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<?php
require_once "../Matrix.php";
class TestMatrix {
function TestMatrix() {
// define test variables
$errorCount = 0;
$warningCount = 0;
$columnwise = array(1.,2.,3.,4.,5.,6.,7.,8.,9.,10.,11.,12.);
$rowwise = array(1.,4.,7.,10.,2.,5.,8.,11.,3.,6.,9.,12.);
$avals = array(array(1.,4.,7.,10.),array(2.,5.,8.,11.),array(3.,6.,9.,12.));
$rankdef = $avals;
$tvals = array(array(1.,2.,3.),array(4.,5.,6.),array(7.,8.,9.),array(10.,11.,12.));
$subavals = array(array(5.,8.,11.),array(6.,9.,12.));
$rvals = array(array(1.,4.,7.),array(2.,5.,8.,11.),array(3.,6.,9.,12.));
$pvals = array(array(1.,1.,1.),array(1.,2.,3.),array(1.,3.,6.));
$ivals = array(array(1.,0.,0.,0.),array(0.,1.,0.,0.),array(0.,0.,1.,0.));
$evals = array(array(0.,1.,0.,0.),array(1.,0.,2.e-7,0.),array(0.,-2.e-7,0.,1.),array(0.,0.,1.,0.));
$square = array(array(166.,188.,210.),array(188.,214.,240.),array(210.,240.,270.));
$sqSolution = array(array(13.),array(15.));
$condmat = array(array(1.,3.),array(7.,9.));
$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.;
$rowsummax = 30.;
$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.);
$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>.");
}
/**
* Print appropriate messages for successful outcome try
* @param string $s
* @param string $e
*/
function try_success($s, $e = "") {
print "> ". $s ."success<br />";
if ($e != "")
print "> Message: ". $e ."<br />";
}
/**
* Print appropriate messages for unsuccessful outcome try
* @param int $count
* @param string $s
* @param string $e
* @return int incremented counter
*/
function try_failure($count, $s, $e="") {
print "> ". $s ."*** failure ***<br />> Message: ". $e ."<br />";
return ++$count;
}
/**
* Print appropriate messages for unsuccessful outcome try
* @param int $count
* @param string $s
* @param string $e
* @return int incremented counter
*/
function try_warning($count, $s, $e="") {
print "> ". $s ."*** warning ***<br />> Message: ". $e ."<br />";
return ++$count;
}
/**
* Check magnitude of difference of "scalars".
* @param float $x
* @param float $y
*/
function checkScalars($x, $y) {
$eps = pow(2.0,-52.0);
if ($x == 0 & abs($y) < 10*$eps) return;
if ($y == 0 & abs($x) < 10*$eps) return;
if (abs($x-$y) > 10 * $eps * max(abs($x),abs($y)))
return false;
else
return true;
}
/**
* Check norm of difference of "vectors".
* @param float $x[]
* @param float $y[]
*/
function checkVectors($x, $y) {
$nx = count($x);
$ny = count($y);
if ($nx == $ny)
for($i=0; $i < $nx; ++$i)
$this->checkScalars($x[$i],$y[$i]);
else
die("Attempt to compare vectors of different lengths");
}
/**
* Check norm of difference of "arrays".
* @param float $x[][]
* @param float $y[][]
*/
function checkArrays($x, $y) {
$A = new Matrix($x);
$B = new Matrix($y);
return $this->checkMatrices($A,$B);
}
/**
* Check norm of difference of "matrices".
* @param matrix $X
* @param matrix $Y
*/
function checkMatrices($X = null, $Y = null) {
if( $X == null || $Y == null )
return false;
$eps = pow(2.0,-52.0);
if ($X->norm1() == 0. & $Y->norm1() < 10*$eps) return true;
if ($Y->norm1() == 0. & $X->norm1() < 10*$eps) return true;
$A = $X->minus($Y);
if ($A->norm1() > 1000 * $eps * max($X->norm1(),$Y->norm1()))
die("The norm of (X-Y) is too large: ".$A->norm1());
else
return true;
}
}
$test = new TestMatrix;
?>
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