ILIAS  release_5-2 Revision v5.2.25-18-g3f80b828510
Public Member Functions | Data Fields | Private Attributes
PHPExcel_Shared_JAMA_LUDecomposition Class Reference
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Public Member Functions

 __construct ($A)
 LU Decomposition constructor. More...
 
 getL ()
 Get lower triangular factor. More...
 
 getU ()
 Get upper triangular factor. More...
 
 getPivot ()
 Return pivot permutation vector. More...
 
 getDoublePivot ()
 Alias for getPivot. More...
 
 isNonsingular ()
 Is the matrix nonsingular? More...
 
 det ()
 Count determinants. More...
 
 solve ($B)
 Solve A*X = B. More...
 

Data Fields

const MatrixSingularException = "Can only perform operation on singular matrix."
 
const MatrixSquareException = "Mismatched Row dimension"
 

Private Attributes

 $LU = array()
 
 $m
 
 $n
 
 $pivsign
 
 $piv = array()
 

Detailed Description

Definition at line 21 of file LUDecomposition.php.

Constructor & Destructor Documentation

◆ __construct()

PHPExcel_Shared_JAMA_LUDecomposition::__construct (   $A)

LU Decomposition constructor.

Parameters
$ARectangular matrix
Returns
Structure to access L, U and piv.

Definition at line 63 of file LUDecomposition.php.

63 {
64 if ($A instanceof PHPExcel_Shared_JAMA_Matrix) {
65 // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
66 $this->LU = $A->getArray();
67 $this->m = $A->getRowDimension();
68 $this->n = $A->getColumnDimension();
69 for ($i = 0; $i < $this->m; ++$i) {
70 $this->piv[$i] = $i;
71 }
72 $this->pivsign = 1;
73 $LUrowi = $LUcolj = array();
74
75 // Outer loop.
76 for ($j = 0; $j < $this->n; ++$j) {
77 // Make a copy of the j-th column to localize references.
78 for ($i = 0; $i < $this->m; ++$i) {
79 $LUcolj[$i] = &$this->LU[$i][$j];
80 }
81 // Apply previous transformations.
82 for ($i = 0; $i < $this->m; ++$i) {
83 $LUrowi = $this->LU[$i];
84 // Most of the time is spent in the following dot product.
85 $kmax = min($i,$j);
86 $s = 0.0;
87 for ($k = 0; $k < $kmax; ++$k) {
88 $s += $LUrowi[$k] * $LUcolj[$k];
89 }
90 $LUrowi[$j] = $LUcolj[$i] -= $s;
91 }
92 // Find pivot and exchange if necessary.
93 $p = $j;
94 for ($i = $j+1; $i < $this->m; ++$i) {
95 if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
96 $p = $i;
97 }
98 }
99 if ($p != $j) {
100 for ($k = 0; $k < $this->n; ++$k) {
101 $t = $this->LU[$p][$k];
102 $this->LU[$p][$k] = $this->LU[$j][$k];
103 $this->LU[$j][$k] = $t;
104 }
105 $k = $this->piv[$p];
106 $this->piv[$p] = $this->piv[$j];
107 $this->piv[$j] = $k;
108 $this->pivsign = $this->pivsign * -1;
109 }
110 // Compute multipliers.
111 if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
112 for ($i = $j+1; $i < $this->m; ++$i) {
113 $this->LU[$i][$j] /= $this->LU[$j][$j];
114 }
115 }
116 }
117 } else {
118 throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
119 }
120 } // function __construct()
PHPExcel_Calculation_Exception
Definition: Exception.php:36
PHPExcel_Shared_JAMA_LUDecomposition\$m
$m
Definition: LUDecomposition.php:36
PHPExcel_Shared_JAMA_LUDecomposition\$n
$n
Definition: LUDecomposition.php:42
PHPExcel_Shared_JAMA_Matrix
PHPExcel root directory.
Definition: Matrix.php:27
PHPExcel_Shared_JAMA_Matrix\ArgumentTypeException
const ArgumentTypeException
Definition: Matrix.php:31

References $m, $n, $t, and PHPExcel_Shared_JAMA_Matrix\ArgumentTypeException.

Member Function Documentation

◆ det()

PHPExcel_Shared_JAMA_LUDecomposition::det ( )

Count determinants.

Returns
array d matrix deterninat

Definition at line 203 of file LUDecomposition.php.

203 {
204 if ($this->m == $this->n) {
205 $d = $this->pivsign;
206 for ($j = 0; $j < $this->n; ++$j) {
207 $d *= $this->LU[$j][$j];
208 }
209 return $d;
210 } else {
211 throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
212 }
213 } // function det()
$d
for($col=0; $col< 50; $col++) $d
Definition: 40duplicateStyle.php:38
PHPExcel_Shared_JAMA_LUDecomposition\$pivsign
$pivsign
Definition: LUDecomposition.php:48
PHPExcel_Shared_JAMA_Matrix\MatrixDimensionException
const MatrixDimensionException
Definition: Matrix.php:33

References $d, $n, $pivsign, and PHPExcel_Shared_JAMA_Matrix\MatrixDimensionException.

◆ getDoublePivot()

PHPExcel_Shared_JAMA_LUDecomposition::getDoublePivot ( )

Alias for getPivot.

See also
getPivot

Definition at line 178 of file LUDecomposition.php.

178 {
179 return $this->getPivot();
180 } // function getDoublePivot()
PHPExcel_Shared_JAMA_LUDecomposition\getPivot
getPivot()
Return pivot permutation vector.
Definition: LUDecomposition.php:168

References getPivot().

