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annotate libcruft/lapack/clanhe.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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7789
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1 REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )
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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 CHARACTER NORM, UPLO
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9 INTEGER LDA, N
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10 * ..
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11 * .. Array Arguments ..
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12 REAL WORK( * )
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13 COMPLEX A( LDA, * )
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14 * ..
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15 *
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16 * Purpose
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17 * =======
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18 *
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19 * CLANHE returns the value of the one norm, or the Frobenius norm, or
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20 * the infinity norm, or the element of largest absolute value of a
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21 * complex hermitian matrix A.
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22 *
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23 * Description
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24 * ===========
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25 *
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26 * CLANHE returns the value
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27 *
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28 * CLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
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29 * (
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30 * ( norm1(A), NORM = '1', 'O' or 'o'
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31 * (
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32 * ( normI(A), NORM = 'I' or 'i'
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33 * (
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34 * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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35 *
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36 * where norm1 denotes the one norm of a matrix (maximum column sum),
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37 * normI denotes the infinity norm of a matrix (maximum row sum) and
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38 * normF denotes the Frobenius norm of a matrix (square root of sum of
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39 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
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40 *
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41 * Arguments
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42 * =========
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43 *
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44 * NORM (input) CHARACTER*1
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45 * Specifies the value to be returned in CLANHE as described
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46 * above.
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47 *
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48 * UPLO (input) CHARACTER*1
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49 * Specifies whether the upper or lower triangular part of the
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50 * hermitian matrix A is to be referenced.
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51 * = 'U': Upper triangular part of A is referenced
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52 * = 'L': Lower triangular part of A is referenced
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53 *
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54 * N (input) INTEGER
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55 * The order of the matrix A. N >= 0. When N = 0, CLANHE is
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56 * set to zero.
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57 *
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58 * A (input) COMPLEX array, dimension (LDA,N)
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59 * The hermitian matrix A. If UPLO = 'U', the leading n by n
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60 * upper triangular part of A contains the upper triangular part
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61 * of the matrix A, and the strictly lower triangular part of A
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62 * is not referenced. If UPLO = 'L', the leading n by n lower
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63 * triangular part of A contains the lower triangular part of
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64 * the matrix A, and the strictly upper triangular part of A is
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65 * not referenced. Note that the imaginary parts of the diagonal
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66 * elements need not be set and are assumed to be zero.
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67 *
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68 * LDA (input) INTEGER
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69 * The leading dimension of the array A. LDA >= max(N,1).
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70 *
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71 * WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
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72 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
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73 * WORK is not referenced.
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74 *
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75 * =====================================================================
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76 *
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77 * .. Parameters ..
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78 REAL ONE, ZERO
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79 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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80 * ..
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81 * .. Local Scalars ..
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82 INTEGER I, J
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83 REAL ABSA, SCALE, SUM, VALUE
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84 * ..
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85 * .. External Functions ..
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86 LOGICAL LSAME
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87 EXTERNAL LSAME
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88 * ..
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89 * .. External Subroutines ..
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90 EXTERNAL CLASSQ
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91 * ..
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92 * .. Intrinsic Functions ..
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93 INTRINSIC ABS, MAX, REAL, SQRT
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94 * ..
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95 * .. Executable Statements ..
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96 *
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97 IF( N.EQ.0 ) THEN
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98 VALUE = ZERO
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99 ELSE IF( LSAME( NORM, 'M' ) ) THEN
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100 *
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101 * Find max(abs(A(i,j))).
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102 *
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103 VALUE = ZERO
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104 IF( LSAME( UPLO, 'U' ) ) THEN
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105 DO 20 J = 1, N
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106 DO 10 I = 1, J - 1
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107 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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108 10 CONTINUE
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109 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) )
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110 20 CONTINUE
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111 ELSE
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112 DO 40 J = 1, N
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113 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) )
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114 DO 30 I = J + 1, N
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115 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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116 30 CONTINUE
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117 40 CONTINUE
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118 END IF
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119 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
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120 $ ( NORM.EQ.'1' ) ) THEN
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121 *
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122 * Find normI(A) ( = norm1(A), since A is hermitian).
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123 *
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124 VALUE = ZERO
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125 IF( LSAME( UPLO, 'U' ) ) THEN
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126 DO 60 J = 1, N
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127 SUM = ZERO
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128 DO 50 I = 1, J - 1
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129 ABSA = ABS( A( I, J ) )
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130 SUM = SUM + ABSA
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131 WORK( I ) = WORK( I ) + ABSA
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132 50 CONTINUE
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133 WORK( J ) = SUM + ABS( REAL( A( J, J ) ) )
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134 60 CONTINUE
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135 DO 70 I = 1, N
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136 VALUE = MAX( VALUE, WORK( I ) )
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137 70 CONTINUE
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138 ELSE
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139 DO 80 I = 1, N
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140 WORK( I ) = ZERO
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141 80 CONTINUE
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142 DO 100 J = 1, N
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143 SUM = WORK( J ) + ABS( REAL( A( J, J ) ) )
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144 DO 90 I = J + 1, N
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145 ABSA = ABS( A( I, J ) )
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146 SUM = SUM + ABSA
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147 WORK( I ) = WORK( I ) + ABSA
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148 90 CONTINUE
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149 VALUE = MAX( VALUE, SUM )
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150 100 CONTINUE
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151 END IF
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152 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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153 *
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154 * Find normF(A).
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155 *
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156 SCALE = ZERO
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157 SUM = ONE
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158 IF( LSAME( UPLO, 'U' ) ) THEN
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159 DO 110 J = 2, N
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160 CALL CLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
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161 110 CONTINUE
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162 ELSE
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163 DO 120 J = 1, N - 1
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164 CALL CLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
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165 120 CONTINUE
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166 END IF
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167 SUM = 2*SUM
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168 DO 130 I = 1, N
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169 IF( REAL( A( I, I ) ).NE.ZERO ) THEN
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170 ABSA = ABS( REAL( A( I, I ) ) )
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171 IF( SCALE.LT.ABSA ) THEN
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172 SUM = ONE + SUM*( SCALE / ABSA )**2
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173 SCALE = ABSA
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174 ELSE
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175 SUM = SUM + ( ABSA / SCALE )**2
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176 END IF
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177 END IF
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178 130 CONTINUE
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179 VALUE = SCALE*SQRT( SUM )
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180 END IF
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181 *
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182 CLANHE = VALUE
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183 RETURN
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184 *
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185 * End of CLANHE
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186 *
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187 END