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2329
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1 * |
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2 ************************************************************************ |
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3 * |
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4 SUBROUTINE DTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, |
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5 $ B, LDB ) |
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6 * .. Scalar Arguments .. |
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7 CHARACTER*1 SIDE, UPLO, TRANSA, DIAG |
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8 INTEGER M, N, LDA, LDB |
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9 DOUBLE PRECISION ALPHA |
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10 * .. Array Arguments .. |
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11 DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
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12 * .. |
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13 * |
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14 * Purpose |
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15 * ======= |
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16 * |
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17 * DTRSM solves one of the matrix equations |
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18 * |
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19 * op( A )*X = alpha*B, or X*op( A ) = alpha*B, |
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20 * |
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21 * where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
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22 * non-unit, upper or lower triangular matrix and op( A ) is one of |
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23 * |
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24 * op( A ) = A or op( A ) = A'. |
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25 * |
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26 * The matrix X is overwritten on B. |
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27 * |
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28 * Parameters |
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29 * ========== |
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30 * |
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31 * SIDE - CHARACTER*1. |
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32 * On entry, SIDE specifies whether op( A ) appears on the left |
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33 * or right of X as follows: |
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34 * |
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35 * SIDE = 'L' or 'l' op( A )*X = alpha*B. |
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36 * |
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37 * SIDE = 'R' or 'r' X*op( A ) = alpha*B. |
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38 * |
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39 * Unchanged on exit. |
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40 * |
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41 * UPLO - CHARACTER*1. |
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42 * On entry, UPLO specifies whether the matrix A is an upper or |
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43 * lower triangular matrix as follows: |
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44 * |
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45 * UPLO = 'U' or 'u' A is an upper triangular matrix. |
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46 * |
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47 * UPLO = 'L' or 'l' A is a lower triangular matrix. |
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48 * |
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49 * Unchanged on exit. |
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50 * |
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51 * TRANSA - CHARACTER*1. |
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52 * On entry, TRANSA specifies the form of op( A ) to be used in |
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53 * the matrix multiplication as follows: |
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54 * |
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55 * TRANSA = 'N' or 'n' op( A ) = A. |
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56 * |
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57 * TRANSA = 'T' or 't' op( A ) = A'. |
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58 * |
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59 * TRANSA = 'C' or 'c' op( A ) = A'. |
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60 * |
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61 * Unchanged on exit. |
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62 * |
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63 * DIAG - CHARACTER*1. |
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64 * On entry, DIAG specifies whether or not A is unit triangular |
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65 * as follows: |
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66 * |
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67 * DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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68 * |
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69 * DIAG = 'N' or 'n' A is not assumed to be unit |
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70 * triangular. |
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71 * |
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72 * Unchanged on exit. |
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73 * |
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74 * M - INTEGER. |
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75 * On entry, M specifies the number of rows of B. M must be at |
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76 * least zero. |
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77 * Unchanged on exit. |
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78 * |
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79 * N - INTEGER. |
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80 * On entry, N specifies the number of columns of B. N must be |
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81 * at least zero. |
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82 * Unchanged on exit. |
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83 * |
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84 * ALPHA - DOUBLE PRECISION. |
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85 * On entry, ALPHA specifies the scalar alpha. When alpha is |
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86 * zero then A is not referenced and B need not be set before |
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87 * entry. |
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88 * Unchanged on exit. |
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89 * |
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90 * A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m |
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91 * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. |
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92 * Before entry with UPLO = 'U' or 'u', the leading k by k |
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93 * upper triangular part of the array A must contain the upper |
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94 * triangular matrix and the strictly lower triangular part of |
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95 * A is not referenced. |
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96 * Before entry with UPLO = 'L' or 'l', the leading k by k |
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97 * lower triangular part of the array A must contain the lower |
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98 * triangular matrix and the strictly upper triangular part of |
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99 * A is not referenced. |
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100 * Note that when DIAG = 'U' or 'u', the diagonal elements of |
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101 * A are not referenced either, but are assumed to be unity. |
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102 * Unchanged on exit. |
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103 * |
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104 * LDA - INTEGER. |
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105 * On entry, LDA specifies the first dimension of A as declared |
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106 * in the calling (sub) program. When SIDE = 'L' or 'l' then |
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107 * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' |
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108 * then LDA must be at least max( 1, n ). |
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109 * Unchanged on exit. |
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110 * |
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111 * B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). |
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112 * Before entry, the leading m by n part of the array B must |
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113 * contain the right-hand side matrix B, and on exit is |
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114 * overwritten by the solution matrix X. |
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115 * |
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116 * LDB - INTEGER. |
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117 * On entry, LDB specifies the first dimension of B as declared |
