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>.";
}
/**
* Multiply Matrices
*
* This function will multiply the current matrix with the matrix provided.
* If current Matrix is denoted by 'A' and the inputted is denoted by 'B',
* When written, this will return AB.
*
* @link http://en.wikipedia.org/wiki/Matrix_multiplication
* @param Matrix $bMatrix The matrix to multiply with the current
* @return Matrix The result of multiplication.
* @throws \Exception $msg explains why operation failed
*/
public function mpMatrix(Matrix $bMatrix)
{
if (!$this->_verify() || !$bMatrix->_verify()) {
$eM1 = $this->toString();
$eM2 = $bMatrix->toString();
throw new \Exception("Either '{$eM1}' and/or '{$eM2}' is not a valid Matrix", Matrix::E_INVALID_MATRIX);
}
$aArray = $this->matrix;
$bArray = $bMatrix->getArray();
//The number of columns in A must match the number of rows in B
if (count($aArray[0]) != count($bArray)) {
$mA = $this->toString();
$mB = $bMatrix->toString();
throw new \Exception("Columns in '{$mA}' don't match Rows of '{$mB}'", Matrix::E_NOT_EQUAL);
}
$rArray = array();
//Loop through rows of Matrix A
for ($i = 0; $i < count($aArray); $i++) {
//Loop through the columns of Matrix B
for ($j = 0; $j < count($bArray[0]); $j++) {
$value = 0;
//loop through the rows of Matrix B
for ($k = 0; $k < count($bArray); $k++) {
$value += $aArray[$i][$k] * $bArray[$k][$j];
}
$rArray[$i][$j] = $value;
}
}
$rMatrix = new Matrix($this->toString($rArray));
return $rMatrix;
}
public function testGetArray()
{
$arr = array(array(1, 2, 3), array(3, 4, 5));
$this->assertEquals($arr, $this->A->getArray());
}
/**
* Constructor: Check for symmetry, then construct the eigenvalue decomposition
*
* @param Matrix $Arg
* @internal param Matrix $Arg Square matrix
*/
public function __construct($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;
// Tri-diagonalize.
$this->tRed();
// Diagonalize.
$this->tql2();
} else {
$this->H = $this->A;
$this->ort = array();
// Reduce to Hessenberg form.
$this->ortHes();
// Reduce Hessenberg to real Schur form.
$this->hqr2();
}
}
