1 | ;; |
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2 | ;; |
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3 | ;; atlas-lapack documentation for the Chicken Scheme module system. |
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4 | ;; |
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5 | |
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6 | (use eggdoc) |
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7 | |
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8 | (define doc |
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9 | `((eggdoc:begin |
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10 | (name "atlas-lapack") |
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11 | (description "An interface to the LAPACK routines implemented in ATLAS.") |
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12 | (author (url "http://chicken.wiki.br/ivan raikov" "Ivan Raikov")) |
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13 | |
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14 | (history |
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15 | (version "1.10" "Bug fix in the detection of ATLAS library") |
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16 | (version "1.9" "Added build system support for libraries linked with f2c") |
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17 | (version "1.8" "Build script updated for better cross-platform compatibility") |
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18 | (version "1.7" "Fixed a bug in the trtri interface") |
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19 | (version "1.6" "Changed matrix copying code to use BLAS routines instead of object-copy") |
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20 | (version "1.5" "License upgrade to GPL v3") |
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21 | (version "1.4" "Added -latlas to the compiler options in the setup script") |
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22 | (version "1.3" "Minor changes in the setup script") |
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23 | (version "1.2" "Bug fix in the setup script") |
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24 | (version "1.1" "Created safe/unsafe variants of each routine, added optional leading dimensions") |
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25 | (version "1.0" "Initial release")) |
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26 | |
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27 | (requires (url "blas.html" "blas")) |
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28 | |
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29 | (usage "(require-extension atlas-lapack)") |
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30 | |
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31 | (download "atlas-lapack.egg") |
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32 | |
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33 | (documentation |
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34 | (p (url "http://math-atlas.sourceforge.net/" "ATLAS") " " |
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35 | "stands for Automatically Tuned Linear Algebra Software. " |
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36 | "Its purpose is to provide portably optimal linear algebra routines. The current version provides a complete " |
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37 | (url "http://www.netlib.org/blas" "BLAS") " API (for both C and Fortran77), and a very small subset of the " |
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38 | (url "http://www.netlib.org/lapack" "LAPACK") " API. " "Please see the documentation for the " |
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39 | (url "blas.html" "blas") " egg for definitions of the ORDER, UPLO, DIAG and TRANSPOSE datatypes.") |
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40 | |
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41 | (subsection |
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42 | "Naming conventions for routines" |
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43 | |
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44 | (p "Every routine in the LAPACK library comes in four flavors, " |
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45 | "each prefixed by the letters S, D, C, and Z, respectively. " |
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46 | "Each letter indicates the format of input data: " |
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47 | (ul |
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48 | (li "S stands for single-precision (32-bit IEEE floating point numbers), ") |
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49 | (li "D stands for double-precision (64-bit IEEE floating point numbers), ") |
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50 | (li "C stands for complex numbers (represented by pairs of 32-bit IEEE floating point numbers), ") |
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51 | (li "Z stands for double complex numbers (represented by pairs of 64-bit IEEE floating point numbers)"))) |
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52 | |
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53 | (p "In addition, each ATLAS-LAPACK routine in this egg comes in three flavors: " |
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54 | (ol (li "Safe, pure (prefix: " (b "atlas-lapack:") ")" |
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55 | (p (i "Safe") " routines check the sizes of their input arguments. " |
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56 | "For example, if a routine is supplied arguments that indicate that " |
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57 | "an input matrix is of dimensions " (i "M") "-by-" (i "N") ", then " |
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58 | "the argument corresponding to that matrix is checked that it is of size " |
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59 | (i "M * N") ". ") |
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60 | (p (i "Pure") " routines do not alter their arguments in any way. " |
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61 | "A new matrix or vector is allocated for the return value of the routine. ")) |
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62 | (li "Safe, destructive (prefix: " (b "atlas-lapack:") ", suffix: !)" |
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63 | (p (i "Safe") " routines check the sizes of their input arguments. " |
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64 | "For example, if a routine is supplied arguments that indicate that " |
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65 | "an input matrix is of dimensions " (i "M") "-by-" (i "N") ", then " |
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66 | "the argument corresponding to that matrix is checked that it is of size " |
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67 | (i "M * N") ". ") |
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68 | (p (i "Destructive") " routines can modify some or all of their arguments. " |
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69 | "They are given names ending in exclamation mark. " |
