public static Matrix inverse(Matrix x) {
int rows = x.getRowDimension();
int cols = x.getColumnDimension();
if (rows < cols) {
Matrix result = inverse(x.transpose());
if (result != null) result = result.transpose();
return result;
}
SingularValueDecomposition svdX = new SingularValueDecomposition(x);
if (svdX.rank() < 1) return null;
double[] singularValues = svdX.getSingularValues();
double tol = Math.max(rows, cols) * singularValues[0] * MACHEPS;
double[] singularValueReciprocals = new double[singularValues.length];
for (int i = 0; i < singularValues.length; i++)
if (Math.abs(singularValues[i]) >= tol) singularValueReciprocals[i] = 1.0 / singularValues[i];
double[][] u = svdX.getU().getArray();
double[][] v = svdX.getV().getArray();
int min = Math.min(cols, u[0].length);
double[][] inverse = new double[cols][rows];
for (int i = 0; i < cols; i++)
for (int j = 0; j < u.length; j++)
for (int k = 0; k < min; k++)
inverse[i][j] += v[i][k] * singularValueReciprocals[k] * u[j][k];
return new Matrix(inverse);
}
/**
* Update the covariance Matrix of the weight posterior distribution (SIGMA) along with its
* cholesky factor:
*
* <p>SIGMA = (A + beta * PHI^t * PHI)^{-1}
*
* <p>SIGMA_chol with SIGMA_chol * SIGMA_chol^t = SIGMA
*/
protected void updateSIGMA() {
Matrix SIGMA_inv = PHI_t.times(PHI_t.transpose());
SIGMA_inv.timesEquals(beta);
SIGMA_inv.plusEquals(A);
/** Update the factor ... */
SECholeskyDecomposition CD = new SECholeskyDecomposition(SIGMA_inv.getArray());
Matrix U = CD.getPTR().times(CD.getL());
SIGMA_chol = U.inverse();
/** Update SIGMA */
SIGMA = (SIGMA_chol.transpose()).times(SIGMA_chol);
}
/**
* Computes the pseudo-inverse of a matrix using Singular Value Decomposition
*
* @param M - the input {@link Matrix}
* @param threshold - the threshold for inverting diagonal elements (suggested 0.001)
* @return the inverted {@link Matrix} or an approximation with lowest possible squared error
*/
public static final Matrix computePseudoInverseMatrix(final Matrix M, final double threshold) {
final SingularValueDecomposition svd = new SingularValueDecomposition(M);
Matrix U = svd.getU(); // U Left Matrix
final Matrix S = svd.getS(); // W
final Matrix V = svd.getV(); // VT Right Matrix
double temp;
// invert S
for (int j = 0; j < S.getRowDimension(); ++j) {
temp = S.get(j, j);
if (temp < threshold) // this is an inaccurate inverting of the matrix
temp = 1.0 / threshold;
else temp = 1.0 / temp;
S.set(j, j, temp);
}
// transponse U
U = U.transpose();
//
// compute result
//
return ((V.times(S)).times(U));
}
/**
* Creation of one muscle.
*
* @param moment nb_segment lines, 3 col : On each line, the influence on the given joint as in
* moment[i,0]+moment[i,1]*sin(moment[i,2]*angle)
* @param minL0 minimum size of muscle
* @param maxL0 maximum size of muscle
*/
public SimpleMuscle() {
// Init
_ln = _minL0.copy();
_vn = new Matrix(1, _ln.getColumnDimension(), 0);
_tn = new Matrix(1, _ln.getColumnDimension(), 0);
_t = new Matrix(1, _ln.getColumnDimension(), 0);
_cpl = new Matrix(1, _minA.getColumnDimension(), 0);
// ratio l/l0=k
// _k = (_maxL0-_minL0) / JamaU.dotP(_mom, _maxA.minus(_minA));
_k = (_maxL0.minus(_minL0)).arrayRightDivide((_maxA.minus(_minA)).times(_mom.transpose()));
_k = _k.uminus();
}
public static void main(String[] argarray) {
CoefArgs args = CoefArgs.parse(argarray);
try {
AllMultilevelCoefs coefs = new AllMultilevelCoefs(args);
Matrix matrix = coefs.matrix(true);
Matrix covar = matrix.transpose().times(matrix);
SingularValueDecomposition svd = covar.svd();
Matrix U = svd.getU();
double[] d1 = normalize(column(U, 1));
double[] d2 = normalize(column(U, 2));
