ILIAS  release_5-4 Revision v5.4.26-12-gabc799a52e6
Public Member Functions | Private Member Functions | Private Attributes
Matrix\Decomposition\QR Class Reference
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Public Member Functions

 __construct (Matrix $matrix)
 
 getHouseholdVectors ()
 
 getQ ()
 
 getR ()
 
 isFullRank ()
 
 solve (Matrix $B)
 Least squares solution of A*X = B. More...
 

Private Member Functions

 hypo ($a, $b)
 
 decompose ()
 QR Decomposition computed by Householder reflections. More...
 

Private Attributes

 $qrMatrix
 
 $rows
 
 $columns
 
 $rDiagonal = []
 

Detailed Description

Definition at line 8 of file QR.php.

Constructor & Destructor Documentation

◆ __construct()

Matrix\Decomposition\QR::__construct ( Matrix  $matrix)

Definition at line 16 of file QR.php.

References Matrix\Matrix\columns(), Matrix\Decomposition\QR\decompose(), Matrix\Matrix\rows(), and Matrix\Matrix\toArray().

17  {
18  $this->qrMatrix = $matrix->toArray();
19  $this->rows = $matrix->rows;
20  $this->columns = $matrix->columns;
21 
22  $this->decompose();
23  }
Matrix\Decomposition\QR\decompose
decompose()
QR Decomposition computed by Householder reflections.
Definition: QR.php:121
$matrix
$matrix
Definition: test.php:18
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Member Function Documentation

◆ decompose()

Matrix\Decomposition\QR::decompose ( )
private

QR Decomposition computed by Householder reflections.

Definition at line 121 of file QR.php.

References Matrix\Decomposition\QR\$columns, $i, Matrix\Decomposition\QR\$rows, $s, and Matrix\Decomposition\QR\hypo().

Referenced by Matrix\Decomposition\QR\__construct().

121  : void
122  {
123  for ($k = 0; $k < $this->columns; ++$k) {
124  // Compute 2-norm of k-th column without under/overflow.
125  $norm = 0.0;
126  for ($i = $k; $i < $this->rows; ++$i) {
127  $norm = $this->hypo($norm, $this->qrMatrix[$i][$k]);
128  }
129  if ($norm != 0.0) {
130  // Form k-th Householder vector.
131  if ($this->qrMatrix[$k][$k] < 0.0) {
132  $norm = -$norm;
133  }
134  for ($i = $k; $i < $this->rows; ++$i) {
135  $this->qrMatrix[$i][$k] /= $norm;
136  }
137  $this->qrMatrix[$k][$k] += 1.0;
138  // Apply transformation to remaining columns.
139  for ($j = $k + 1; $j < $this->columns; ++$j) {
140  $s = 0.0;
141  for ($i = $k; $i < $this->rows; ++$i) {
142  $s += $this->qrMatrix[$i][$k] * $this->qrMatrix[$i][$j];
143  }
144  $s = -$s / $this->qrMatrix[$k][$k];
145  for ($i = $k; $i < $this->rows; ++$i) {
146  $this->qrMatrix[$i][$j] += $s * $this->qrMatrix[$i][$k];
147  }
148  }
149  }
150  $this->rDiagonal[$k] = -$norm;
151  }
152  }
$s
$s
Definition: pwgen.php:45
$i
$i
Definition: disco.tpl.php:19
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◆ getHouseholdVectors()

Matrix\Decomposition\QR::getHouseholdVectors ( )

Definition at line 25 of file QR.php.

References Matrix\Decomposition\QR\$columns, $row, and Matrix\Decomposition\QR\$rows.

25  : Matrix
26  {
27  $householdVectors = [];
28  for ($row = 0; $row < $this->rows; ++$row) {
29  for ($column = 0; $column < $this->columns; ++$column) {
30  if ($row >= $column) {
31  $householdVectors[$row][$column] = $this->qrMatrix[$row][$column];
32  } else {
33  $householdVectors[$row][$column] = 0.0;
34  }
35  }
36  }
37 
38  return new Matrix($householdVectors);
39  }
$row
$row
Definition: migrateto20.php:360
Matrix
Class for the creating "special" Matrices.
Definition: Builder.php:11

◆ getQ()

Matrix\Decomposition\QR::getQ ( )

Definition at line 41 of file QR.php.

References Matrix\Decomposition\QR\$columns, $i, $row, Matrix\Decomposition\QR\$rows, and $s.

Referenced by Matrix\Decomposition\QR\solve().

