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Walter Hupfeld
2024-02-16 15:35:01 +01:00
parent 6e85cec1da
commit 0df6729f8b
393 changed files with 173746 additions and 6 deletions
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16
vendor/PhpSpreadsheet/Shared/JAMA/CHANGELOG.TXT vendored Normal file
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Mar 1, 2005 11:15 AST by PM
+ For consistency, renamed Math.php to Maths.java, utils to util,
tests to test, docs to doc -
+ Removed conditional logic from top of Matrix class.
+ Switched to using hypo function in Maths.php for all php-hypot calls.
NOTE TO SELF: Need to make sure that all decompositions have been
switched over to using the bundled hypo.
Feb 25, 2005 at 10:00 AST by PM
+ Recommend using simpler Error.php instead of JAMA_Error.php but
can be persuaded otherwise.

147
vendor/PhpSpreadsheet/Shared/JAMA/CholeskyDecomposition.php vendored Normal file
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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
/**
* Cholesky decomposition class.
*
* For a symmetric, positive definite matrix A, the Cholesky decomposition
* is an lower triangular matrix L so that A = L*L'.
*
* If the matrix is not symmetric or positive definite, the constructor
* returns a partial decomposition and sets an internal flag that may
* be queried by the isSPD() method.
*
* @author Paul Meagher
* @author Michael Bommarito
*
* @version 1.2
*/
class CholeskyDecomposition
{
/**
* Decomposition storage.
*
* @var array
*/
private $L = [];
/**
* Matrix row and column dimension.
*
* @var int
*/
private $m;
/**
* Symmetric positive definite flag.
*
* @var bool
*/
private $isspd = true;
/**
* CholeskyDecomposition.
*
* Class constructor - decomposes symmetric positive definite matrix
*
* @param Matrix $A Matrix square symmetric positive definite matrix
*/
public function __construct(Matrix $A)
{
$this->L = $A->getArray();
$this->m = $A->getRowDimension();
for ($i = 0; $i < $this->m; ++$i) {
for ($j = $i; $j < $this->m; ++$j) {
for ($sum = $this->L[$i][$j], $k = $i - 1; $k >= 0; --$k) {
$sum -= $this->L[$i][$k] * $this->L[$j][$k];
}
if ($i == $j) {
if ($sum >= 0) {
$this->L[$i][$i] = sqrt($sum);
} else {
$this->isspd = false;
}
} else {
if ($this->L[$i][$i] != 0) {
$this->L[$j][$i] = $sum / $this->L[$i][$i];
}
}
}
for ($k = $i + 1; $k < $this->m; ++$k) {
$this->L[$i][$k] = 0.0;
}
}
}
/**
* Is the matrix symmetric and positive definite?
*
* @return bool
*/
public function isSPD()
{
return $this->isspd;
}
/**
* getL.
*
* Return triangular factor.
*
* @return Matrix Lower triangular matrix
*/
public function getL()
{
return new Matrix($this->L);
}
/**
* Solve A*X = B.
*
* @param $B Row-equal matrix
*
* @return Matrix L * L' * X = B
*/
public function solve(Matrix $B)
{
if ($B->getRowDimension() == $this->m) {
if ($this->isspd) {
$X = $B->getArrayCopy();
$nx = $B->getColumnDimension();
for ($k = 0; $k < $this->m; ++$k) {
for ($i = $k + 1; $i < $this->m; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->L[$i][$k];
}
}
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->L[$k][$k];
}
}
for ($k = $this->m - 1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->L[$k][$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->L[$k][$i];
}
}
}
return new Matrix($X, $this->m, $nx);
}
throw new CalculationException(Matrix::MATRIX_SPD_EXCEPTION);
}
throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
}
}

863
vendor/PhpSpreadsheet/Shared/JAMA/EigenvalueDecomposition.php vendored Normal file
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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
/**
* Class to obtain eigenvalues and eigenvectors of a real matrix.
*
* If A is symmetric, then A = V*D*V' where the eigenvalue matrix D
* is diagonal and the eigenvector matrix V is orthogonal (i.e.
* A = V.times(D.times(V.transpose())) and V.times(V.transpose())
* equals the identity matrix).
*
* If A is not symmetric, then the eigenvalue matrix D is block diagonal
* with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
* lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
* columns of V represent the eigenvectors in the sense that A*V = V*D,
* i.e. A.times(V) equals V.times(D). The matrix V may be badly
* conditioned, or even singular, so the validity of the equation
* A = V*D*inverse(V) depends upon V.cond().
*
* @author Paul Meagher
*
* @version 1.1
*/
class EigenvalueDecomposition
{
/**
* Row and column dimension (square matrix).
*
* @var int
*/
private $n;
/**
* Arrays for internal storage of eigenvalues.
*
* @var array
*/
private $d = [];
private $e = [];
/**
* Array for internal storage of eigenvectors.
*
* @var array
*/
private $V = [];
/**
* Array for internal storage of nonsymmetric Hessenberg form.
*
* @var array
*/
private $H = [];
/**
* Working storage for nonsymmetric algorithm.
*
* @var array
*/
private $ort;
/**
* Used for complex scalar division.
*
* @var float
*/
private $cdivr;
private $cdivi;
/**
* Symmetric Householder reduction to tridiagonal form.
*/
private function tred2(): void
{
// This is derived from the Algol procedures tred2 by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
$this->d = $this->V[$this->n - 1];
// Householder reduction to tridiagonal form.
for ($i = $this->n - 1; $i > 0; --$i) {
$i_ = $i - 1;
// Scale to avoid under/overflow.
$h = $scale = 0.0;
$scale += array_sum(array_map('abs', $this->d));
if ($scale == 0.0) {
$this->e[$i] = $this->d[$i_];
$this->d = array_slice($this->V[$i_], 0, $i_);
for ($j = 0; $j < $i; ++$j) {
$this->V[$j][$i] = $this->V[$i][$j] = 0.0;
}
} else {
// Generate Householder vector.
for ($k = 0; $k < $i; ++$k) {
$this->d[$k] /= $scale;
$h += $this->d[$k] ** 2;
}
$f = $this->d[$i_];
$g = sqrt($h);
if ($f > 0) {
$g = -$g;
}
$this->e[$i] = $scale * $g;
$h = $h - $f * $g;
$this->d[$i_] = $f - $g;
for ($j = 0; $j < $i; ++$j) {
$this->e[$j] = 0.0;
}
// Apply similarity transformation to remaining columns.
for ($j = 0; $j < $i; ++$j) {
$f = $this->d[$j];
$this->V[$j][$i] = $f;
$g = $this->e[$j] + $this->V[$j][$j] * $f;
for ($k = $j + 1; $k <= $i_; ++$k) {
$g += $this->V[$k][$j] * $this->d[$k];
$this->e[$k] += $this->V[$k][$j] * $f;
}
$this->e[$j] = $g;
}
$f = 0.0;
for ($j = 0; $j < $i; ++$j) {
$this->e[$j] /= $h;
$f += $this->e[$j] * $this->d[$j];
}
$hh = $f / (2 * $h);
for ($j = 0; $j < $i; ++$j) {
$this->e[$j] -= $hh * $this->d[$j];
}
for ($j = 0; $j < $i; ++$j) {
$f = $this->d[$j];
$g = $this->e[$j];
for ($k = $j; $k <= $i_; ++$k) {
$this->V[$k][$j] -= ($f * $this->e[$k] + $g * $this->d[$k]);
}
$this->d[$j] = $this->V[$i - 1][$j];
$this->V[$i][$j] = 0.0;
}
}
$this->d[$i] = $h;
}
// Accumulate transformations.