String[] genes = coefs.genes();
DataFrame<MultilevelCoefs.XYPoint> points =
new DataFrame<MultilevelCoefs.XYPoint>(MultilevelCoefs.XYPoint.class);
for (int i = 0; i < genes.length; i++) {
double[] gr = row(matrix, i);
double x = inner(gr, d1), y = inner(gr, d2);
MultilevelCoefs.XYPoint point = new MultilevelCoefs.XYPoint(x, y, genes[i]);
points.addObject(point);
System.out.println(point.toString());
}
System.out.println("U: ");
println(U, System.out);
ModelScatter scatter = new ModelScatter();
scatter.addModels(points.iterator());
scatter.setProperty(ModelScatter.colorKey, Coloring.clearer(Color.red));
coefs.save(
new File(
String.format(
"C:\\Documents and Settings\\tdanford\\Desktop\\sigma_%s.txt", args.compare)));
new ModelScatter.InteractiveFrame(scatter, "PCA");
} catch (IOException e) {
e.printStackTrace();
}
}
/** Update beta (same as for the "normal" regression rvm) */
protected void updateBeta() {
/** Calculate gammas && their sum: gamma_i = 1 - alpha_i * SIGMA_ii */
double[] gammas = new double[basisSet.size()];
for (int j = 0; j < basisSet.size(); j++) {
gammas[j] = 1.0d - alpha[basisSet.get(j)] * SIGMA.get(j, j);
}
double sumGammas = 0;
for (int j = 0; j < gammas.length; j++) {
sumGammas += gammas[j];
}
/** Calculate delta = t - PHI * mu */
Matrix DELTA = (new Matrix(t)).minus(PHI_t.transpose().times(mu));
/** beta = N - sum_i(gamma_i) / norm_l2(DELTA)^2 */
beta = x.length - sumGammas / innerProduct(DELTA.getRowPackedCopy(), DELTA.getRowPackedCopy());
}
/* ERROR DETERMINATION */
private void determineError() {
double var_est = 1 / ((double) getDegreesOfFreedom()) * sumOfSquares();
Matrix J = calcJ();
Matrix JT = J.transpose();
Matrix err = (JT.times(J)).inverse();
covar = err.times(var_est);
param_stdDev = new double[numFittable];
double[][] matrixVals = new double[numFittable][numFittable];
for (int i = 0; i < numFittable; i++) {
param_stdDev[i] = Math.sqrt(covar.get(i, i));
matrixVals[i][i] = param_stdDev[i];
}
for (int i = 0; i < numFittable; i++) {
for (int j = i; j < numFittable; j++) {
matrixVals[i][j] = covar.get(i, j) / (matrixVals[i][i] * matrixVals[j][j]);
}
}
corr = new Matrix(matrixVals);
}
/**
* use the online model to predict the target position given the positions measured at the bpms
*/
public void performAnalysis(final List<BPM> bpms) throws Exception {
final int measurementCount = VIEW_SCREEN_MEASUREMENTS.size();
double meanDifference = 0.0; // TODO: CKA - NEVER USED
final Matrix diag = new Matrix(measurementCount, 2);
final Matrix viewScreenMeas = new Matrix(measurementCount, 1);
final List<TargetAnalysisResultRecord> rawResults =
new ArrayList<TargetAnalysisResultRecord>(measurementCount);
int row = 0;
for (final ViewScreenMeasurement measurement : VIEW_SCREEN_MEASUREMENTS) {
final TargetAnalysisResultRecord rawResult = predictWithMatcher(bpms, measurement);
rawResults.add(rawResult);
final double measuredPosition = rawResult.getMeasuredPosition();
viewScreenMeas.set(row, 0, measuredPosition);
diag.set(row, 0, 1.0);
diag.set(row, 1, rawResult.getPredictedPosition());
meanDifference += rawResult.getMeasuredPosition() - rawResult.getPredictedPosition();
++row;
}
meanDifference /= measurementCount;
final Matrix diagT = diag.transpose();
final Matrix coef = diagT.times(diag).inverse().times(diagT).times(viewScreenMeas);
final double offset = coef.get(0, 0);
final double scale = coef.get(1, 0);
final List<TargetAnalysisResultRecord> results = new ArrayList<TargetAnalysisResultRecord>();
double errorSum = 0.0;
for (final TargetAnalysisResultRecord rawResult : rawResults) {
final double predictedPosition = scale * rawResult.getPredictedPosition() + offset;
