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;
-?>