for ($i = 0; $i < $this->n - 1; ++$i) {
$this->V[$this->n - 1][$i] = $this->V[$i][$i];
$this->V[$i][$i] = 1.0;
$h = $this->d[$i + 1];
if ($h != 0.0) {
for ($k = 0; $k <= $i; ++$k) {
$this->d[$k] = $this->V[$k][$i + 1] / $h;
}
for ($j = 0; $j <= $i; ++$j) {
$g = 0.0;
for ($k = 0; $k <= $i; ++$k) {
$g += $this->V[$k][$i + 1] * $this->V[$k][$j];
}
for ($k = 0; $k <= $i; ++$k) {
$this->V[$k][$j] -= $g * $this->d[$k];
}
}
}
for ($k = 0; $k <= $i; ++$k) {
$this->V[$k][$i + 1] = 0.0;
}
}
$this->d = $this->V[$this->n - 1];
$this->V[$this->n - 1] = array_fill(0, $j, 0.0);
$this->V[$this->n - 1][$this->n - 1] = 1.0;
$this->e[0] = 0.0;
}
/**
* Symmetric tridiagonal QL algorithm.
*
* This is derived from the Algol procedures tql2, by
* Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
* Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
* Fortran subroutine in EISPACK.
*/
private function tql2(): void
{
for ($i = 1; $i < $this->n; ++$i) {
$this->e[$i - 1] = $this->e[$i];
}
$this->e[$this->n - 1] = 0.0;
$f = 0.0;
$tst1 = 0.0;
$eps = 2.0 ** (-52.0);
for ($l = 0; $l < $this->n; ++$l) {
// Find small subdiagonal element
$tst1 = max($tst1, abs($this->d[$l]) + abs($this->e[$l]));
$m = $l;
while ($m < $this->n) {
if (abs($this->e[$m]) <= $eps * $tst1) {
break;
}
++$m;
}
// If m == l, $this->d[l] is an eigenvalue,
// otherwise, iterate.
if ($m > $l) {
$iter = 0;
do {
// Could check iteration count here.
++$iter;
// Compute implicit shift
$g = $this->d[$l];
$p = ($this->d[$l + 1] - $g) / (2.0 * $this->e[$l]);
$r = hypo($p, 1.0);
if ($p < 0) {
$r *= -1;
}
$this->d[$l] = $this->e[$l] / ($p + $r);
$this->d[$l + 1] = $this->e[$l] * ($p + $r);
$dl1 = $this->d[$l + 1];
$h = $g - $this->d[$l];
for ($i = $l + 2; $i < $this->n; ++$i) {
$this->d[$i] -= $h;
}
$f += $h;
// Implicit QL transformation.
$p = $this->d[$m];
$c = 1.0;
$c2 = $c3 = $c;
$el1 = $this->e[$l + 1];
$s = $s2 = 0.0;
for ($i = $m - 1; $i >= $l; --$i) {
$c3 = $c2;
$c2 = $c;
$s2 = $s;
$g = $c * $this->e[$i];
$h = $c * $p;
$r = hypo($p, $this->e[$i]);
$this->e[$i + 1] = $s * $r;
$s = $this->e[$i] / $r;
$c = $p / $r;
$p = $c * $this->d[$i] - $s * $g;
$this->d[$i + 1] = $h + $s * ($c * $g + $s * $this->d[$i]);
// Accumulate transformation.
for ($k = 0; $k < $this->n; ++$k) {
$h = $this->V[$k][$i + 1];
$this->V[$k][$i + 1] = $s * $this->V[$k][$i] + $c * $h;
$this->V[$k][$i] = $c * $this->V[$k][$i] - $s * $h;
}
}
$p = -$s * $s2 * $c3 * $el1 * $this->e[$l] / $dl1;
$this->e[$l] = $s * $p;
$this->d[$l] = $c * $p;
// Check for convergence.
} while (abs($this->e[$l]) > $eps * $tst1);
}
$this->d[$l] = $this->d[$l] + $f;
$this->e[$l] = 0.0;
}
// Sort eigenvalues and corresponding vectors.
for ($i = 0; $i < $this->n - 1; ++$i) {
$k = $i;
$p = $this->d[$i];
for ($j = $i + 1; $j < $this->n; ++$j) {
if ($this->d[$j] < $p) {
$k = $j;
$p = $this->d[$j];
}
}
if ($k != $i) {
$this->d[$k] = $this->d[$i];
$this->d[$i] = $p;
for ($j = 0; $j < $this->n; ++$j) {
$p = $this->V[$j][$i];
$this->V[$j][$i] = $this->V[$j][$k];
$this->V[$j][$k] = $p;
}
}
}
}
/**
* Nonsymmetric reduction to Hessenberg form.
*
* This is derived from the Algol procedures orthes and ortran,
* by Martin and Wilkinson, Handbook for Auto. Comp.,
* Vol.ii-Linear Algebra, and the corresponding
* Fortran subroutines in EISPACK.
*/
private function orthes(): void
{
$low = 0;
$high = $this->n - 1;
for ($m = $low + 1; $m <= $high - 1; ++$m) {
// Scale column.
$scale = 0.0;
for ($i = $m; $i <= $high; ++$i) {
$scale = $scale + abs($this->H[$i][$m - 1]);
}
if ($scale != 0.0) {
// Compute Householder transformation.
$h = 0.0;
for ($i = $high; $i >= $m; --$i) {
$this->ort[$i] = $this->H[$i][$m - 1] / $scale;
$h += $this->ort[$i] * $this->ort[$i];
}
$g = sqrt($h);
if ($this->ort[$m] > 0) {
$g *= -1;
}
$h -= $this->ort[$m] * $g;
$this->ort[$m] -= $g;
// Apply Householder similarity transformation
// H = (I -u * u' / h) * H * (I -u * u') / h)
for ($j = $m; $j < $this->n; ++$j) {
$f = 0.0;
for ($i = $high; $i >= $m; --$i) {
$f += $this->ort[$i] * $this->H[$i][$j];
}
$f /= $h;
for ($i = $m; $i <= $high; ++$i) {
$this->H[$i][$j] -= $f * $this->ort[$i];
}
}
for ($i = 0; $i <= $high; ++$i) {
$f = 0.0;
for ($j = $high; $j >= $m; --$j) {
$f += $this->ort[$j] * $this->H[$i][$j];
}
$f = $f / $h;
for ($j = $m; $j <= $high; ++$j) {
$this->H[$i][$j] -= $f * $this->ort[$j];
}
}
$this->ort[$m] = $scale * $this->ort[$m];
$this->H[$m][$m - 1] = $scale * $g;
}
}
// Accumulate transformations (Algol's ortran).
for ($i = 0; $i < $this->n; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
$this->V[$i][$j] = ($i == $j ? 1.0 : 0.0);
}
}
for ($m = $high - 1; $m >= $low + 1; --$m) {
if ($this->H[$m][$m - 1] != 0.0) {
for ($i = $m + 1; $i <= $high; ++$i) {
$this->ort[$i] = $this->H[$i][$m - 1];
}
for ($j = $m; $j <= $high; ++$j) {
$g = 0.0;
for ($i = $m; $i <= $high; ++$i) {
$g += $this->ort[$i] * $this->V[$i][$j];
}
// Double division avoids possible underflow
$g = ($g / $this->ort[$m]) / $this->H[$m][$m - 1];
for ($i = $m; $i <= $high; ++$i) {
$this->V[$i][$j] += $g * $this->ort[$i];
}
}
}
}
}
/**
* Performs complex division.