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70 | "The matrix factorization routines in LAPACK overwrite the input matrix argument " |
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71 | "with the result of the factorization, and the linear system solvers overwrite " |
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72 | "the right-hand side vector with the system solution. " |
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73 | "Please consult the LAPACK documentation to determine which functions modify " |
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74 | "their input arguments. ")) |
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75 | (li "Unsafe, destructive (prefix: " (b "unsafe-atlas-lapack:") ", suffix: !)" |
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76 | (p (i "Unsafe") " routines do not check the sizes of their input arguments. " |
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77 | "They invoke the corresponding ATLAS-LAPACK routines directly. " |
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78 | "Unsafe routines do not have pure variants. ")))) |
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79 | |
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80 | (p "For example, function " (i "xGESV") " (N-by-N linear system solver) " |
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81 | "comes in the following variants: " |
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82 | (table (tr (th (b "LAPACK name")) |
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83 | (th (b "Safe, pure")) |
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84 | (th (b "Safe, destructive")) |
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85 | (th (b "Unsafe, destructive"))) |
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86 | (tr (td (i "SGESV")) |
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87 | (td (i "atlas-lapack:sgesv")) |
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88 | (td (i "atlas-lapack:sgesv!")) |
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89 | (td (i "unsafe-atlas-lapack:sgesv!"))) |
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90 | (tr (td (i "DGESV")) |
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91 | (td (i "atlas-lapack:dgesv")) |
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92 | (td (i "atlas-lapack:dgesv!")) |
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93 | (td (i "unsafe-atlas-lapack:dgesv!"))) |
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94 | (tr (td (i "CGESV")) |
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95 | (td (i "atlas-lapack:cgesv")) |
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96 | (td (i "atlas-lapack:cgesv!")) |
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97 | (td (i "unsafe-atlas-lapack:cgesv!"))) |
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98 | (tr (td (i "ZGESV")) |
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99 | (td (i "atlas-lapack:zgesv")) |
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100 | (td (i "atlas-lapack:zgesv!")) |
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101 | (td (i "unsafe-atlas-lapack:zgesv!")))))) |
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102 | |
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103 | (subsection "LAPACK driver routines" |
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104 | (subsubsection "General linear system solving" |
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105 | (procedure "atlas-lapack:sgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR * S32VECTOR" |
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106 | (procedure "atlas-lapack:dgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR * S32VECTOR") |
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107 | (procedure "atlas-lapack:cgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR * S32VECTOR") |
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108 | (procedure "atlas-lapack:zgesv:: ORDER * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR * S32VECTOR") |
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109 | (p "The routines compute the solution to a system of linear equations " |
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110 | (i "A * X = B") ", where " (i "A") " is an N-by-N matrix and " (i "X") |
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111 | " and " (i "B") " are N-by-NRHS matrices. " |
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112 | "Optional arguments " (i "LDA") " and " (i "LDB") |
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113 | " are the leading dimensions of arrays " (i "A") " and " (i "B") |
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114 | ", respectively. " |
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115 | "LU decomposition with partial pivoting and row interchanges " |
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116 | "is used to factor " (i "A") " as " (i "A = P * L * U") ", " |
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117 | "where " (i "P") " is a permutation matrix, " (i "L") |
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118 | " is unit lower triangular, and " (i "U") " is upper triangular. " |
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119 | "The factored form of " (i "A") " is then used to solve the system. " |
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120 | "The return values are: " |
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121 | (ol (li "a matrix containing the factors " (i "L") " and " (i "U") |
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122 | " from the factorization " (i "A = P*L*U") "; " ) |
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123 | (li "the N-by-NRHS solution matrix " (i "X")) |
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124 | (li " a vector with pivot indices: for 1 <= i <= min(M,N), " |
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125 | "row " (i "i") " of the matrix " (i "A") " was interchanged with " |
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126 | "row pivot(" (i "i") ")"))))) |
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127 | |
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128 | (subsubsection "Symmetric positive definite linear system solving" |
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129 | (procedure "atlas-lapack:sposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR" |
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130 | (procedure "atlas-lapack:dposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR") |
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131 | (procedure "atlas-lapack:cposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR * F32VECTOR") |
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132 | (procedure "atlas-lapack:zposv:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR * F64VECTOR") |
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133 | (p "The routines compute the solution to a system of linear equations " |
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134 | (i "A * X = B") ", where " (i "A") |
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135 | " is an N-by-N symmetric positive definite matrix and " (i "X") |
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136 | " and " (i "B") " are N-by-NRHS matrices. " |