41  : Matrix
42  {
43  $qGrid = [];
44 
45  $rowCount = $this->rows;
46  for ($k = $this->columns - 1; $k >= 0; --$k) {
47  for ($i = 0; $i < $this->rows; ++$i) {
48  $qGrid[$i][$k] = 0.0;
49  }
50  $qGrid[$k][$k] = 1.0;
51  if ($this->columns > $this->rows) {
52  $qGrid = array_slice($qGrid, 0, $this->rows);
53  }
54 
55  for ($j = $k; $j < $this->columns; ++$j) {
56  if (isset($this->qrMatrix[$k], $this->qrMatrix[$k][$k]) && $this->qrMatrix[$k][$k] != 0.0) {
57  $s = 0.0;
58  for ($i = $k; $i < $this->rows; ++$i) {
59  $s += $this->qrMatrix[$i][$k] * $qGrid[$i][$j];
60  }
61  $s = -$s / $this->qrMatrix[$k][$k];
62  for ($i = $k; $i < $this->rows; ++$i) {
63  $qGrid[$i][$j] += $s * $this->qrMatrix[$i][$k];
64  }
65  }
66  }
67  }
68 
69  array_walk(
70  $qGrid,
71  function (&$row) use ($rowCount) {
72  $row = array_reverse($row);
73  $row = array_slice($row, 0, $rowCount);
74  }
75  );
76 
77  return new Matrix($qGrid);
78  }
$s
$s
Definition: pwgen.php:45
$row
$row
Definition: migrateto20.php:360
$i
$i
Definition: disco.tpl.php:19
Matrix
Class for the creating "special" Matrices.
Definition: Builder.php:11
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◆ getR()

Matrix\Decomposition\QR::getR ( )

Definition at line 80 of file QR.php.

References Matrix\Decomposition\QR\$columns, and $row.

Referenced by Matrix\Decomposition\QR\solve().

80  : Matrix
81  {
82  $rGrid = [];
83 
84  for ($row = 0; $row < $this->columns; ++$row) {
85  for ($column = 0; $column < $this->columns; ++$column) {
86  if ($row < $column) {
87  $rGrid[$row][$column] = $this->qrMatrix[$row][$column] ?? 0.0;
88  } elseif ($row === $column) {
89  $rGrid[$row][$column] = $this->rDiagonal[$row] ?? 0.0;
90  } else {
91  $rGrid[$row][$column] = 0.0;
92  }
93  }
94  }
95 
96  if ($this->columns > $this->rows) {
97  $rGrid = array_slice($rGrid, 0, $this->rows);
98  }
99 
100  return new Matrix($rGrid);
101  }
$row
$row
Definition: migrateto20.php:360
Matrix
Class for the creating "special" Matrices.
Definition: Builder.php:11
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◆ hypo()

Matrix\Decomposition\QR::hypo (   $a,
  $b 
)
private

Definition at line 103 of file QR.php.

References $r.

Referenced by Matrix\Decomposition\QR\decompose().

103  : float
104  {
105  if (abs($a) > abs($b)) {
106  $r = $b / $a;
107  $r = abs($a) * sqrt(1 + $r * $r);
108  } elseif ($b != 0.0) {
109  $r = $a / $b;
110  $r = abs($b) * sqrt(1 + $r * $r);
111  } else {
112  $r = 0.0;
113  }
114 
115  return $r;
116  }
$r
$r
Definition: example_031.php:79
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◆ isFullRank()

Matrix\Decomposition\QR::isFullRank ( )

Definition at line 154 of file QR.php.

References Matrix\Decomposition\QR\$columns.

Referenced by Matrix\Decomposition\QR\solve().

154  : bool
155  {
156  for ($j = 0; $j < $this->columns; ++$j) {
157  if ($this->rDiagonal[$j] == 0.0) {
158  return false;
159  }
160  }
161 
162  return true;
163  }
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◆ solve()

Matrix\Decomposition\QR::solve ( Matrix  $B)

Least squares solution of A*X = B.

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

Definition at line 174 of file QR.php.

References Matrix\Decomposition\QR\getQ(), Matrix\Decomposition\QR\getR(), Matrix\Decomposition\QR\isFullRank(), and Matrix\Matrix\rows().

174  : Matrix
175  {
176  if ($B->rows !== $this->rows) {
177  throw new Exception('Matrix row dimensions are not equal');
178  }
179 
180  if (!$this->isFullRank()) {
181  throw new Exception('Can only perform this operation on a full-rank matrix');
182  }
183 
184  // Compute Y = transpose(Q)*B
185  $Y = $this->getQ()->transpose()
186  ->multiply($B);
187  // Solve R*X = Y;
188  return $this->getR()->inverse()
189  ->multiply($Y);
190  }
Matrix
Class for the creating "special" Matrices.
Definition: Builder.php:11
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Field Documentation

◆ $columns

Matrix\Decomposition\QR::$columns
private

Definition at line 12 of file QR.php.

Referenced by Matrix\Decomposition\QR\decompose(), Matrix\Decomposition\QR\getHouseholdVectors(), Matrix\Decomposition\QR\getQ(), Matrix\Decomposition\QR\getR(), and Matrix\Decomposition\QR\isFullRank().

◆ $qrMatrix

Matrix\Decomposition\QR::$qrMatrix
private

Definition at line 10 of file QR.php.

◆ $rDiagonal

Matrix\Decomposition\QR::$rDiagonal = []
private

Definition at line 14 of file QR.php.

◆ $rows

Matrix\Decomposition\QR::$rows
private

Definition at line 11 of file QR.php.

Referenced by Matrix\Decomposition\QR\decompose(), Matrix\Decomposition\QR\getHouseholdVectors(), and Matrix\Decomposition\QR\getQ().

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