*
* @param mixed $xr
* @param mixed $xi
* @param mixed $yr
* @param mixed $yi
*/
private function cdiv($xr, $xi, $yr, $yi): void
{
if (abs($yr) > abs($yi)) {
$r = $yi / $yr;
$d = $yr + $r * $yi;
$this->cdivr = ($xr + $r * $xi) / $d;
$this->cdivi = ($xi - $r * $xr) / $d;
} else {
$r = $yr / $yi;
$d = $yi + $r * $yr;
$this->cdivr = ($r * $xr + $xi) / $d;
$this->cdivi = ($r * $xi - $xr) / $d;
}
}
/**
* Nonsymmetric reduction from Hessenberg to real Schur form.
*
* Code is derived from the Algol procedure hqr2,
* by Martin and Wilkinson, Handbook for Auto. Comp.,
* Vol.ii-Linear Algebra, and the corresponding
* Fortran subroutine in EISPACK.
*/
private function hqr2(): void
{
// Initialize
$nn = $this->n;
$n = $nn - 1;
$low = 0;
$high = $nn - 1;
$eps = 2.0 ** (-52.0);
$exshift = 0.0;
$p = $q = $r = $s = $z = 0;
// Store roots isolated by balanc and compute matrix norm
$norm = 0.0;
for ($i = 0; $i < $nn; ++$i) {
if (($i < $low) || ($i > $high)) {
$this->d[$i] = $this->H[$i][$i];
$this->e[$i] = 0.0;
}
for ($j = max($i - 1, 0); $j < $nn; ++$j) {
$norm = $norm + abs($this->H[$i][$j]);
}
}
// Outer loop over eigenvalue index
$iter = 0;
while ($n >= $low) {
// Look for single small sub-diagonal element
$l = $n;
while ($l > $low) {
$s = abs($this->H[$l - 1][$l - 1]) + abs($this->H[$l][$l]);
if ($s == 0.0) {
$s = $norm;
}
if (abs($this->H[$l][$l - 1]) < $eps * $s) {
break;
}
--$l;
}
// Check for convergence
// One root found
if ($l == $n) {
$this->H[$n][$n] = $this->H[$n][$n] + $exshift;
$this->d[$n] = $this->H[$n][$n];
$this->e[$n] = 0.0;
--$n;
$iter = 0;
// Two roots found
} elseif ($l == $n - 1) {
$w = $this->H[$n][$n - 1] * $this->H[$n - 1][$n];
$p = ($this->H[$n - 1][$n - 1] - $this->H[$n][$n]) / 2.0;
$q = $p * $p + $w;
$z = sqrt(abs($q));
$this->H[$n][$n] = $this->H[$n][$n] + $exshift;
$this->H[$n - 1][$n - 1] = $this->H[$n - 1][$n - 1] + $exshift;
$x = $this->H[$n][$n];
// Real pair
if ($q >= 0) {
if ($p >= 0) {
$z = $p + $z;
} else {
$z = $p - $z;
}
$this->d[$n - 1] = $x + $z;
$this->d[$n] = $this->d[$n - 1];
if ($z != 0.0) {
$this->d[$n] = $x - $w / $z;
}
$this->e[$n - 1] = 0.0;
$this->e[$n] = 0.0;
$x = $this->H[$n][$n - 1];
$s = abs($x) + abs($z);
$p = $x / $s;
$q = $z / $s;
$r = sqrt($p * $p + $q * $q);
$p = $p / $r;
$q = $q / $r;
// Row modification
for ($j = $n - 1; $j < $nn; ++$j) {
$z = $this->H[$n - 1][$j];
$this->H[$n - 1][$j] = $q * $z + $p * $this->H[$n][$j];
$this->H[$n][$j] = $q * $this->H[$n][$j] - $p * $z;
}
// Column modification
for ($i = 0; $i <= $n; ++$i) {
$z = $this->H[$i][$n - 1];
$this->H[$i][$n - 1] = $q * $z + $p * $this->H[$i][$n];
$this->H[$i][$n] = $q * $this->H[$i][$n] - $p * $z;
}
// Accumulate transformations
for ($i = $low; $i <= $high; ++$i) {
$z = $this->V[$i][$n - 1];
$this->V[$i][$n - 1] = $q * $z + $p * $this->V[$i][$n];
$this->V[$i][$n] = $q * $this->V[$i][$n] - $p * $z;
}
// Complex pair
} else {
$this->d[$n - 1] = $x + $p;
$this->d[$n] = $x + $p;
$this->e[$n - 1] = $z;
$this->e[$n] = -$z;
}
$n = $n - 2;
$iter = 0;
// No convergence yet
} else {
// Form shift
$x = $this->H[$n][$n];
$y = 0.0;
$w = 0.0;
if ($l < $n) {
$y = $this->H[$n - 1][$n - 1];
$w = $this->H[$n][$n - 1] * $this->H[$n - 1][$n];
}
// Wilkinson's original ad hoc shift
if ($iter == 10) {
$exshift += $x;
for ($i = $low; $i <= $n; ++$i) {
$this->H[$i][$i] -= $x;
}
$s = abs($this->H[$n][$n - 1]) + abs($this->H[$n - 1][$n - 2]);
$x = $y = 0.75 * $s;
$w = -0.4375 * $s * $s;
}
// MATLAB's new ad hoc shift
if ($iter == 30) {
$s = ($y - $x) / 2.0;
$s = $s * $s + $w;
if ($s > 0) {
$s = sqrt($s);
if ($y < $x) {
$s = -$s;
}
$s = $x - $w / (($y - $x) / 2.0 + $s);
for ($i = $low; $i <= $n; ++$i) {
$this->H[$i][$i] -= $s;
}
$exshift += $s;
$x = $y = $w = 0.964;
}
}
// Could check iteration count here.