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137 | "Optional arguments " (i "LDA") " and " (i "LDB") |
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138 | " are the leading dimensions of arrays " (i "A") " and " (i "B") |
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139 | ", respectively. " |
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140 | "Cholesky decomposition is used to factor " (i "A") " as " |
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141 | (ul (li (i "A = U**T * U") " if UPLO = " (b "blas:Upper")) |
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142 | (li (i "A = L * L**T") " if UPLO = " (b "blas:Lower"))) |
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143 | "where " (i "U") " is an upper triangular, and " (i "L") |
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144 | " is a lower triangular matrix. " |
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145 | "The factored form of " (i "A") " is then used to solve the system. " |
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146 | "The return values are: " |
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147 | (ol |
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148 | (li "the factor " (i "U") " or " (i "L") |
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149 | "from the Cholesky factorization, " |
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150 | "depending on the value of argument UPLO.") |
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151 | (li "the N-by-NRHS solution matrix " (i "X"))))))) |
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152 | |
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153 | |
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154 | (subsection "LAPACK computational routines" |
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155 | (subsubsection "General matrix factorization" |
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156 | (procedure "atlas-lapack:sgetrf:: ORDER * M * N * A * [LDA] -> F32VECTOR * S32VECTOR" |
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157 | (procedure "atlas-lapack:dgetrf:: ORDER * M * N * A * [LDA] -> F64VECTOR * S32VECTOR") |
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158 | (procedure "atlas-lapack:cgetrf:: ORDER * M * N * A * [LDA] -> F32VECTOR * S32VECTOR") |
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159 | (procedure "atlas-lapack:zgetrf:: ORDER * M * N * A * [LDA] -> F64VECTOR * S32VECTOR") |
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160 | (p "These routines compute an LU factorization of a general M-by-N matrix " |
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161 | (i "A") " using partial pivoting with row interchanges. " |
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162 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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163 | (i "A") ". " |
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164 | "The return values are: " |
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165 | (ol (li "a matrix containing the factors " (i "L") " and " (i "U") |
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166 | " from the factorization " (i "A = P*L*U") "; " ) |
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167 | (li " a vector with pivot indices: for 1 <= i <= min(M,N), " |
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168 | "row " (i "i") " of the matrix was interchanged with " |
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169 | "row pivot(" (i "i") ")"))))) |
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170 | |
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171 | (subsubsection "General linear system solving using factorization" |
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172 | (procedure "atlas-lapack:sgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR" |
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173 | (procedure "atlas-lapack:dgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR") |
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174 | (procedure "atlas-lapack:cgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR") |
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175 | (procedure "atlas-lapack:zgetrs:: ORDER * TRANSPOSE * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR") |
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176 | (p "These routines solve a system of linear equations " |
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177 | (i "A * X = B") " or " (i "A' * X = B") " with a general N-by-N matrix " |
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178 | (i "A") " using the LU factorization computed by the xGETRF routines. " |
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179 | "Argument " (i "NRHS") " is the number of right-hand sides " |
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180 | "(i.e. number of columns in " (i "B") "). " |
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181 | "Optional arguments " (i "LDA") " and " (i "LDB") |
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182 | " are the leading dimensions of arrays " (i "A") " and " (i "B") |
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183 | ", respectively. " |
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184 | "The return value is the solution matrix " (i "X") "."))) |
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185 | |
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186 | (subsubsection "General matrix invert using factorization" |
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187 | (procedure "atlas-lapack:sgetri:: ORDER * N * A * PIVOT * [LDA] -> F32VECTOR" |
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188 | (procedure "atlas-lapack:dgetri:: ORDER * N * A * PIVOT * [LDA] -> F64VECTOR") |
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189 | (procedure "atlas-lapack:cgetri:: ORDER * N * A * PIVOT * [LDA] -> F32VECTOR") |
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190 | (procedure "atlas-lapack:zgetri:: ORDER * N * A * PIVOT * [LDA] -> F64VECTOR") |
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191 | (p "These routines compute the inverse of a matrix " |
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192 | "using the LU factorization computed by the xGETRF routines. " |
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193 | "Argument " (i "A") " must contain the factors L and U from the " |
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194 | "LU factorization computed by xGETRF. Argument " (i "PIVOT") " must be " |
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195 | "the pivot vector returned by the factorization routine. " |
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196 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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197 | (i "A") ". " |
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198 | "The return value is the inverse of the original matrix " (i "A") "."))) |
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199 | |
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200 | (subsubsection "Symmetric positive definite matrix factorization" |
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201 | (procedure "atlas-lapack:spotrf:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR" |
