private function _construct_view_matrix(Vertex $origin, Matrix $orientation) { $this->_origin = $origin; $this->_tT = new Matrix(array('preset' => Matrix::TRANSLATION, 'vtc' => (new Vector(array('dest' => $origin)))->opposite())); $this->_tR = $orientation->transpose(); print $this->_tT; print $this->_tR; $this->_view_matrix = $this->_tR->mult($this->_tT); if (self::$verbose) { echo "Camera instance constructed." . PHP_EOL; } }
function TestMatrix() { // define test variables $errorCount = 0; $warningCount = 0; $columnwise = array(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0); $rowwise = array(1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0); $avals = array(array(1.0, 4.0, 7.0, 10.0), array(2.0, 5.0, 8.0, 11.0), array(3.0, 6.0, 9.0, 12.0)); $rankdef = $avals; $tvals = array(array(1.0, 2.0, 3.0), array(4.0, 5.0, 6.0), array(7.0, 8.0, 9.0), array(10.0, 11.0, 12.0)); $subavals = array(array(5.0, 8.0, 11.0), array(6.0, 9.0, 12.0)); $rvals = array(array(1.0, 4.0, 7.0), array(2.0, 5.0, 8.0, 11.0), array(3.0, 6.0, 9.0, 12.0)); $pvals = array(array(1.0, 1.0, 1.0), array(1.0, 2.0, 3.0), array(1.0, 3.0, 6.0)); $ivals = array(array(1.0, 0.0, 0.0, 0.0), array(0.0, 1.0, 0.0, 0.0), array(0.0, 0.0, 1.0, 0.0)); $evals = array(array(0.0, 1.0, 0.0, 0.0), array(1.0, 0.0, 2.0E-7, 0.0), array(0.0, -2.0E-7, 0.0, 1.0), array(0.0, 0.0, 1.0, 0.0)); $square = array(array(166.0, 188.0, 210.0), array(188.0, 214.0, 240.0), array(210.0, 240.0, 270.0)); $sqSolution = array(array(13.0), array(15.0)); $condmat = array(array(1.0, 3.0), array(7.0, 9.0)); $rows = 3; $cols = 4; $invalidID = 5; /* should trigger bad shape for construction with val */ $raggedr = 0; /* (raggedr,raggedc) should be out of bounds in ragged array */ $raggedc = 4; $validID = 3; /* leading dimension of intended test Matrices */ $nonconformld = 4; /* leading dimension which is valid, but nonconforming */ $ib = 1; /* index ranges for sub Matrix */ $ie = 2; $jb = 1; $je = 3; $rowindexset = array(1, 2); $badrowindexset = array(1, 3); $columnindexset = array(1, 2, 3); $badcolumnindexset = array(1, 2, 4); $columnsummax = 33.0; $rowsummax = 30.0; $sumofdiagonals = 15; $sumofsquares = 650; /** * Test matrix methods */ /** * Constructors and constructor-like methods: * * Matrix(double[], int) * Matrix(double[][]) * Matrix(int, int) * Matrix(int, int, double) * Matrix(int, int, double[][]) * constructWithCopy(double[][]) * random(int,int) * identity(int) */ echo "<p>Testing constructors and constructor-like methods...</p>"; $A = new Matrix($columnwise, 3); if ($A instanceof Matrix) { $this->try_success("Column-packed constructor..."); } else { $errorCount = $this->try_failure($errorCount, "Column-packed constructor...", "Unable to construct Matrix"); } $T = new Matrix($tvals); if ($T instanceof Matrix) { $this->try_success("2D array constructor..."); } else { $errorCount = $this->try_failure($errorCount, "2D array constructor...", "Unable to construct Matrix"); } $A = new Matrix($columnwise, $validID); $B = new Matrix($avals); $tmp = $B->get(0, 0); $avals[0][0] = 0.0; $C = $B->minus($A); $avals[0][0] = $tmp; $B = Matrix::constructWithCopy($avals); $tmp = $B->get(0, 0); $avals[0][0] = 0.0; /** check that constructWithCopy behaves properly **/ if ($tmp - $B->get(0, 0) != 0.0) { $errorCount = $this->try_failure($errorCount, "constructWithCopy... ", "copy not effected... data visible outside"); } else { $this->try_success("constructWithCopy... ", ""); } $I = new Matrix($ivals); if ($this->checkMatrices($I, Matrix::identity(3, 4))) { $this->try_success("identity... ", ""); } else { $errorCount = $this->try_failure($errorCount, "identity... ", "identity Matrix not successfully created"); } /** * Access Methods: * * getColumnDimension() * getRowDimension() * getArray() * getArrayCopy() * getColumnPackedCopy() * getRowPackedCopy() * get(int,int) * getMatrix(int,int,int,int) * getMatrix(int,int,int[]) * getMatrix(int[],int,int) * getMatrix(int[],int[]) * set(int,int,double) * setMatrix(int,int,int,int,Matrix) * setMatrix(int,int,int[],Matrix) * setMatrix(int[],int,int,Matrix) * setMatrix(int[],int[],Matrix) */ print "<p>Testing access methods...</p>"; $B = new Matrix($avals); if ($B->getRowDimension() == $rows) { $this->try_success("getRowDimension..."); } else { $errorCount = $this->try_failure($errorCount, "getRowDimension..."); } if ($B->getColumnDimension() == $cols) { $this->try_success("getColumnDimension..."); } else { $errorCount = $this->try_failure($errorCount, "getColumnDimension..."); } $barray = $B->getArray(); if ($this->checkArrays($barray, $avals)) { $this->try_success("getArray..."); } else { $errorCount = $this->try_failure($errorCount, "getArray..."); } $bpacked = $B->getColumnPackedCopy(); if ($this->checkArrays($bpacked, $columnwise)) { $this->try_success("getColumnPackedCopy..."); } else { $errorCount = $this->try_failure($errorCount, "getColumnPackedCopy..."); } $bpacked = $B->getRowPackedCopy(); if ($this->checkArrays($bpacked, $rowwise)) { $this->try_success("getRowPackedCopy..."); } else { $errorCount = $this->try_failure($errorCount, "getRowPackedCopy..."); } /** * Array-like methods: * minus * minusEquals * plus * plusEquals * arrayLeftDivide * arrayLeftDivideEquals * arrayRightDivide * arrayRightDivideEquals * arrayTimes * arrayTimesEquals * uminus */ print "<p>Testing array-like methods...</p>"; /** * I/O methods: * read * print * serializable: * writeObject * readObject */ print "<p>Testing I/O methods...</p>"; /** * Test linear algebra methods */ echo "<p>Testing linear algebra methods...<p>"; $A = new Matrix($columnwise, 3); if ($this->checkMatrices($A->transpose(), $T)) { $this->try_success("Transpose check..."); } else { $errorCount = $this->try_failure($errorCount, "Transpose check...", "Matrices are not equal"); } if ($this->checkScalars($A->norm1(), $columnsummax)) { $this->try_success("Maximum column sum..."); } else { $errorCount = $this->try_failure($errorCount, "Maximum column sum...", "Incorrect: " . $A->norm1() . " != " . $columnsummax); } if ($this->checkScalars($A->normInf(), $rowsummax)) { $this->try_success("Maximum row sum..."); } else { $errorCount = $this->try_failure($errorCount, "Maximum row sum...", "Incorrect: " . $A->normInf() . " != " . $rowsummax); } if ($this->checkScalars($A->normF(), sqrt($sumofsquares))) { $this->try_success("Frobenius norm..."); } else { $errorCount = $this->try_failure($errorCount, "Frobenius norm...", "Incorrect:" . $A->normF() . " != " . sqrt($sumofsquares)); } if ($this->checkScalars($A->trace(), $sumofdiagonals)) { $this->try_success("Matrix trace..."); } else { $errorCount = $this->try_failure($errorCount, "Matrix trace...", "Incorrect: " . $A->trace() . " != " . $sumofdiagonals); } $B = $A->getMatrix(0, $A->getRowDimension(), 0, $A->getRowDimension()); if ($B->det() == 0) { $this->try_success("Matrix determinant..."); } else { $errorCount = $this->try_failure($errorCount, "Matrix determinant...", "Incorrect: " . $B->det() . " != " . 0); } $A = new Matrix($columnwise, 3); $SQ = new Matrix($square); if ($this->checkMatrices($SQ, $A->times($A->transpose()))) { $this->try_success("times(Matrix)..."); } else { $errorCount = $this->try_failure($errorCount, "times(Matrix)...", "Unable to multiply matrices"); $SQ->toHTML(); $AT->toHTML(); } $A = new Matrix($columnwise, 4); $QR = $A->qr(); $R = $QR->getR(); $Q = $QR->getQ(); if ($this->checkMatrices($A, $Q->times($R))) { $this->try_success("QRDecomposition...", ""); } else { $errorCount = $this->try_failure($errorCount, "QRDecomposition...", "incorrect qr decomposition calculation"); } $A = new Matrix($columnwise, 4); $SVD = $A->svd(); $U = $SVD->getU(); $S = $SVD->getS(); $V = $SVD->getV(); if ($this->checkMatrices($A, $U->times($S->times($V->transpose())))) { $this->try_success("SingularValueDecomposition...", ""); } else { $errorCount = $this->try_failure($errorCount, "SingularValueDecomposition...", "incorrect singular value decomposition calculation"); } $n = $A->getColumnDimension(); $A = $A->getMatrix(0, $n - 1, 0, $n - 1); $A->set(0, 0, 0.0); $LU = $A->lu(); $L = $LU->getL(); if ($this->checkMatrices($A->getMatrix($LU->getPivot(), 0, $n - 1), $L->times($LU->getU()))) { $this->try_success("LUDecomposition...", ""); } else { $errorCount = $this->try_failure($errorCount, "LUDecomposition...", "incorrect LU decomposition calculation"); } $X = $A->inverse(); if ($this->checkMatrices($A->times($X), Matrix::identity(3, 3))) { $this->try_success("inverse()...", ""); } else { $errorCount = $this->try_failure($errorCount, "inverse()...", "incorrect inverse calculation"); } $DEF = new Matrix($rankdef); if ($this->checkScalars($DEF->rank(), min($DEF->getRowDimension(), $DEF->getColumnDimension()) - 1)) { $this->try_success("Rank..."); } else { $this->try_failure("Rank...", "incorrect rank calculation"); } $B = new Matrix($condmat); $SVD = $B->svd(); $singularvalues = $SVD->getSingularValues(); if ($this->checkScalars($B->cond(), $singularvalues[0] / $singularvalues[min($B->getRowDimension(), $B->getColumnDimension()) - 1])) { $this->try_success("Condition number..."); } else { $this->try_failure("Condition number...", "incorrect condition number calculation"); } $SUB = new Matrix($subavals); $O = new Matrix($SUB->getRowDimension(), 1, 1.0); $SOL = new Matrix($sqSolution); $SQ = $SUB->getMatrix(0, $SUB->getRowDimension() - 1, 0, $SUB->getRowDimension() - 1); if ($this->checkMatrices($SQ->solve($SOL), $O)) { $this->try_success("solve()...", ""); } else { $errorCount = $this->try_failure($errorCount, "solve()...", "incorrect lu solve calculation"); } $A = new Matrix($pvals); $Chol = $A->chol(); $L = $Chol->getL(); if ($this->checkMatrices($A, $L->times($L->transpose()))) { $this->try_success("CholeskyDecomposition...", ""); } else { $errorCount = $this->try_failure($errorCount, "CholeskyDecomposition...", "incorrect Cholesky decomposition calculation"); } $X = $Chol->solve(Matrix::identity(3, 3)); if ($this->checkMatrices($A->times($X), Matrix::identity(3, 3))) { $this->try_success("CholeskyDecomposition solve()...", ""); } else { $errorCount = $this->try_failure($errorCount, "CholeskyDecomposition solve()...", "incorrect Choleskydecomposition solve calculation"); } $Eig = $A->eig(); $D = $Eig->getD(); $V = $Eig->getV(); if ($this->checkMatrices($A->times($V), $V->times($D))) { $this->try_success("EigenvalueDecomposition (symmetric)...", ""); } else { $errorCount = $this->try_failure($errorCount, "EigenvalueDecomposition (symmetric)...", "incorrect symmetric Eigenvalue decomposition calculation"); } $A = new Matrix($evals); $Eig = $A->eig(); $D = $Eig->getD(); $V = $Eig->getV(); if ($this->checkMatrices($A->times($V), $V->times($D))) { $this->try_success("EigenvalueDecomposition (nonsymmetric)...", ""); } else { $errorCount = $this->try_failure($errorCount, "EigenvalueDecomposition (nonsymmetric)...", "incorrect nonsymmetric Eigenvalue decomposition calculation"); } print "<b>{$errorCount} total errors</b>."; }
public function testTranspose() { $matrix = new Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]); $transposed = $matrix->transpose(); $result = new Matrix([[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]); $this->assertTrue($transposed->equals($result)); }
public function inverse() { if ($this->u_size !== $this->u_stride || !compare($d = $this->determinant(), 0)) { return null; } $result = new Matrix($this->u_size, $this->u_stride); for ($i = 0; $i < $this->u_size; $i++) { $resultOffset = $i * $this->u_stride; for ($j = 0; $j < $this->u_stride; $j++) { $result->u_data[$resultOffset + $j] = (double) ((($i + 1 + $j + 1) % 2 == 0 ? 1 : -1) * $this->minor($i, $j)->determinant()); } } return $result->transpose()->multiply(1 / $d); }
public function testTranspose() { $arr1 = [[1, 2], [3, 4]]; $mat1 = new Matrix($arr1); $t = $mat1->transpose(); $testArr = [[1, 3], [2, 4]]; $this->assertSame($t->getInnerArray(), $testArr); }
/** * Compute the inverse of the matrix on which this method is found (A*A(-1)=I). * * (cofactor(a))T/(det a) * * @link http://www.mathwords.com/i/inverse_of_a_matrix.htm * @return Matrix * @throws \InvalidArgumentException * @throws \RangeException */ public function inverse() { if (!$this->isSquareMatrix()) { throw new \RangeException('Not a square matrix!'); } $newMatrix = []; /** @noinspection ForeachInvariantsInspection */ for ($i = 0; $i < $this->rows; ++$i) { /** @noinspection ForeachInvariantsInspection */ for ($j = 0; $j < $this->columns; ++$j) { $subMatrix = $this->getSubMatrix($i, $j); if (($i + $j) % 2 === 0) { $newMatrix[$i][$j] = $subMatrix->determinant(); } else { $newMatrix[$i][$j] = -$subMatrix->determinant(); } } } $cofactorMatrix = new Matrix($newMatrix); return $cofactorMatrix->transpose()->scalarDivide($this->determinant()); }