$iter = $iter + 1;
// Look for two consecutive small sub-diagonal elements
$m = $n - 2;
while ($m >= $l) {
$z = $this->H[$m][$m];
$r = $x - $z;
$s = $y - $z;
$p = ($r * $s - $w) / $this->H[$m + 1][$m] + $this->H[$m][$m + 1];
$q = $this->H[$m + 1][$m + 1] - $z - $r - $s;
$r = $this->H[$m + 2][$m + 1];
$s = abs($p) + abs($q) + abs($r);
$p = $p / $s;
$q = $q / $s;
$r = $r / $s;
if ($m == $l) {
break;
}
if (
abs($this->H[$m][$m - 1]) * (abs($q) + abs($r)) <
$eps * (abs($p) * (abs($this->H[$m - 1][$m - 1]) + abs($z) + abs($this->H[$m + 1][$m + 1])))
) {
break;
}
--$m;
}
for ($i = $m + 2; $i <= $n; ++$i) {
$this->H[$i][$i - 2] = 0.0;
if ($i > $m + 2) {
$this->H[$i][$i - 3] = 0.0;
}
}
// Double QR step involving rows l:n and columns m:n
for ($k = $m; $k <= $n - 1; ++$k) {
$notlast = ($k != $n - 1);
if ($k != $m) {
$p = $this->H[$k][$k - 1];
$q = $this->H[$k + 1][$k - 1];
$r = ($notlast ? $this->H[$k + 2][$k - 1] : 0.0);
$x = abs($p) + abs($q) + abs($r);
if ($x != 0.0) {
$p = $p / $x;
$q = $q / $x;
$r = $r / $x;
}
}
if ($x == 0.0) {
break;
}
$s = sqrt($p * $p + $q * $q + $r * $r);
if ($p < 0) {
$s = -$s;
}
if ($s != 0) {
if ($k != $m) {
$this->H[$k][$k - 1] = -$s * $x;
} elseif ($l != $m) {
$this->H[$k][$k - 1] = -$this->H[$k][$k - 1];
}
$p = $p + $s;
$x = $p / $s;
$y = $q / $s;
$z = $r / $s;
$q = $q / $p;
$r = $r / $p;
// Row modification
for ($j = $k; $j < $nn; ++$j) {
$p = $this->H[$k][$j] + $q * $this->H[$k + 1][$j];
if ($notlast) {
$p = $p + $r * $this->H[$k + 2][$j];
$this->H[$k + 2][$j] = $this->H[$k + 2][$j] - $p * $z;
}
$this->H[$k][$j] = $this->H[$k][$j] - $p * $x;
$this->H[$k + 1][$j] = $this->H[$k + 1][$j] - $p * $y;
}
// Column modification
$iMax = min($n, $k + 3);
for ($i = 0; $i <= $iMax; ++$i) {
$p = $x * $this->H[$i][$k] + $y * $this->H[$i][$k + 1];
if ($notlast) {
$p = $p + $z * $this->H[$i][$k + 2];
$this->H[$i][$k + 2] = $this->H[$i][$k + 2] - $p * $r;
}
$this->H[$i][$k] = $this->H[$i][$k] - $p;
$this->H[$i][$k + 1] = $this->H[$i][$k + 1] - $p * $q;
}
// Accumulate transformations
for ($i = $low; $i <= $high; ++$i) {
$p = $x * $this->V[$i][$k] + $y * $this->V[$i][$k + 1];
if ($notlast) {
$p = $p + $z * $this->V[$i][$k + 2];
$this->V[$i][$k + 2] = $this->V[$i][$k + 2] - $p * $r;
}
$this->V[$i][$k] = $this->V[$i][$k] - $p;
$this->V[$i][$k + 1] = $this->V[$i][$k + 1] - $p * $q;
}
} // ($s != 0)
} // k loop
} // check convergence
} // while ($n >= $low)
// Backsubstitute to find vectors of upper triangular form
if ($norm == 0.0) {
return;
}
for ($n = $nn - 1; $n >= 0; --$n) {
$p = $this->d[$n];
$q = $this->e[$n];
// Real vector
if ($q == 0) {
$l = $n;
$this->H[$n][$n] = 1.0;
for ($i = $n - 1; $i >= 0; --$i) {
$w = $this->H[$i][$i] - $p;
$r = 0.0;
for ($j = $l; $j <= $n; ++$j) {
$r = $r + $this->H[$i][$j] * $this->H[$j][$n];
}
if ($this->e[$i] < 0.0) {
$z = $w;
$s = $r;
} else {
$l = $i;
if ($this->e[$i] == 0.0) {
if ($w != 0.0) {
$this->H[$i][$n] = -$r / $w;
} else {
$this->H[$i][$n] = -$r / ($eps * $norm);
}
// Solve real equations
} else {
$x = $this->H[$i][$i + 1];
$y = $this->H[$i + 1][$i];
$q = ($this->d[$i] - $p) * ($this->d[$i] - $p) + $this->e[$i] * $this->e[$i];
$t = ($x * $s - $z * $r) / $q;
$this->H[$i][$n] = $t;
if (abs($x) > abs($z)) {
$this->H[$i + 1][$n] = (-$r - $w * $t) / $x;
} else {
$this->H[$i + 1][$n] = (-$s - $y * $t) / $z;
}
}
// Overflow control
$t = abs($this->H[$i][$n]);
if (($eps * $t) * $t > 1) {
for ($j = $i; $j <= $n; ++$j) {
$this->H[$j][$n] = $this->H[$j][$n] / $t;
}
}
}
}
// Complex vector
} elseif ($q < 0) {
$l = $n - 1;
// Last vector component imaginary so matrix is triangular
if (abs($this->H[$n][$n - 1]) > abs($this->H[$n - 1][$n])) {
$this->H[$n - 1][$n - 1] = $q / $this->H[$n][$n - 1];
$this->H[$n - 1][$n] = -($this->H[$n][$n] - $p) / $this->H[$n][$n - 1];
} else {
$this->cdiv(0.0, -$this->H[$n - 1][$n], $this->H[$n - 1][$n - 1] - $p, $q);
$this->H[$n - 1][$n - 1] = $this->cdivr;
$this->H[$n - 1][$n] = $this->cdivi;
}
$this->H[$n][$n - 1] = 0.0;
$this->H[$n][$n] = 1.0;
for ($i = $n - 2; $i >= 0; --$i) {
// double ra,sa,vr,vi;
$ra = 0.0;
$sa = 0.0;
for ($j = $l; $j <= $n; ++$j) {
$ra = $ra + $this->H[$i][$j] * $this->H[$j][$n - 1];
$sa = $sa + $this->H[$i][$j] * $this->H[$j][$n];
}
$w = $this->H[$i][$i] - $p;
if ($this->e[$i] < 0.0) {
$z = $w;
$r = $ra;
$s = $sa;
} else {
$l = $i;
if ($this->e[$i] == 0) {
$this->cdiv(-$ra, -$sa, $w, $q);
$this->H[$i][$n - 1] = $this->cdivr;
$this->H[$i][$n] = $this->cdivi;
} else {
// Solve complex equations
$x = $this->H[$i][$i + 1];
$y = $this->H[$i + 1][$i];
$vr = ($this->d[$i] - $p) * ($this->d[$i] - $p) + $this->e[$i] * $this->e[$i] - $q * $q;
$vi = ($this->d[$i] - $p) * 2.0 * $q;
if ($vr == 0.0 & $vi == 0.0) {
$vr = $eps * $norm * (abs($w) + abs($q) + abs($x) + abs($y) + abs($z));
}
$this->cdiv($x * $r - $z * $ra + $q * $sa, $x * $s - $z * $sa - $q * $ra, $vr, $vi);
$this->H[$i][$n - 1] = $this->cdivr;
$this->H[$i][$n] = $this->cdivi;
if (abs($x) > (abs($z) + abs($q))) {
$this->H[$i + 1][$n - 1] = (-$ra - $w * $this->H[$i][$n - 1] + $q * $this->H[$i][$n]) / $x;
$this->H[$i + 1][$n] = (-$sa - $w * $this->H[$i][$n] - $q * $this->H[$i][$n - 1]) / $x;
} else {
$this->cdiv(-$r - $y * $this->H[$i][$n - 1], -$s - $y * $this->H[$i][$n], $z, $q);
$this->H[$i + 1][$n - 1] = $this->cdivr;
$this->H[$i + 1][$n] = $this->cdivi;
}
}
// Overflow control
$t = max(abs($this->H[$i][$n - 1]), abs($this->H[$i][$n]));
if (($eps * $t) * $t > 1) {
for ($j = $i; $j <= $n; ++$j) {
$this->H[$j][$n - 1] = $this->H[$j][$n - 1] / $t;
$this->H[$j][$n] = $this->H[$j][$n] / $t;
}
}
} // end else
} // end for
} // end else for complex case
} // end for
// Vectors of isolated roots
for ($i = 0; $i < $nn; ++$i) {
if ($i < $low | $i > $high) {
for ($j = $i; $j < $nn; ++$j) {
$this->V[$i][$j] = $this->H[$i][$j];
}
}
}
// Back transformation to get eigenvectors of original matrix
for ($j = $nn - 1; $j >= $low; --$j) {
for ($i = $low; $i <= $high; ++$i) {
$z = 0.0;
$kMax = min($j, $high);
for ($k = $low; $k <= $kMax; ++$k) {
$z = $z + $this->V[$i][$k] * $this->H[$k][$j];
}
$this->V[$i][$j] = $z;
}
}
}
// end hqr2
/**
* Constructor: Check for symmetry, then construct the eigenvalue decomposition.
