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>."; }
/** * 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); } else { throw new Exception(JAMAError(MatrixRankException)); } } else { throw new Exception(JAMAError(MatrixDimensionException)); } }
/** * @dataProvider dataProviderForDirectProduct */ public function testDirectProduct(array $A, array $B, array $expected) { $A = new Vector($A); $B = new Vector($B); $AB = $A->directProduct($B); $expected = new Matrix($expected); $this->assertEquals($expected->getMatrix(), $AB->getMatrix()); }
function MatrixFitRoute($route) { require_once 'matrix.php'; $this->refreshPosibleTruck(); $route_possible_trucks = $this->getPossibleTrucks($route); $copy_possible_trucks = $this->truck_possible; $list_all_possible_trucks = array(); foreach ($copy_possible_trucks as $value) { $list_all_possible_trucks = array_merge($list_all_possible_trucks, $value); } $list_all_possible_trucks = array_unique(array_merge($list_all_possible_trucks, $route_possible_trucks)); $pending_routes = array_keys($this->routes); array_push($pending_routes, "new"); $assigned_trucks = array(); //create white_matrix $white_matrix = array(); foreach ($list_all_possible_trucks as $truck_id) { $white_matrix[$truck_id] = array(); foreach ($pending_routes as $route_id) { if ($route_id == "new") { $white_matrix[$truck_id][$route_id] = in_array($truck_id, $route_possible_trucks) ? 1 : 0; } else { $white_matrix[$truck_id][$route_id] = in_array($truck_id, $copy_possible_trucks[$route_id]) ? 1 : 0; } } } $grey_matrix = new Matrix($white_matrix); //basic required condition for solution if (!$grey_matrix->possible()) { return false; } //cardinality==1 check for $route. this means that the route has only one truck that it can use. foreach ($grey_matrix->getColumnKeys() as $route_id) { if ($grey_matrix->getColumnCardinal($route_id) == 1) { $truck_id = $grey_matrix->getFirstPositiveRow($route_id); if ($truck_id === false) { trigger_error("Looked for positive row but found none", E_USER_ERROR); } else { $assigned_trucks[$truck_id] = $route_id; $grey_matrix->deleteRow($truck_id); $grey_matrix->deleteColumn($route_id); } } } //cardinality==1 check for $truck. this means that there is only one route that can use this truck foreach ($grey_matrix->getRowKeys() as $truck_id) { if ($grey_matrix->getRowCardinal($truck_id) == 1) { $route_id = $grey_matrix->getFirstPositiveColumn($truck_id); if ($route_id === false) { trigger_error("Looked for positive col but found none", E_USER_ERROR); } else { $assigned_trucks[$truck_id] = $route_id; $grey_matrix->deleteRow($truck_id); $grey_matrix->deleteColumn($route_id); } } } //trivial solution found if (count($grey_matrix->getColumnKeys()) < 1) { return $assigned_trucks; } //check again for basic condition before continuing if (!$grey_matrix->possible()) { return false; } //iterate while there are still routes to be fit, we will include exit statments under certain conditions inside the loop $black_matrix = new Matrix($grey_matrix->getMatrix()); $ignores = array(); $routes_ids = $black_matrix->getColumnKeys(); $last_route_id = end($routes_ids); $first_route_id = reset($routes_ids); $max_loop = $black_matrix->maximumIterations(); $loop_count = 0; while (true) { if ($loop_count >= $max_loop) { trigger_error("loops count exceeded logical max loop, please check the code for errors", E_USER_ERROR); } $black_matrix = new Matrix($grey_matrix->getMatrix()); //recreate for loop $routes_ids = $black_matrix->getColumnKeys(); //recreate for loop $assignments = array(); // list of assignments for solution $previous_route_id = false; $previous_route_value = false; $n = 1; //for slice porpuses foreach ($routes_ids as $route_id) { if ($black_matrix->possible() === false) { return false; } if (count($black_matrix->getColumnKeys()) == 0 || count($black_matrix->getRowKeys()) == 0) { return false; } if (!isset($ignores[$route_id])) { $ignores[$route_id] = array(); } $fix_truck = $black_matrix->getFirstPositiveRow($route_id, $ignores[$route_id]); //there are no more positive values availables if ($fix_truck === false) { //no more subsitituions left if ($route_id == $first_route_id) { return false; } else { $previous_step = $previous_route_value; if ($previous_step === false) { trigger_error("something went wrong while searching for the previous positive of {$previous_route_id}", E_USER_ERROR); } else { array_push($ignores[$previous_route_id], $previous_step); } $ignores = array_slice($ignores, 0, $n, TRUE); break; //restart loop } } else { $n += 1; $assignments[$fix_truck] = $route_id; $black_matrix->deleteRow($fix_truck); $black_matrix->deleteColumn($route_id); $previous_route_id = $route_id; $previous_route_value = $fix_truck; //A solution was found, hurray! if ($route_id == $last_route_id) { return array_merge($assigned_trucks, $assignments); } } } } }
/** * @dataProvider dataProviderForKroneckerProduct */ public function testKroneckerProduct(array $A, array $B, array $expected) { $A = new Matrix($A); $B = new Matrix($B); $A⊗B = $A->kroneckerProduct($B); $expected = new Matrix($expected); $this->assertEquals($expected->getMatrix(), $A⊗B->getMatrix()); }
/** * @dataProvider dataProviderMulti */ public function testGetMatrix(array $A) { $S = new SquareMatrix($A); $M = new Matrix($A); $this->assertEquals($M->getMatrix(), $S->getMatrix()); }