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62 | *> \verbatim |
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63 | *> X is REAL array, dimension (N) |
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64 | *> The vector for which a scaled sum of squares is computed. |
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65 | *> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. |
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66 | *> \endverbatim |
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67 | *> |
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68 | *> \param[in] INCX |
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69 | *> \verbatim |
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70 | *> INCX is INTEGER |
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71 | *> The increment between successive values of the vector X. |
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72 | *> INCX > 0. |
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73 | *> \endverbatim |
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74 | *> |
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75 | *> \param[in,out] SCALE |
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76 | *> \verbatim |
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77 | *> SCALE is REAL |
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78 | *> On entry, the value scale in the equation above. |
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79 | *> On exit, SCALE is overwritten with scl , the scaling factor |
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80 | *> for the sum of squares. |
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81 | *> \endverbatim |
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82 | *> |
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83 | *> \param[in,out] SUMSQ |
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84 | *> \verbatim |
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85 | *> SUMSQ is REAL |
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86 | *> On entry, the value sumsq in the equation above. |
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87 | *> On exit, SUMSQ is overwritten with smsq , the basic sum of |
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88 | *> squares from which scl has been factored out. |
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89 | *> \endverbatim |
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90 | * |
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91 | * Authors: |
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92 | * ======== |
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93 | * |
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94 | *> \author Univ. of Tennessee |
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95 | *> \author Univ. of California Berkeley |
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96 | *> \author Univ. of Colorado Denver |
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97 | *> \author NAG Ltd. |
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98 | * |
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99 | *> \date November 2011 |
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100 | * |
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101 | *> \ingroup auxOTHERauxiliary |
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102 | * |
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103 | * ===================================================================== |
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104 | SUBROUTINE SLASSQ( N, X, INCX, SCALE, SUMSQ ) |
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105 | * |
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106 | * -- LAPACK auxiliary routine (version 3.4.0) -- |
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107 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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108 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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109 | * November 2011 |
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110 | * |
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111 | * .. Scalar Arguments .. |
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112 | INTEGER INCX, N |
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113 | REAL SCALE, SUMSQ |
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114 | * .. |
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115 | * .. Array Arguments .. |
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116 | REAL X( * ) |
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117 | * .. |
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118 | * |
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119 | * ===================================================================== |
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120 | * |
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121 | * .. Parameters .. |
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122 | REAL ZERO |
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123 | PARAMETER ( ZERO = 0.0E+0 ) |
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124 | * .. |
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125 | * .. Local Scalars .. |
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126 | INTEGER IX |
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127 | REAL ABSXI |
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128 | * .. |
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129 | * .. Intrinsic Functions .. |
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130 | INTRINSIC ABS |
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131 | * .. |
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132 | * .. Executable Statements .. |
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133 | * |
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134 | IF( N.GT.0 ) THEN |
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135 | DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX |
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136 | IF( X( IX ).NE.ZERO ) THEN |
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137 | ABSXI = ABS( X( IX ) ) |
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138 | IF( SCALE.LT.ABSXI ) THEN |
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139 | SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 |
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140 | SCALE = ABSXI |
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141 | ELSE |
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142 | SUMSQ = SUMSQ + ( ABSXI / SCALE )**2 |
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143 | END IF |
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144 | END IF |
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145 | 10 CONTINUE |
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146 | END IF |
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147 | RETURN |
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148 | * |
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149 | * End of SLASSQ |
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150 | * |
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151 | END |
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