*
* @param mixed $Arg A Square matrix
*/
public function __construct($Arg)
{
$this->A = $Arg->getArray();
$this->n = $Arg->getColumnDimension();
$issymmetric = true;
for ($j = 0; ($j < $this->n) & $issymmetric; ++$j) {
for ($i = 0; ($i < $this->n) & $issymmetric; ++$i) {
$issymmetric = ($this->A[$i][$j] == $this->A[$j][$i]);
}
}
if ($issymmetric) {
$this->V = $this->A;
// Tridiagonalize.
$this->tred2();
// Diagonalize.
$this->tql2();
} else {
$this->H = $this->A;
$this->ort = [];
// Reduce to Hessenberg form.
$this->orthes();
// Reduce Hessenberg to real Schur form.
$this->hqr2();
}
}
/**
* Return the eigenvector matrix.
*
* @return Matrix V
*/
public function getV()
{
return new Matrix($this->V, $this->n, $this->n);
}
/**
* Return the real parts of the eigenvalues.
*
* @return array real(diag(D))
*/
public function getRealEigenvalues()
{
return $this->d;
}
/**
* Return the imaginary parts of the eigenvalues.
*
* @return array imag(diag(D))
*/
public function getImagEigenvalues()
{
return $this->e;
}
/**
* Return the block diagonal eigenvalue matrix.
*
* @return Matrix D
*/
public function getD()
{
for ($i = 0; $i < $this->n; ++$i) {
$D[$i] = array_fill(0, $this->n, 0.0);
$D[$i][$i] = $this->d[$i];
if ($this->e[$i] == 0) {
continue;
}
$o = ($this->e[$i] > 0) ? $i + 1 : $i - 1;
$D[$i][$o] = $this->e[$i];
}
return new Matrix($D);
}
}

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vendor/PhpSpreadsheet/Shared/JAMA/LUDecomposition.php vendored Normal file
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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
/**
* For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
* and a permutation vector piv of length m so that A(piv,:) = L*U.
* If m < n, then L is m-by-m and U is m-by-n.
*
* The LU decompostion with pivoting always exists, even if the matrix is
* singular, so the constructor will never fail. The primary use of the
* LU decomposition is in the solution of square systems of simultaneous
* linear equations. This will fail if isNonsingular() returns false.
*
* @author Paul Meagher
* @author Bartosz Matosiuk
* @author Michael Bommarito
*
* @version 1.1
*/
class LUDecomposition
{
const MATRIX_SINGULAR_EXCEPTION = 'Can only perform operation on singular matrix.';
const MATRIX_SQUARE_EXCEPTION = 'Mismatched Row dimension';
/**
* Decomposition storage.
*
* @var array
*/
private $LU = [];
/**
* Row dimension.
*
* @var int
*/
private $m;
/**
* Column dimension.
*
* @var int
*/
private $n;
/**
* Pivot sign.
*
* @var int
*/
private $pivsign;
/**
* Internal storage of pivot vector.
*
* @var array
*/
private $piv = [];
/**
* LU Decomposition constructor.
*
* @param Matrix $A Rectangular matrix
*/
public function __construct($A)
{
if ($A instanceof Matrix) {
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
$this->LU = $A->getArray();
$this->m = $A->getRowDimension();
$this->n = $A->getColumnDimension();
for ($i = 0; $i < $this->m; ++$i) {
$this->piv[$i] = $i;
}
$this->pivsign = 1;
$LUrowi = $LUcolj = [];
// Outer loop.
for ($j = 0; $j < $this->n; ++$j) {
// Make a copy of the j-th column to localize references.
for ($i = 0; $i < $this->m; ++$i) {
$LUcolj[$i] = &$this->LU[$i][$j];
}
// Apply previous transformations.
for ($i = 0; $i < $this->m; ++$i) {
$LUrowi = $this->LU[$i];
// Most of the time is spent in the following dot product.
$kmax = min($i, $j);
$s = 0.0;
for ($k = 0; $k < $kmax; ++$k) {
$s += $LUrowi[$k] * $LUcolj[$k];
}
$LUrowi[$j] = $LUcolj[$i] -= $s;
}
// Find pivot and exchange if necessary.
$p = $j;
for ($i = $j + 1; $i < $this->m; ++$i) {
if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
$p = $i;
}
}
if ($p != $j) {
for ($k = 0; $k < $this->n; ++$k) {
$t = $this->LU[$p][$k];
$this->LU[$p][$k] = $this->LU[$j][$k];
$this->LU[$j][$k] = $t;
}
$k = $this->piv[$p];
$this->piv[$p] = $this->piv[$j];
$this->piv[$j] = $k;
$this->pivsign = $this->pivsign * -1;
}
// Compute multipliers.
if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
for ($i = $j + 1; $i < $this->m; ++$i) {
$this->LU[$i][$j] /= $this->LU[$j][$j];
}
}
}
} else {
throw new CalculationException(Matrix::ARGUMENT_TYPE_EXCEPTION);
}
}
// function __construct()
/**
* Get lower triangular factor.
*
* @return Matrix Lower triangular factor
*/
public function getL()
{
for ($i = 0; $i < $this->m; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i > $j) {
$L[$i][$j] = $this->LU[$i][$j];
} elseif ($i == $j) {
$L[$i][$j] = 1.0;
} else {
$L[$i][$j] = 0.0;
}
}
}
return new Matrix($L);
}
// function getL()
/**
* Get upper triangular factor.
*
* @return Matrix Upper triangular factor
*/
public function getU()
{
for ($i = 0; $i < $this->n; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i <= $j) {
$U[$i][$j] = $this->LU[$i][$j];
} else {
$U[$i][$j] = 0.0;
}
}
}
return new Matrix($U);
}
// function getU()
/**
* Return pivot permutation vector.
*
* @return array Pivot vector
*/
public function getPivot()
{
return $this->piv;
}
// function getPivot()
/**
* Alias for getPivot.
*
* @see getPivot
*/
public function getDoublePivot()
{
return $this->getPivot();
}
// function getDoublePivot()
/**
* Is the matrix nonsingular?
*
* @return bool true if U, and hence A, is nonsingular
*/
public function isNonsingular()
{
for ($j = 0; $j < $this->n; ++$j) {
if ($this->LU[$j][$j] == 0) {
return false;
}
}
return true;
}
// function isNonsingular()
/**
* Count determinants.
*
* @return array d matrix deterninat
*/
public function det()
{
if ($this->m == $this->n) {
$d = $this->pivsign;
for ($j = 0; $j < $this->n; ++$j) {
$d *= $this->LU[$j][$j];
}
return $d;
}
throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
}
// function det()
/**
* Solve A*X = B.
*
* @param mixed $B a Matrix with as many rows as A and any number of columns
*
* @return Matrix X so that L*U*X = B(piv,:)
*/
public function solve($B)
{
if ($B->getRowDimension() == $this->m) {
if ($this->isNonsingular()) {
// Copy right hand side with pivoting
$nx = $B->getColumnDimension();
$X = $B->getMatrix($this->piv, 0, $nx - 1);
// Solve L*Y = B(piv,:)
for ($k = 0; $k < $this->n; ++$k) {
for ($i = $k + 1; $i < $this->n; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
}
}
}
// Solve U*X = Y;
for ($k = $this->n - 1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$k][$j] /= $this->LU[$k][$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
}
}
}
return $X;
}
throw new CalculationException(self::MATRIX_SINGULAR_EXCEPTION);
}
throw new CalculationException(self::MATRIX_SQUARE_EXCEPTION);
}
}

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vendor/PhpSpreadsheet/Shared/JAMA/QRDecomposition.php vendored Normal file
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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
/**
* For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
* orthogonal matrix Q and an n-by-n upper triangular matrix R so that
* A = Q*R.
*
* The QR decompostion always exists, even if the matrix does not have
* full rank, so the constructor will never fail. The primary use of the
* QR decomposition is in the least squares solution of nonsquare systems
* of simultaneous linear equations. This will fail if isFullRank()
* returns false.
*
* @author Paul Meagher
*
* @version 1.1
*/
class QRDecomposition
{
const MATRIX_RANK_EXCEPTION = 'Can only perform operation on full-rank matrix.';
/**
* Array for internal storage of decomposition.
*
* @var array
*/
private $QR = [];
/**
* Row dimension.
*
* @var int
*/
private $m;
/**
* Column dimension.
*
* @var int
*/
private $n;
/**
* Array for internal storage of diagonal of R.
*
* @var array
*/
private $Rdiag = [];
/**
* QR Decomposition computed by Householder reflections.
*
* @param matrix $A Rectangular matrix
*/
public function __construct($A)
{
if ($A instanceof Matrix) {
// Initialize.
$this->QR = $A->getArray();
$this->m = $A->getRowDimension();
$this->n = $A->getColumnDimension();
// Main loop.
for ($k = 0; $k < $this->n; ++$k) {
// Compute 2-norm of k-th column without under/overflow.
$nrm = 0.0;
for ($i = $k; $i < $this->m; ++$i) {
$nrm = hypo($nrm, $this->QR[$i][$k]);
}
if ($nrm != 0.0) {
// Form k-th Householder vector.
if ($this->QR[$k][$k] < 0) {
$nrm = -$nrm;
}
for ($i = $k; $i < $this->m; ++$i) {
$this->QR[$i][$k] /= $nrm;
}
$this->QR[$k][$k] += 1.0;
// Apply transformation to remaining columns.
for ($j = $k + 1; $j < $this->n; ++$j) {
$s = 0.0;
for ($i = $k; $i < $this->m; ++$i) {
$s += $this->QR[$i][$k] * $this->QR[$i][$j];
}
$s = -$s / $this->QR[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$this->QR[$i][$j] += $s * $this->QR[$i][$k];
}
}
}
$this->Rdiag[$k] = -$nrm;
}
} else {
throw new CalculationException(Matrix::ARGUMENT_TYPE_EXCEPTION);
}
}
// function __construct()
/**
* Is the matrix full rank?
*
* @return bool true if R, and hence A, has full rank, else false
*/
public function isFullRank()
{
for ($j = 0; $j < $this->n; ++$j) {
if ($this->Rdiag[$j] == 0) {
return false;
}
}
return true;
}
// function isFullRank()
/**
* Return the Householder vectors.
*
* @return Matrix Lower trapezoidal matrix whose columns define the reflections
*/
public function getH()
{
$H = [];
for ($i = 0; $i < $this->m; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i >= $j) {
$H[$i][$j] = $this->QR[$i][$j];
} else {
$H[$i][$j] = 0.0;
}
}
}
return new Matrix($H);
}
// function getH()
/**
* Return the upper triangular factor.
*
* @return Matrix upper triangular factor
*/
public function getR()
{
$R = [];
for ($i = 0; $i < $this->n; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i < $j) {
$R[$i][$j] = $this->QR[$i][$j];
} elseif ($i == $j) {
$R[$i][$j] = $this->Rdiag[$i];
} else {
$R[$i][$j] = 0.0;
}
}
}
return new Matrix($R);
}
// function getR()
/**
* Generate and return the (economy-sized) orthogonal factor.
*
* @return Matrix orthogonal factor
*/
public function getQ()
{
$Q = [];
for ($k = $this->n - 1; $k >= 0; --$k) {
for ($i = 0; $i < $this->m; ++$i) {
$Q[$i][$k] = 0.0;
}
$Q[$k][$k] = 1.0;
for ($j = $k; $j < $this->n; ++$j) {
if ($this->QR[$k][$k] != 0) {
$s = 0.0;
for ($i = $k; $i < $this->m; ++$i) {
$s += $this->QR[$i][$k] * $Q[$i][$j];
}
$s = -$s / $this->QR[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$Q[$i][$j] += $s * $this->QR[$i][$k];
}
}
}
}
return new Matrix($Q);
}
// function getQ()
/**
* Least squares solution of A*X = B.
*
* @param Matrix $B a Matrix with as many rows as A and any number of columns
*
* @return Matrix matrix that minimizes the two norm of Q*R*X-B
*/
public function solve($B)
{
if ($B->getRowDimension() == $this->m) {
if ($this->isFullRank()) {
// Copy right hand side
$nx = $B->getColumnDimension();
$X = $B->getArrayCopy();
// Compute Y = transpose(Q)*B
for ($k = 0; $k < $this->n; ++$k) {
for ($j = 0; $j < $nx; ++$j) {
$s = 0.0;
for ($i = $k; $i < $this->m; ++$i) {
$s += $this->QR[$i][$k] * $X[$i][$j];
}
$s = -$s / $this->QR[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$X[$i][$j] += $s * $this->QR[$i][$k];
}
}
}
// Solve R*X = Y;
for ($k = $this->n - 1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->Rdiag[$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->QR[$i][$k];
}
}
}
$X = new Matrix($X);
return $X->getMatrix(0, $this->n - 1, 0, $nx);
}
throw new CalculationException(self::MATRIX_RANK_EXCEPTION);
}
throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
}
}

528
vendor/PhpSpreadsheet/Shared/JAMA/SingularValueDecomposition.php vendored Normal file
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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
/**
* For an m-by-n matrix A with m >= n, the singular value decomposition is
* an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
* an n-by-n orthogonal matrix V so that A = U*S*V'.
*
* The singular values, sigma[$k] = S[$k][$k], are ordered so that
* sigma[0] >= sigma[1] >= ... >= sigma[n-1].
*
* The singular value decompostion always exists, so the constructor will
* never fail. The matrix condition number and the effective numerical
* rank can be computed from this decomposition.
*
* @author Paul Meagher
*
* @version 1.1
*/
class SingularValueDecomposition
{
/**
* Internal storage of U.
*
* @var array
*/
private $U = [];
/**
* Internal storage of V.
*
* @var array
*/
private $V = [];
/**
* Internal storage of singular values.