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202 | (procedure "atlas-lapack:dpotrf:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR") |
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203 | (procedure "atlas-lapack:cpotrf:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR") |
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204 | (procedure "atlas-lapack:zpotrf:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR") |
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205 | (p "These routines compute the Cholesky factorization of a " |
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206 | "symmetric positive definite matrix " (i "A") ". " |
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207 | "The factorization has the form: " |
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208 | (ul (li (i "A = U**T * U") " if UPLO = " (b "blas:Upper")) |
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209 | (li (i "A = L * L**T") " if UPLO = " (b "blas:Lower"))) |
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210 | "where " (i "U") " is an upper triangular, and " (i "L") |
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211 | " is a lower triangular matrix. " |
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212 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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213 | (i "A") ". " |
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214 | "The return value is the factor " (i "U") " or " (i "L") |
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215 | "from the Cholesky factorization, " |
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216 | "depending on the value of argument UPLO."))) |
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217 | |
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218 | (subsubsection "Symmetric positive definite matrix solving using factorization" |
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219 | (procedure "atlas-lapack:spotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR" |
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220 | (procedure "atlas-lapack:dpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR") |
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221 | (procedure "atlas-lapack:cpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F32VECTOR") |
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222 | (procedure "atlas-lapack:zpotrs:: ORDER * UPLO * N * NRHS * A * B * [LDA] * [LDB] -> F64VECTOR") |
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223 | (p "These routines solve a system of linear equations " |
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224 | (i "A * X = B") " with a symmetric positive definite matrix " (i "A") |
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225 | " using the Cholesky factorization computed by the xPOTRF routines. " |
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226 | "Argument " (i "A") " is the triangular factor " (i "U") " or " (i "L") |
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227 | " as computed by xPOTRF. " |
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228 | "Argument " (i "NRHS") " is the number of right-hand sides " |
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229 | "(i.e. number of columns in " (i "B") "). " |
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230 | "Argument UPLO indicates whether upper or lower triangle of A is stored " |
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231 | "(" (b "blas:Upper") " or " (b "blas:Lower") "). " |
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232 | "Optional arguments " (i "LDA") " and " (i "LDB") |
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233 | " are the leading dimensions of arrays " (i "A") " and " (i "B") |
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234 | ", respectively. " |
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235 | "The return value is the solution matrix " (i "X") "."))) |
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236 | |
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237 | (subsubsection "Symmetric positive definite matrix invert using factorization" |
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238 | (procedure "atlas-lapack:spotri:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR" |
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239 | (procedure "atlas-lapack:dpotri:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR") |
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240 | (procedure "atlas-lapack:cpotri:: ORDER * UPLO * N * A * [LDA] -> F32VECTOR") |
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241 | (procedure "atlas-lapack:zpotri:: ORDER * UPLO * N * A * [LDA] -> F64VECTOR") |
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242 | |
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243 | (p "These routines compute the inverse of a symmetric positive definite " |
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244 | "matrix " (i "A") " using the Cholesky factorization " (i "A = U**T*U") |
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245 | " or " (i "A = L*L**T") " computed by xPOTRF. " |
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246 | "Argument " (i "A") " is the triangular factor " (i "U") " or " (i "L") |
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247 | " as computed by xPOTRF. " |
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248 | "Argument UPLO indicates whether upper or lower triangle of A is stored " |
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249 | "(" (b "blas:Upper") " or " (b "blas:Lower") "). " |
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250 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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251 | (i "A") ". " |
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252 | "The return value is the upper or lower triangle of the inverse of " |
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253 | (i "A") "."))) |
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254 | |
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255 | (subsubsection "Triangular matrix invert" |
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256 | (procedure "atlas-lapack:strtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR" |
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257 | (procedure "atlas-lapack:dtrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR") |
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258 | (procedure "atlas-lapack:ctrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR") |
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259 | (procedure "atlas-lapack:ztrtri:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR") |
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260 | (p "These routines compute the inverse of a triangular matrix " (i "A") |
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261 | ". " |
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262 | "Argument " (i "A") " is the triangular factor " (i "U") " or " (i "L") |
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263 | " as computed by xPOTRF. " |
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264 | "Argument UPLO indicates whether upper or lower triangle of A is stored " |
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265 | "(" (b "blas:Upper") " or " (b "blas:Lower") "). " |