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118 * in the calling (sub) program. LDB must be at least |
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119 * max( 1, m ). |
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120 * Unchanged on exit. |
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121 * |
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122 * |
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123 * Level 3 Blas routine. |
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124 * |
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125 * |
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126 * -- Written on 8-February-1989. |
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127 * Jack Dongarra, Argonne National Laboratory. |
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128 * Iain Duff, AERE Harwell. |
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129 * Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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130 * Sven Hammarling, Numerical Algorithms Group Ltd. |
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131 * |
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132 * |
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133 * .. External Functions .. |
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134 LOGICAL LSAME |
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135 EXTERNAL LSAME |
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136 * .. External Subroutines .. |
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137 EXTERNAL XERBLA |
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138 * .. Intrinsic Functions .. |
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139 INTRINSIC MAX |
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140 * .. Local Scalars .. |
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141 LOGICAL LSIDE, NOUNIT, UPPER |
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142 INTEGER I, INFO, J, K, NROWA |
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143 DOUBLE PRECISION TEMP |
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144 * .. Parameters .. |
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145 DOUBLE PRECISION ONE , ZERO |
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146 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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147 * .. |
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148 * .. Executable Statements .. |
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149 * |
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150 * Test the input parameters. |
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151 * |
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152 LSIDE = LSAME( SIDE , 'L' ) |
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153 IF( LSIDE )THEN |
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154 NROWA = M |
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155 ELSE |
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156 NROWA = N |
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157 END IF |
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158 NOUNIT = LSAME( DIAG , 'N' ) |
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159 UPPER = LSAME( UPLO , 'U' ) |
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160 * |
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161 INFO = 0 |
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162 IF( ( .NOT.LSIDE ).AND. |
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163 $ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN |
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164 INFO = 1 |
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165 ELSE IF( ( .NOT.UPPER ).AND. |
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166 $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN |
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167 INFO = 2 |
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168 ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND. |
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169 $ ( .NOT.LSAME( TRANSA, 'T' ) ).AND. |
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170 $ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN |
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171 INFO = 3 |
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172 ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND. |
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173 $ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN |
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174 INFO = 4 |
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175 ELSE IF( M .LT.0 )THEN |
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176 INFO = 5 |
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177 ELSE IF( N .LT.0 )THEN |
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178 INFO = 6 |
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179 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN |
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180 INFO = 9 |
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181 ELSE IF( LDB.LT.MAX( 1, M ) )THEN |
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182 INFO = 11 |
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183 END IF |
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184 IF( INFO.NE.0 )THEN |
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185 CALL XERBLA( 'DTRSM ', INFO ) |
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186 RETURN |
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187 END IF |
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188 * |
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189 * Quick return if possible. |
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190 * |
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191 IF( N.EQ.0 ) |
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192 $ RETURN |
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193 * |
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194 * And when alpha.eq.zero. |
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195 * |
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196 IF( ALPHA.EQ.ZERO )THEN |
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197 DO 20, J = 1, N |
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198 DO 10, I = 1, M |
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199 B( I, J ) = ZERO |
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200 10 CONTINUE |
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201 20 CONTINUE |
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202 RETURN |
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203 END IF |
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204 * |
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205 * Start the operations. |
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206 * |
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207 IF( LSIDE )THEN |
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208 IF( LSAME( TRANSA, 'N' ) )THEN |
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209 * |
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210 * Form B := alpha*inv( A )*B. |
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211 * |
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212 IF( UPPER )THEN |
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213 DO 60, J = 1, N |
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214 IF( ALPHA.NE.ONE )THEN |
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215 DO 30, I = 1, M |
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216 B( I, J ) = ALPHA*B( I, J ) |
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217 30 CONTINUE |
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218 END IF |
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219 DO 50, K = M, 1, -1 |
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220 IF( B( K, J ).NE.ZERO )THEN |
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221 IF( NOUNIT ) |
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222 $ B( K, J ) = B( K, J )/A( K, K ) |
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223 DO 40, I = 1, K - 1 |
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224 B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) |
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225 40 CONTINUE |
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226 END IF |
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227 50 CONTINUE |
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228 60 CONTINUE |
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229 ELSE |
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230 DO 100, J = 1, N |
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231 IF( ALPHA.NE.ONE )THEN |
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232 DO 70, I = 1, M |
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233 B( I, J ) = ALPHA*B( I, J ) |
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234 70 CONTINUE |
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235 END IF |
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236 DO 90 K = 1, M |
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237 IF( B( K, J ).NE.ZERO )THEN |
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238 IF( NOUNIT ) |
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239 $ B( K, J ) = B( K, J )/A( K, K ) |
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240 DO 80, I = K + 1, M |
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241 B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) |
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242 80 CONTINUE |
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243 END IF |
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244 90 CONTINUE |
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245 100 CONTINUE |
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246 END IF |
