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());
}