*
* @var array
*/
private $s = [];
/**
* Row dimension.
*
* @var int
*/
private $m;
/**
* Column dimension.
*
* @var int
*/
private $n;
/**
* Construct the singular value decomposition.
*
* Derived from LINPACK code.
*
* @param mixed $Arg Rectangular matrix
*/
public function __construct($Arg)
{
// Initialize.
$A = $Arg->getArrayCopy();
$this->m = $Arg->getRowDimension();
$this->n = $Arg->getColumnDimension();
$nu = min($this->m, $this->n);
$e = [];
$work = [];
$wantu = true;
$wantv = true;
$nct = min($this->m - 1, $this->n);
$nrt = max(0, min($this->n - 2, $this->m));
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
$kMax = max($nct, $nrt);
for ($k = 0; $k < $kMax; ++$k) {
if ($k < $nct) {
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[$k].
// Compute 2-norm of k-th column without under/overflow.
$this->s[$k] = 0;
for ($i = $k; $i < $this->m; ++$i) {
$this->s[$k] = hypo($this->s[$k], $A[$i][$k]);
}
if ($this->s[$k] != 0.0) {
if ($A[$k][$k] < 0.0) {
$this->s[$k] = -$this->s[$k];
}
for ($i = $k; $i < $this->m; ++$i) {
$A[$i][$k] /= $this->s[$k];
}
$A[$k][$k] += 1.0;
}
$this->s[$k] = -$this->s[$k];
}
for ($j = $k + 1; $j < $this->n; ++$j) {
if (($k < $nct) & ($this->s[$k] != 0.0)) {
// Apply the transformation.
$t = 0;
for ($i = $k; $i < $this->m; ++$i) {
$t += $A[$i][$k] * $A[$i][$j];
}
$t = -$t / $A[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$A[$i][$j] += $t * $A[$i][$k];
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
$e[$j] = $A[$k][$j];
}
}
if ($wantu && ($k < $nct)) {
// Place the transformation in U for subsequent back
// multiplication.
for ($i = $k; $i < $this->m; ++$i) {
$this->U[$i][$k] = $A[$i][$k];
}
}
if ($k < $nrt) {
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[$k].
// Compute 2-norm without under/overflow.
$e[$k] = 0;
for ($i = $k + 1; $i < $this->n; ++$i) {
$e[$k] = hypo($e[$k], $e[$i]);
}
if ($e[$k] != 0.0) {
if ($e[$k + 1] < 0.0) {
$e[$k] = -$e[$k];
}
for ($i = $k + 1; $i < $this->n; ++$i) {
$e[$i] /= $e[$k];
}
$e[$k + 1] += 1.0;
}
$e[$k] = -$e[$k];
if (($k + 1 < $this->m) && ($e[$k] != 0.0)) {
// Apply the transformation.
for ($i = $k + 1; $i < $this->m; ++$i) {
$work[$i] = 0.0;
}
for ($j = $k + 1; $j < $this->n; ++$j) {
for ($i = $k + 1; $i < $this->m; ++$i) {
$work[$i] += $e[$j] * $A[$i][$j];
}
}
for ($j = $k + 1; $j < $this->n; ++$j) {
$t = -$e[$j] / $e[$k + 1];
for ($i = $k + 1; $i < $this->m; ++$i) {
$A[$i][$j] += $t * $work[$i];
}
}
}
if ($wantv) {
// Place the transformation in V for subsequent
// back multiplication.
for ($i = $k + 1; $i < $this->n; ++$i) {
$this->V[$i][$k] = $e[$i];
}
}
}
}
// Set up the final bidiagonal matrix or order p.
$p = min($this->n, $this->m + 1);
if ($nct < $this->n) {
$this->s[$nct] = $A[$nct][$nct];
}
if ($this->m < $p) {
$this->s[$p - 1] = 0.0;
}
if ($nrt + 1 < $p) {
$e[$nrt] = $A[$nrt][$p - 1];
}
$e[$p - 1] = 0.0;
// If required, generate U.
if ($wantu) {
for ($j = $nct; $j < $nu; ++$j) {
for ($i = 0; $i < $this->m; ++$i) {
$this->U[$i][$j] = 0.0;
}
$this->U[$j][$j] = 1.0;
}
for ($k = $nct - 1; $k >= 0; --$k) {
if ($this->s[$k] != 0.0) {
for ($j = $k + 1; $j < $nu; ++$j) {
$t = 0;
for ($i = $k; $i < $this->m; ++$i) {
$t += $this->U[$i][$k] * $this->U[$i][$j];
}
$t = -$t / $this->U[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$this->U[$i][$j] += $t * $this->U[$i][$k];
}
}
for ($i = $k; $i < $this->m; ++$i) {
$this->U[$i][$k] = -$this->U[$i][$k];
}
$this->U[$k][$k] = 1.0 + $this->U[$k][$k];
for ($i = 0; $i < $k - 1; ++$i) {
$this->U[$i][$k] = 0.0;
}
} else {
for ($i = 0; $i < $this->m; ++$i) {
$this->U[$i][$k] = 0.0;
}
$this->U[$k][$k] = 1.0;
}
}
}
// If required, generate V.
if ($wantv) {
for ($k = $this->n - 1; $k >= 0; --$k) {
if (($k < $nrt) && ($e[$k] != 0.0)) {
for ($j = $k + 1; $j < $nu; ++$j) {
$t = 0;
for ($i = $k + 1; $i < $this->n; ++$i) {
$t += $this->V[$i][$k] * $this->V[$i][$j];
}
$t = -$t / $this->V[$k + 1][$k];
for ($i = $k + 1; $i < $this->n; ++$i) {
$this->V[$i][$j] += $t * $this->V[$i][$k];
}
}
}
for ($i = 0; $i < $this->n; ++$i) {
$this->V[$i][$k] = 0.0;
}
$this->V[$k][$k] = 1.0;
}
}
// Main iteration loop for the singular values.
$pp = $p - 1;
$iter = 0;
$eps = 2.0 ** (-52.0);
while ($p > 0) {
// Here is where a test for too many iterations would go.
// This section of the program inspects for negligible
// elements in the s and e arrays. On completion the
// variables kase and k are set as follows:
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for ($k = $p - 2; $k >= -1; --$k) {
if ($k == -1) {
break;
}
if (abs($e[$k]) <= $eps * (abs($this->s[$k]) + abs($this->s[$k + 1]))) {
$e[$k] = 0.0;
break;
}
}
if ($k == $p - 2) {
$kase = 4;
} else {
for ($ks = $p - 1; $ks >= $k; --$ks) {
if ($ks == $k) {
break;
}
$t = ($ks != $p ? abs($e[$ks]) : 0.) + ($ks != $k + 1 ? abs($e[$ks - 1]) : 0.);
if (abs($this->s[$ks]) <= $eps * $t) {
$this->s[$ks] = 0.0;
break;
}
}
if ($ks == $k) {
$kase = 3;
} elseif ($ks == $p - 1) {
$kase = 1;
} else {
$kase = 2;
$k = $ks;
}
}
++$k;
// Perform the task indicated by kase.
switch ($kase) {
// Deflate negligible s(p).