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◆ getL()

PHPExcel_Shared_JAMA_LUDecomposition::getL ( )

Get lower triangular factor.

Returns
array Lower triangular factor

Definition at line 128 of file LUDecomposition.php.

128 {
129 for ($i = 0; $i < $this->m; ++$i) {
130 for ($j = 0; $j < $this->n; ++$j) {
131 if ($i > $j) {
132 $L[$i][$j] = $this->LU[$i][$j];
133 } elseif ($i == $j) {
134 $L[$i][$j] = 1.0;
135 } else {
136 $L[$i][$j] = 0.0;
137 }
138 }
139 }
140 return new PHPExcel_Shared_JAMA_Matrix($L);
141 } // function getL()

References $m, and $n.

◆ getPivot()

PHPExcel_Shared_JAMA_LUDecomposition::getPivot ( )

Return pivot permutation vector.

Returns
array Pivot vector

Definition at line 168 of file LUDecomposition.php.

168 {
169 return $this->piv;
170 } // function getPivot()
PHPExcel_Shared_JAMA_LUDecomposition\$piv
$piv
Definition: LUDecomposition.php:54

References $piv.

Referenced by getDoublePivot().

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◆ getU()

PHPExcel_Shared_JAMA_LUDecomposition::getU ( )

Get upper triangular factor.

Returns
array Upper triangular factor

Definition at line 149 of file LUDecomposition.php.

149 {
150 for ($i = 0; $i < $this->n; ++$i) {
151 for ($j = 0; $j < $this->n; ++$j) {
152 if ($i <= $j) {
153 $U[$i][$j] = $this->LU[$i][$j];
154 } else {
155 $U[$i][$j] = 0.0;
156 }
157 }
158 }
159 return new PHPExcel_Shared_JAMA_Matrix($U);
160 } // function getU()

References $n.

◆ isNonsingular()

PHPExcel_Shared_JAMA_LUDecomposition::isNonsingular ( )

Is the matrix nonsingular?

Returns
true if U, and hence A, is nonsingular.

Definition at line 188 of file LUDecomposition.php.

188 {
189 for ($j = 0; $j < $this->n; ++$j) {
190 if ($this->LU[$j][$j] == 0) {
191 return false;
192 }
193 }
194 return true;
195 } // function isNonsingular()

References $n.

Referenced by solve().

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◆ solve()

PHPExcel_Shared_JAMA_LUDecomposition::solve (   $B)

Solve A*X = B.

Parameters
$BA Matrix with as many rows as A and any number of columns.
Returns
X so that L*U*X = B(piv,:) @PHPExcel_Calculation_Exception IllegalArgumentException Matrix row dimensions must agree. @PHPExcel_Calculation_Exception RuntimeException Matrix is singular.

Definition at line 224 of file LUDecomposition.php.

224 {
225 if ($B->getRowDimension() == $this->m) {
226 if ($this->isNonsingular()) {
227 // Copy right hand side with pivoting
228 $nx = $B->getColumnDimension();
229 $X = $B->getMatrix($this->piv, 0, $nx-1);
230 // Solve L*Y = B(piv,:)
231 for ($k = 0; $k < $this->n; ++$k) {
232 for ($i = $k+1; $i < $this->n; ++$i) {
233 for ($j = 0; $j < $nx; ++$j) {
234 $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
235 }
236 }
237 }
238 // Solve U*X = Y;
239 for ($k = $this->n-1; $k >= 0; --$k) {
240 for ($j = 0; $j < $nx; ++$j) {
241 $X->A[$k][$j] /= $this->LU[$k][$k];
242 }
243 for ($i = 0; $i < $k; ++$i) {
244 for ($j = 0; $j < $nx; ++$j) {
245 $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
246 }
247 }
248 }
249 return $X;
250 } else {
251 throw new PHPExcel_Calculation_Exception(self::MatrixSingularException);
252 }
253 } else {
254 throw new PHPExcel_Calculation_Exception(self::MatrixSquareException);
255 }
256 } // function solve()
MatrixSingularException
const MatrixSingularException
Definition: Error.php:54
PHPExcel_Shared_JAMA_LUDecomposition\isNonsingular
isNonsingular()
Is the matrix nonsingular?
Definition: LUDecomposition.php:188

References $n, isNonsingular(), and MatrixSingularException.

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Field Documentation

◆ $LU

PHPExcel_Shared_JAMA_LUDecomposition::$LU = array()
private

Definition at line 30 of file LUDecomposition.php.

◆ $m

PHPExcel_Shared_JAMA_LUDecomposition::$m
private

Definition at line 36 of file LUDecomposition.php.

Referenced by __construct(), and getL().

◆ $n

PHPExcel_Shared_JAMA_LUDecomposition::$n
private

Definition at line 42 of file LUDecomposition.php.

Referenced by __construct(), det(), getL(), getU(), isNonsingular(), and solve().

◆ $piv

PHPExcel_Shared_JAMA_LUDecomposition::$piv = array()
private

Definition at line 54 of file LUDecomposition.php.

Referenced by getPivot().

◆ $pivsign

PHPExcel_Shared_JAMA_LUDecomposition::$pivsign
private

Definition at line 48 of file LUDecomposition.php.

Referenced by det().

◆ MatrixSingularException

const PHPExcel_Shared_JAMA_LUDecomposition::MatrixSingularException = "Can only perform operation on singular matrix."

Definition at line 23 of file LUDecomposition.php.

◆ MatrixSquareException

const PHPExcel_Shared_JAMA_LUDecomposition::MatrixSquareException = "Mismatched Row dimension"

Definition at line 24 of file LUDecomposition.php.

The documentation for this class was generated from the following file: