ILIAS  release_5-3 Revision v5.3.23-19-g915713cf615
Public Member Functions | Data Fields | Private Attributes
PHPExcel_Shared_JAMA_QRDecomposition Class Reference
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Public Member Functions

 __construct ($A)
 QR Decomposition computed by Householder reflections. More...
 
 isFullRank ()
 Is the matrix full rank? More...
 
 getH ()
 Return the Householder vectors. More...
 
 getR ()
 Return the upper triangular factor. More...
 
 getQ ()
 Generate and return the (economy-sized) orthogonal factor. More...
 
 solve ($B)
 Least squares solution of A*X = B. More...
 

Data Fields

const MatrixRankException = "Can only perform operation on full-rank matrix."
 

Private Attributes

 $QR = array()
 
 $m
 
 $n
 
 $Rdiag = array()
 

Detailed Description

Definition at line 19 of file QRDecomposition.php.

Constructor & Destructor Documentation

◆ __construct()

PHPExcel_Shared_JAMA_QRDecomposition::__construct (   $A)

QR Decomposition computed by Householder reflections.

Parameters
matrix$ARectangular matrix
Returns
Structure to access R and the Householder vectors and compute Q.

Definition at line 54 of file QRDecomposition.php.

54 {
55 if($A instanceof PHPExcel_Shared_JAMA_Matrix) {
56 // Initialize.
57 $this->QR = $A->getArrayCopy();
58 $this->m = $A->getRowDimension();
59 $this->n = $A->getColumnDimension();
60 // Main loop.
61 for ($k = 0; $k < $this->n; ++$k) {
62 // Compute 2-norm of k-th column without under/overflow.
63 $nrm = 0.0;
64 for ($i = $k; $i < $this->m; ++$i) {
65 $nrm = hypo($nrm, $this->QR[$i][$k]);
66 }
67 if ($nrm != 0.0) {
68 // Form k-th Householder vector.
69 if ($this->QR[$k][$k] < 0) {
70 $nrm = -$nrm;
71 }
72 for ($i = $k; $i < $this->m; ++$i) {
73 $this->QR[$i][$k] /= $nrm;
74 }
75 $this->QR[$k][$k] += 1.0;
76 // Apply transformation to remaining columns.
77 for ($j = $k+1; $j < $this->n; ++$j) {
78 $s = 0.0;
79 for ($i = $k; $i < $this->m; ++$i) {
80 $s += $this->QR[$i][$k] * $this->QR[$i][$j];
81 }
82 $s = -$s/$this->QR[$k][$k];
83 for ($i = $k; $i < $this->m; ++$i) {
84 $this->QR[$i][$j] += $s * $this->QR[$i][$k];
85 }
86 }
87 }
88 $this->Rdiag[$k] = -$nrm;
89 }
90 } else {
91 throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
92 }
93 } // function __construct()
hypo
hypo($a, $b)
Definition: Maths.php:14
PHPExcel_Calculation_Exception
Definition: Exception.php:36
PHPExcel_Shared_JAMA_Matrix
PHPExcel root directory.
Definition: Matrix.php:27
PHPExcel_Shared_JAMA_Matrix\ArgumentTypeException
const ArgumentTypeException
Definition: Matrix.php:31
PHPExcel_Shared_JAMA_QRDecomposition\$n
$n
Definition: QRDecomposition.php:39
PHPExcel_Shared_JAMA_QRDecomposition\$m
$m
Definition: QRDecomposition.php:33
$i
$i
Definition: disco.tpl.php:19
$s
$s
Definition: pwgen.php:45

References $i, $m, $n, $s, PHPExcel_Shared_JAMA_Matrix\ArgumentTypeException, and hypo().

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Member Function Documentation

◆ getH()

PHPExcel_Shared_JAMA_QRDecomposition::getH ( )

Return the Householder vectors.

Returns
Matrix Lower trapezoidal matrix whose columns define the reflections

Definition at line 116 of file QRDecomposition.php.

116 {
117 for ($i = 0; $i < $this->m; ++$i) {
118 for ($j = 0; $j < $this->n; ++$j) {
119 if ($i >= $j) {
120 $H[$i][$j] = $this->QR[$i][$j];
121 } else {
122 $H[$i][$j] = 0.0;
123 }
124 }
125 }
126 return new PHPExcel_Shared_JAMA_Matrix($H);
127 } // function getH()

References $i, $m, and $n.

◆ getQ()

PHPExcel_Shared_JAMA_QRDecomposition::getQ ( )

Generate and return the (economy-sized) orthogonal factor.

Returns
Matrix orthogonal factor

Definition at line 156 of file QRDecomposition.php.

156 {
157 for ($k = $this->n-1; $k >= 0; --$k) {
158 for ($i = 0; $i < $this->m; ++$i) {
159 $Q[$i][$k] = 0.0;
160 }
161 $Q[$k][$k] = 1.0;
162 for ($j = $k; $j < $this->n; ++$j) {
163 if ($this->QR[$k][$k] != 0) {
164 $s = 0.0;
165 for ($i = $k; $i < $this->m; ++$i) {
166 $s += $this->QR[$i][$k] * $Q[$i][$j];
167 }
168 $s = -$s/$this->QR[$k][$k];
169 for ($i = $k; $i < $this->m; ++$i) {
170 $Q[$i][$j] += $s * $this->QR[$i][$k];
171 }
172 }
173 }
174 }
175 /*
176 for($i = 0; $i < count($Q); ++$i) {
177 for($j = 0; $j < count($Q); ++$j) {
178 if(! isset($Q[$i][$j]) ) {
179 $Q[$i][$j] = 0;
180 }
181 }
182 }
183 */
184 return new PHPExcel_Shared_JAMA_Matrix($Q);
185 } // function getQ()

References $i, $m, $n, and $s.

◆ getR()

PHPExcel_Shared_JAMA_QRDecomposition::getR ( )

Return the upper triangular factor.

Returns
Matrix upper triangular factor

Definition at line 135 of file QRDecomposition.php.

135 {
136 for ($i = 0; $i < $this->n; ++$i) {
137 for ($j = 0; $j < $this->n; ++$j) {
138 if ($i < $j) {
139 $R[$i][$j] = $this->QR[$i][$j];
140 } elseif ($i == $j) {
141 $R[$i][$j] = $this->Rdiag[$i];
142 } else {
143 $R[$i][$j] = 0.0;
144 }
145 }
146 }
147 return new PHPExcel_Shared_JAMA_Matrix($R);
148 } // function getR()

References $i, and $n.

◆ isFullRank()

PHPExcel_Shared_JAMA_QRDecomposition::isFullRank ( )

Is the matrix full rank?

Returns
boolean true if R, and hence A, has full rank, else false.

Definition at line 101 of file QRDecomposition.php.

101 {
102 for ($j = 0; $j < $this->n; ++$j) {
103 if ($this->Rdiag[$j] == 0) {
104 return false;
105 }
106 }
107 return true;
108 } // function isFullRank()

References $n.

Referenced by solve().

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◆ solve()

PHPExcel_Shared_JAMA_QRDecomposition::solve (   $B)

Least squares solution of A*X = B.

Parameters
Matrix$BA Matrix with as many rows as A and any number of columns.
Returns
Matrix Matrix that minimizes the two norm of Q*R*X-B.

Definition at line 194 of file QRDecomposition.php.

194 {
195 if ($B->getRowDimension() == $this->m) {
196 if ($this->isFullRank()) {
197 // Copy right hand side
198 $nx = $B->getColumnDimension();
199 $X = $B->getArrayCopy();
200 // Compute Y = transpose(Q)*B
201 for ($k = 0; $k < $this->n; ++$k) {
202 for ($j = 0; $j < $nx; ++$j) {
203 $s = 0.0;
204 for ($i = $k; $i < $this->m; ++$i) {
205 $s += $this->QR[$i][$k] * $X[$i][$j];
206 }
207 $s = -$s/$this->QR[$k][$k];
208 for ($i = $k; $i < $this->m; ++$i) {
209 $X[$i][$j] += $s * $this->QR[$i][$k];
210 }
211 }
212 }
213 // Solve R*X = Y;
214 for ($k = $this->n-1; $k >= 0; --$k) {
215 for ($j = 0; $j < $nx; ++$j) {
216 $X[$k][$j] /= $this->Rdiag[$k];
217 }
218 for ($i = 0; $i < $k; ++$i) {
219 for ($j = 0; $j < $nx; ++$j) {
220 $X[$i][$j] -= $X[$k][$j]* $this->QR[$i][$k];
221 }
222 }
223 }
224 $X = new PHPExcel_Shared_JAMA_Matrix($X);
225 return ($X->getMatrix(0, $this->n-1, 0, $nx));
226 } else {
227 throw new PHPExcel_Calculation_Exception(self::MatrixRankException);
228 }
229 } else {
230 throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
231 }
232 } // function solve()
PHPExcel_Shared_JAMA_Matrix\MatrixDimensionException
const MatrixDimensionException
Definition: Matrix.php:33
PHPExcel_Shared_JAMA_QRDecomposition\isFullRank
isFullRank()
Is the matrix full rank?
Definition: QRDecomposition.php:101
MatrixRankException
const MatrixRankException
Definition: Error.php:57

References $i, $m, $n, $s, isFullRank(), PHPExcel_Shared_JAMA_Matrix\MatrixDimensionException, and MatrixRankException.

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Field Documentation

◆ $m

PHPExcel_Shared_JAMA_QRDecomposition::$m
private

Definition at line 33 of file QRDecomposition.php.

Referenced by __construct(), getH(), getQ(), and solve().

◆ $n

PHPExcel_Shared_JAMA_QRDecomposition::$n
private

Definition at line 39 of file QRDecomposition.php.

Referenced by __construct(), getH(), getQ(), getR(), isFullRank(), and solve().

◆ $QR

PHPExcel_Shared_JAMA_QRDecomposition::$QR = array()
private

Definition at line 27 of file QRDecomposition.php.

◆ $Rdiag

PHPExcel_Shared_JAMA_QRDecomposition::$Rdiag = array()
private

Definition at line 45 of file QRDecomposition.php.

◆ MatrixRankException

const PHPExcel_Shared_JAMA_QRDecomposition::MatrixRankException = "Can only perform operation on full-rank matrix."

Definition at line 21 of file QRDecomposition.php.

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