case 1:
$f = $e[$p - 2];
$e[$p - 2] = 0.0;
for ($j = $p - 2; $j >= $k; --$j) {
$t = hypo($this->s[$j], $f);
$cs = $this->s[$j] / $t;
$sn = $f / $t;
$this->s[$j] = $t;
if ($j != $k) {
$f = -$sn * $e[$j - 1];
$e[$j - 1] = $cs * $e[$j - 1];
}
if ($wantv) {
for ($i = 0; $i < $this->n; ++$i) {
$t = $cs * $this->V[$i][$j] + $sn * $this->V[$i][$p - 1];
$this->V[$i][$p - 1] = -$sn * $this->V[$i][$j] + $cs * $this->V[$i][$p - 1];
$this->V[$i][$j] = $t;
}
}
}
break;
// Split at negligible s(k).
case 2:
$f = $e[$k - 1];
$e[$k - 1] = 0.0;
for ($j = $k; $j < $p; ++$j) {
$t = hypo($this->s[$j], $f);
$cs = $this->s[$j] / $t;
$sn = $f / $t;
$this->s[$j] = $t;
$f = -$sn * $e[$j];
$e[$j] = $cs * $e[$j];
if ($wantu) {
for ($i = 0; $i < $this->m; ++$i) {
$t = $cs * $this->U[$i][$j] + $sn * $this->U[$i][$k - 1];
$this->U[$i][$k - 1] = -$sn * $this->U[$i][$j] + $cs * $this->U[$i][$k - 1];
$this->U[$i][$j] = $t;
}
}
}
break;
// Perform one qr step.
case 3:
// Calculate the shift.
$scale = max(max(max(max(abs($this->s[$p - 1]), abs($this->s[$p - 2])), abs($e[$p - 2])), abs($this->s[$k])), abs($e[$k]));
$sp = $this->s[$p - 1] / $scale;
$spm1 = $this->s[$p - 2] / $scale;
$epm1 = $e[$p - 2] / $scale;
$sk = $this->s[$k] / $scale;
$ek = $e[$k] / $scale;
$b = (($spm1 + $sp) * ($spm1 - $sp) + $epm1 * $epm1) / 2.0;
$c = ($sp * $epm1) * ($sp * $epm1);
$shift = 0.0;
if (($b != 0.0) || ($c != 0.0)) {
$shift = sqrt($b * $b + $c);
if ($b < 0.0) {
$shift = -$shift;
}
$shift = $c / ($b + $shift);
}
$f = ($sk + $sp) * ($sk - $sp) + $shift;
$g = $sk * $ek;
// Chase zeros.
for ($j = $k; $j < $p - 1; ++$j) {
$t = hypo($f, $g);
$cs = $f / $t;
$sn = $g / $t;
if ($j != $k) {
$e[$j - 1] = $t;
}
$f = $cs * $this->s[$j] + $sn * $e[$j];
$e[$j] = $cs * $e[$j] - $sn * $this->s[$j];
$g = $sn * $this->s[$j + 1];
$this->s[$j + 1] = $cs * $this->s[$j + 1];
if ($wantv) {
for ($i = 0; $i < $this->n; ++$i) {
$t = $cs * $this->V[$i][$j] + $sn * $this->V[$i][$j + 1];
$this->V[$i][$j + 1] = -$sn * $this->V[$i][$j] + $cs * $this->V[$i][$j + 1];
$this->V[$i][$j] = $t;
}
}
$t = hypo($f, $g);
$cs = $f / $t;
$sn = $g / $t;
$this->s[$j] = $t;
$f = $cs * $e[$j] + $sn * $this->s[$j + 1];
$this->s[$j + 1] = -$sn * $e[$j] + $cs * $this->s[$j + 1];
$g = $sn * $e[$j + 1];
$e[$j + 1] = $cs * $e[$j + 1];
if ($wantu && ($j < $this->m - 1)) {
for ($i = 0; $i < $this->m; ++$i) {
$t = $cs * $this->U[$i][$j] + $sn * $this->U[$i][$j + 1];
$this->U[$i][$j + 1] = -$sn * $this->U[$i][$j] + $cs * $this->U[$i][$j + 1];
$this->U[$i][$j] = $t;
}
}
}
$e[$p - 2] = $f;
$iter = $iter + 1;
break;
// Convergence.
case 4:
// Make the singular values positive.
if ($this->s[$k] <= 0.0) {
$this->s[$k] = ($this->s[$k] < 0.0 ? -$this->s[$k] : 0.0);
if ($wantv) {
for ($i = 0; $i <= $pp; ++$i) {
$this->V[$i][$k] = -$this->V[$i][$k];
}
}
}
// Order the singular values.
while ($k < $pp) {
if ($this->s[$k] >= $this->s[$k + 1]) {
break;
}
$t = $this->s[$k];
$this->s[$k] = $this->s[$k + 1];
$this->s[$k + 1] = $t;
if ($wantv && ($k < $this->n - 1)) {
for ($i = 0; $i < $this->n; ++$i) {
$t = $this->V[$i][$k + 1];
$this->V[$i][$k + 1] = $this->V[$i][$k];
$this->V[$i][$k] = $t;
}
}
if ($wantu && ($k < $this->m - 1)) {
for ($i = 0; $i < $this->m; ++$i) {
$t = $this->U[$i][$k + 1];
$this->U[$i][$k + 1] = $this->U[$i][$k];
$this->U[$i][$k] = $t;
}
}
++$k;
}
$iter = 0;
--$p;
break;
} // end switch
} // end while
}
/**
* Return the left singular vectors.
*
* @return Matrix U
*/
public function getU()
{
return new Matrix($this->U, $this->m, min($this->m + 1, $this->n));
}
/**
* Return the right singular vectors.
*
* @return Matrix V
*/
public function getV()
{
return new Matrix($this->V);
}
/**
* Return the one-dimensional array of singular values.
*
* @return array diagonal of S
*/
public function getSingularValues()
{
return $this->s;
}
/**
* Return the diagonal matrix of singular values.
*
* @return Matrix S
*/
public function getS()
{
for ($i = 0; $i < $this->n; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
$S[$i][$j] = 0.0;
}
$S[$i][$i] = $this->s[$i];
}
return new Matrix($S);
}
/**
* Two norm.
*
* @return float max(S)
*/
public function norm2()
{
return $this->s[0];
}
/**
* Two norm condition number.
*
* @return float max(S)/min(S)
*/
public function cond()
{
return $this->s[0] / $this->s[min($this->m, $this->n) - 1];
}
/**
* Effective numerical matrix rank.
*
* @return int Number of nonnegligible singular values
*/
public function rank()
{
$eps = 2.0 ** (-52.0);
$tol = max($this->m, $this->n) * $this->s[0] * $eps;
$r = 0;
$iMax = count($this->s);
for ($i = 0; $i < $iMax; ++$i) {
if ($this->s[$i] > $tol) {
++$r;
}
}
return $r;
}
}

31
vendor/PhpSpreadsheet/Shared/JAMA/utils/Maths.php vendored Normal file
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@@ -0,0 +1,31 @@
<?php
/**
* Pythagorean Theorem:.
*
* a = 3
* b = 4
* r = sqrt(square(a) + square(b))
* r = 5
*
* r = sqrt(a^2 + b^2) without under/overflow.
*
* @param mixed $a
* @param mixed $b
*
* @return float
*/
function hypo($a, $b)
{
if (abs($a) > abs($b)) {
$r = $b / $a;
$r = abs($a) * sqrt(1 + $r * $r);
} elseif ($b != 0) {
$r = $a / $b;
$r = abs($b) * sqrt(1 + $r * $r);
} else {
$r = 0.0;
}
return $r;
}