Testing access methods...
"; $B = new Matrix($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 "Testing array-like methods...
"; /** * I/O methods: * read * print * serializable: * writeObject * readObject */ print "Testing I/O methods...
"; /** * Test linear algebra methods */ echo "Testing linear algebra methods...
";
$A = new Matrix($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("{$errorCount} total errors.");
}
/**
* Print appropriate messages for successful outcome try
* @param string $s
* @param string $e
*/
function try_success($s, $e = "") {
print "> ". $s ."success
";
if ($e != "")
print "> Message: ". $e ."
";
}
/**
* 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 ***
> Message: ". $e ."
";
return ++$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 ***
> Message: ". $e ."
";
return ++$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;
?>