我看到了这个问题，并弹出了这个想法。
在 PHP 中有没有一种有效的方法来做到这一点？
编辑
最好有演示？
问问题
6975 次
6 回答
2
您可以为此使用梨包Math_Matrix。
于 2009-11-28T01:31:39.720 回答
1
这个包声称能够做你正在寻找的东西。
于 2009-11-28T01:32:08.940 回答
0
/**
* matrix_inverse
*
* Matrix Inverse
* Guass-Jordan Elimination Method
* Reduced Row Eshelon Form (RREF)
*
* In linear algebra an n-by-n (square) matrix A is called invertible (some
* authors use nonsingular or nondegenerate) if there exists an n-by-n matrix B
* such that AB = BA = In where In denotes the n-by-n identity matrix and the
* multiplication used is ordinary matrix multiplication. If this is the case,
* then the matrix B is uniquely determined by A and is called the inverse of A,
* denoted by A-1. It follows from the theory of matrices that if for finite
* square matrices A and B, then also non-square matrices (m-by-n matrices for
* which m ? n) do not have an inverse. However, in some cases such a matrix may
* have a left inverse or right inverse. If A is m-by-n and the rank of A is
* equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I.
* If A has rank m, then it has a right inverse: an n-by-m matrix B such that
* AB = I.
*
* A square matrix that is not invertible is called singular or degenerate. A
* square matrix is singular if and only if its determinant is 0. Singular
* matrices are rare in the sense that if you pick a random square matrix over
* a continuous uniform distribution on its entries, it will almost surely not
* be singular.
*
* While the most common case is that of matrices over the real or complex
* numbers, all these definitions can be given for matrices over any commutative
* ring. However, in this case the condition for a square matrix to be
* invertible is that its determinant is invertible in the ring, which in
* general is a much stricter requirement than being nonzero. The conditions for
* existence of left-inverse resp. right-inverse are more complicated since a
* notion of rank does not exist over rings.
*/
public function matrix_inverse($m1)
{
$rows = $this->rows($m1);
$cols = $this->columns($m1);
if ($rows != $cols)
{
die("Matrim1 is not square. Can not be inverted.");
}
$m2 = $this->eye($rows);
for ($j = 0; $j < $cols; $j++)
{
$factor = $m1[$j][$j];
if ($this->debug)
{
fms_writeln('Divide Row [' . $j . '] by ' . $m1[$j][$j] . ' (to
give us a "1" in the desired position):');
}
$m1 = $this->rref_div($m1, $j, $factor);
$m2 = $this->rref_div($m2, $j, $factor);
if ($this->debug)
{
$this->disp2($m1, $m2);
}
for ($i = 0; $i < $rows; $i++)
{
if ($i != $j)
{
$factor = $m1[$i][$j];
if ($this->debug)
{
$this->writeln('Row[' . $i . '] - ' . number_format($factor, 4) . ' ×
Row[' . $j . '] (to give us 0 in the desired position):');
}
$m1 = $this->rref_sub($m1, $i, $factor, $j);
$m2 = $this->rref_sub($m2, $i, $factor, $j);
if ($this->debug)
{
$this->disp2($m1, $m2);
}
}
}
}
return $m2;
}
于 2013-04-02T15:08:08.410 回答
0
这里测试代码https://gist.github.com/unix1/7510208 只有 identity_matrix() 和 invert() 函数就足够了
于 2014-04-15T11:57:15.563 回答
0
有一个能够反转矩阵的开源PHP 库。
你需要做的就是
<?php
include_once ("Matrix.class.php");
$matrixA = new Matrix(array(array(0, 1), array(2, 6)));
echo $matrixA->getInverse()->getMathMl();
?>
于 2012-06-24T16:40:19.977 回答
0