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266 | "Argument DIAG indicates whether A is non-unit triangular or " |
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267 | "unit triangular " "(" (b "blas:NonUnit") " or " (b "blas:Unit") "). " |
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268 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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269 | (i "A") ". " |
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270 | "The return value is the triangular inverse of the input matrix, " |
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271 | "in the same storage format."))) |
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272 | |
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273 | (subsubsection "Auxilliary routines" |
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274 | (procedure "atlas-lapack:slauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR" |
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275 | (procedure "atlas-lapack:dlauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR") |
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276 | (procedure "atlas-lapack:clauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F32VECTOR") |
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277 | (procedure "atlas-lapack:zlauum:: ORDER * UPLO * DIAG * N * A * [LDA] -> F64VECTOR") |
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278 | (p "These routines compute the product " (i "U * U'") " or " |
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279 | (i "L' * L") ", where the triangular factor " (i "U") " or " |
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280 | (i "L") " is stored in the upper or lower triangular part of the array " |
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281 | (i "A") ". " |
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282 | "Argument UPLO indicates whether upper or lower triangle of A is stored " |
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283 | "(" (b "blas:Upper") " or " (b "blas:Lower") "). " |
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284 | "Optional argument " (i "LDA") " is the leading dimension of array " |
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285 | (i "A") ". " |
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286 | "The return value is the lower triangle of the lower triangular product, " |
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287 | " or the upper triangle of upper triangular product, " |
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288 | "in the respective storage format."))) |
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289 | )) |
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290 | |
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291 | (examples (pre #<<EOF |
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292 | |
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293 | (require-extension srfi-4) |
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294 | (require-extension blas) |
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295 | (require-extension atlas-lapack) |
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296 | |
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297 | (define order blas:ColMajor) |
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298 | (define n 4) |
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299 | (define nrhs 1) |
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300 | |
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301 | ;; Solve the equations |
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302 | ;; |
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303 | ;; Ax = b, |
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304 | ;; |
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305 | ;; where A is the general matrix |
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306 | |
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307 | (define A (f64vector 1.8 5.25 1.58 -1.11 ;; column-major order |
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308 | 2.88 -2.95 -2.69 -0.66 |
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309 | 2.05 -0.95 -2.90 -0.59 |
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310 | -0.89 -3.80 -1.04 0.80)) |
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311 | ;; |
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312 | ;; and b is |
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313 | ;; |
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314 | (define b (f64vector 9.52 24.35 0.77 -6.22)) |
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315 | |
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316 | ;; A and b are not modified |
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317 | (define x (atlas-lapack:dgesv order n nrhs A b)) |
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318 | |
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319 | ;; A is overwritten with its LU decomposition, and |
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320 | ;; b is overwritten with the solution of the system |
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321 | (atlas-lapack:dgesv! order n nrhs A b) |
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322 | |
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323 | EOF |
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324 | )) |
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325 | |
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326 | (license |
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327 | "Copyright 2007-2009 Ivan Raikov and the Okinawa Institute of Science and Technology |
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328 | |
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329 | This program is free software: you can redistribute it and/or modify |
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330 | it under the terms of the GNU General Public License as published by |
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331 | the Free Software Foundation, either version 3 of the License, or (at |
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332 | your option) any later version. |
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333 | |
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334 | This program is distributed in the hope that it will be useful, but |
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335 | WITHOUT ANY WARRANTY; without even the implied warranty of |
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336 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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337 | General Public License for more details. |
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338 | |
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339 | A full copy of the GPL license can be found at |
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340 | <http://www.gnu.org/licenses/>.")))) |
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341 | |
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342 | |
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343 | (if (eggdoc->html doc) (void)) |
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