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247 ELSE |
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248 * |
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249 * Form B := alpha*inv( A' )*B. |
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250 * |
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251 IF( UPPER )THEN |
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252 DO 130, J = 1, N |
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253 DO 120, I = 1, M |
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254 TEMP = ALPHA*B( I, J ) |
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255 DO 110, K = 1, I - 1 |
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256 TEMP = TEMP - A( K, I )*B( K, J ) |
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257 110 CONTINUE |
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258 IF( NOUNIT ) |
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259 $ TEMP = TEMP/A( I, I ) |
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260 B( I, J ) = TEMP |
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261 120 CONTINUE |
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262 130 CONTINUE |
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263 ELSE |
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264 DO 160, J = 1, N |
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265 DO 150, I = M, 1, -1 |
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266 TEMP = ALPHA*B( I, J ) |
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267 DO 140, K = I + 1, M |
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268 TEMP = TEMP - A( K, I )*B( K, J ) |
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269 140 CONTINUE |
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270 IF( NOUNIT ) |
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271 $ TEMP = TEMP/A( I, I ) |
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272 B( I, J ) = TEMP |
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273 150 CONTINUE |
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274 160 CONTINUE |
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275 END IF |
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276 END IF |
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277 ELSE |
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278 IF( LSAME( TRANSA, 'N' ) )THEN |
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279 * |
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280 * Form B := alpha*B*inv( A ). |
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281 * |
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282 IF( UPPER )THEN |
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283 DO 210, J = 1, N |
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284 IF( ALPHA.NE.ONE )THEN |
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285 DO 170, I = 1, M |
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286 B( I, J ) = ALPHA*B( I, J ) |
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287 170 CONTINUE |
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288 END IF |
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289 DO 190, K = 1, J - 1 |
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290 IF( A( K, J ).NE.ZERO )THEN |
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291 DO 180, I = 1, M |
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292 B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) |
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293 180 CONTINUE |
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294 END IF |
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295 190 CONTINUE |
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296 IF( NOUNIT )THEN |
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297 TEMP = ONE/A( J, J ) |
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298 DO 200, I = 1, M |
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299 B( I, J ) = TEMP*B( I, J ) |
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300 200 CONTINUE |
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301 END IF |
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302 210 CONTINUE |
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303 ELSE |
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304 DO 260, J = N, 1, -1 |
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305 IF( ALPHA.NE.ONE )THEN |
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306 DO 220, I = 1, M |
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307 B( I, J ) = ALPHA*B( I, J ) |
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308 220 CONTINUE |
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309 END IF |
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310 DO 240, K = J + 1, N |
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311 IF( A( K, J ).NE.ZERO )THEN |
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312 DO 230, I = 1, M |
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313 B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) |
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314 230 CONTINUE |
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315 END IF |
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316 240 CONTINUE |
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317 IF( NOUNIT )THEN |
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318 TEMP = ONE/A( J, J ) |
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319 DO 250, I = 1, M |
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320 B( I, J ) = TEMP*B( I, J ) |
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321 250 CONTINUE |
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322 END IF |
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323 260 CONTINUE |
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324 END IF |
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325 ELSE |
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326 * |
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327 * Form B := alpha*B*inv( A' ). |
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328 * |
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329 IF( UPPER )THEN |
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330 DO 310, K = N, 1, -1 |
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331 IF( NOUNIT )THEN |
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332 TEMP = ONE/A( K, K ) |
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333 DO 270, I = 1, M |
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334 B( I, K ) = TEMP*B( I, K ) |
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335 270 CONTINUE |
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336 END IF |
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337 DO 290, J = 1, K - 1 |
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338 IF( A( J, K ).NE.ZERO )THEN |
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339 TEMP = A( J, K ) |
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340 DO 280, I = 1, M |
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341 B( I, J ) = B( I, J ) - TEMP*B( I, K ) |
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342 280 CONTINUE |
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343 END IF |
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344 290 CONTINUE |
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345 IF( ALPHA.NE.ONE )THEN |
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346 DO 300, I = 1, M |
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347 B( I, K ) = ALPHA*B( I, K ) |
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348 300 CONTINUE |
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349 END IF |
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350 310 CONTINUE |
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351 ELSE |
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352 DO 360, K = 1, N |
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353 IF( NOUNIT )THEN |
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354 TEMP = ONE/A( K, K ) |
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355 DO 320, I = 1, M |
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356 B( I, K ) = TEMP*B( I, K ) |
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357 320 CONTINUE |
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358 END IF |
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359 DO 340, J = K + 1, N |
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360 IF( A( J, K ).NE.ZERO )THEN |
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361 TEMP = A( J, K ) |
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362 DO 330, I = 1, M |
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363 B( I, J ) = B( I, J ) - TEMP*B( I, K ) |
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364 330 CONTINUE |
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365 END IF |
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366 340 CONTINUE |
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367 IF( ALPHA.NE.ONE )THEN |
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368 DO 350, I = 1, M |
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369 B( I, K ) = ALPHA*B( I, K ) |
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370 350 CONTINUE |
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371 END IF |
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372 360 CONTINUE |
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373 END IF |
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374 END IF |
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375 END IF |
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376 * |
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377 RETURN |
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378 * |
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379 * End of DTRSM . |
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380 * |
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381 END |