是的，有几种方法可以在 php 中完成此操作。有一些可用的库。或者，您可以维护自己的类并根据需要进行自定义。这是我们内部库的摘录，该库基于链接中描述的数学方法。课程结束时有一个演示供进一步参考。
https://www.intmath.com/matrices-determinants/inverse-matrix-gauss-jordan-elimination.php
class MatrixLibrary
{
//Gauss-Jordan elimination method for matrix inverse
public function inverseMatrix(array $matrix)
{
//TODO $matrix validation
$matrixCount = count($matrix);
$identityMatrix = $this->identityMatrix($matrixCount);
$augmentedMatrix = $this->appendIdentityMatrixToMatrix($matrix, $identityMatrix);
$inverseMatrixWithIdentity = $this->createInverseMatrix($augmentedMatrix);
$inverseMatrix = $this->removeIdentityMatrix($inverseMatrixWithIdentity);
return $inverseMatrix;
}
private function createInverseMatrix(array $matrix)
{
$numberOfRows = count($matrix);
for($i=0; $i<$numberOfRows; $i++)
{
$matrix = $this->oneOperation($matrix, $i, $i);
for($j=0; $j<$numberOfRows; $j++)
{
if($i !== $j)
{
$matrix = $this->zeroOperation($matrix, $j, $i, $i);
}
}
}
$inverseMatrixWithIdentity = $matrix;
return $inverseMatrixWithIdentity;
}
private function oneOperation(array $matrix, $rowPosition, $zeroPosition)
{
if($matrix[$rowPosition][$zeroPosition] !== 1)
{
$numberOfCols = count($matrix[$rowPosition]);
if($matrix[$rowPosition][$zeroPosition] === 0)
{
$divisor = 0.0000000001;
$matrix[$rowPosition][$zeroPosition] = 0.0000000001;
}
else
{
$divisor = $matrix[$rowPosition][$zeroPosition];
}
for($i=0; $i<$numberOfCols; $i++)
{
$matrix[$rowPosition][$i] = $matrix[$rowPosition][$i] / $divisor;
}
}
return $matrix;
}
private function zeroOperation(array $matrix, $rowPosition, $zeroPosition, $subjectRow)
{
$numberOfCols = count($matrix[$rowPosition]);
if($matrix[$rowPosition][$zeroPosition] !== 0)
{
$numberToSubtract = $matrix[$rowPosition][$zeroPosition];
for($i=0; $i<$numberOfCols; $i++)
{
$matrix[$rowPosition][$i] = $matrix[$rowPosition][$i] - $numberToSubtract * $matrix[$subjectRow][$i];
}
}
return $matrix;
}
private function removeIdentityMatrix(array $matrix)
{
$inverseMatrix = array();
$matrixCount = count($matrix);
for($i=0; $i<$matrixCount; $i++)
{
$inverseMatrix[$i] = array_slice($matrix[$i], $matrixCount);
}
return $inverseMatrix;
}
private function appendIdentityMatrixToMatrix(array $matrix, array $identityMatrix)
{
//TODO $matrix & $identityMatrix compliance validation (same number of rows/columns, etc)
$augmentedMatrix = array();
for($i=0; $i<count($matrix); $i++)
{
$augmentedMatrix[$i] = array_merge($matrix[$i], $identityMatrix[$i]);
}
return $augmentedMatrix;
}
public function identityMatrix(int $size)
{
//TODO validate $size
$identityMatrix = array();
for($i=0; $i<$size; $i++)
{
for($j=0; $j<$size; $j++)
{
if($i == $j)
{
$identityMatrix[$i][$j] = 1;
}
else
{
$identityMatrix[$i][$j] = 0;
}
}
}
return $identityMatrix;
}
}
$matrix = array(
array(11, 3, 12),
array(8, 7, 10),
array(13, 14, 15),
);
$matrixLibrary = new MatrixLibrary();
$inverseMatrix = $matrixLibrary->inverseMatrix($matrix);
print_r($inverseMatrix);
/*
Array
(
[0] => Array
(
[0] => 0.33980582524272
[1] => -1.1941747572816
[2] => 0.52427184466019
)
[1] => Array
(
[0] => -0.097087378640777
[1] => -0.087378640776699
[2] => 0.13592233009709
)
[2] => Array
(
[0] => -0.20388349514563
[1] => 1.1165048543689
[2] => -0.51456310679612
)
)
*/
于 2018-08-13T04:45:38.400 回答