final double measuredPosition = rawResult.getMeasuredPosition();
final TargetAnalysisResultRecord result =
new TargetAnalysisResultRecord(measuredPosition, predictedPosition);
results.add(result);
errorSum += (measuredPosition - predictedPosition) * (measuredPosition - predictedPosition);
}
final double rmsError = Math.sqrt(errorSum / rawResults.size());
_scale = scale;
_offset = offset;
_rmsError = rmsError;
}
/**
* 输出特征脸 根据特征向量得出Image类型
*
* @param args
*/
public static Image[] getFeatureFaces() {
double[][] rfVec = Features.getInstance().getResultFeatureVector();
Matrix mat = new Matrix(rfVec);
mat = mat.transpose();
rfVec = mat.getArray();
Image[] img = new Image[rfVec.length];
for (int i = 0; i < rfVec.length; i++) {
System.out.println("i:" + i);
// 这一步可能会有压缩损失
// 最好找一个方法，直接从double[]转换成Image
// 将double[]转换成int[]
int[][] rfVecInt = new int[rfVec.length][rfVec[0].length];
// System.out.println("[" + rfVec.length + "]" + "[" + rfVec[0].length + "]");
for (int j = 0; j < rfVec[0].length; j++) {
// rfVecInt[i][j] = (int)rfVec[i][j];//无四舍五入
rfVecInt[i][j] =
Integer.parseInt(new java.text.DecimalFormat("0").format(rfVec[i][j])); // 四舍五入
// System.out.print(rfVecInt[i][j] + " ");
// ----------------整个if语句是测试语句，要删除
// if(i==9)
// {
// System.out.println("Yes!");
// rfVecInt[i][j] = Integer.parseInt(new
// java.text.DecimalFormat("0").format(rfVec[i][j]));//四舍五入
// }
// ----------------以上为测试语句
}
System.out.println("i:" + i);
img[i] = getImgByPixels(width, height, rfVecInt[i]);
// System.out.println();
// img[i] = getImgByPixels(128, 128, rfVecInt[i]);
}
// System.out.println("img length:" + img.length);
return img;
}
/**
* Compute the scalars s_m, q_m which are part of the criterium for inclusion / deletion of the
* given basis m:
*
* <p>S_m = beta * phi^t_m * phi_m - beta^2 * phi^t_m * PHI * SIGMA * PHI^t * phi_m Q_m = beta *
* phi^t_m * t - beta^2 * phi^t_m * PHI * SIGMA * PHI^t * t
*
* <p>s_m = alpha_m * S_m / (alpha_m - S_m) q_m = alpha_m * Q_m / (alpha_m - S_m)
*/
protected void updateCriteriumScalars(int selectedBasis) {
Matrix SigmaStuff = (PHI_t.transpose()).times(SIGMA.times(PHI_t));
double S =
beta * innerProduct(phi[selectedBasis], phi[selectedBasis])
- beta
* beta
* innerProduct(
phi[selectedBasis],
SigmaStuff.times(new Matrix(phi[selectedBasis], phi[selectedBasis].length))
.getRowPackedCopy());
double Q =
beta * innerProduct(phi[selectedBasis], tVector)
- beta
* beta
* innerProduct(
phi[selectedBasis], SigmaStuff.times(new Matrix(t)).getRowPackedCopy());
s = alpha[selectedBasis] * S / (alpha[selectedBasis] - S);
q = alpha[selectedBasis] * Q / (alpha[selectedBasis] - S);
}
/** 计算协方差矩阵 传入形参为 <方法：计算每张图片的均差> 的返回值 (其实这并不是协方差矩阵，若需要协方差矩阵，再用该矩阵除以N即可) */
public static double[][] calCovarianceMatrix(double[][] vec) {
int length = vec.length; // length指向量的维数，X={1,2,3,...,length}
int n = vec[0].length; // n指向量的个数，X1,X2,X3...Xn;
Matrix vecOld = new Matrix(vec);
// System.out.println("vecOld:");
// vecOld.print(6, 2);
// System.out.println();
Matrix vecTrans = vecOld.transpose(); // 获取转置矩阵
// System.out.println("vecTrans:");
// vecTrans.print(6, 2);
double[][] covArr = new double[nOld][nOld]; // 初始化协方差矩阵
// 构造协方差矩阵
// Matrix cov = vecOld.times(vecTrans);
Matrix cov = vecTrans.times(vecOld);
covArr = cov.getArray();
// 由于最终计算并不需要协方差矩阵，仅仅要的是一部分，所以不用除以N
// 除以N
// for(int i=0; i<n; i++)
// {
// for(int j=0; j<length; j++)
// {
// covArr[i][j] = covArr[i][j] / n;
// }
// }
Features.getInstance().setCovarianceMatrix(covArr);
return covArr;
}
public double defaultHypothesis(Matrix input) throws IllegalArgumentException {
double z = ((parameter.transpose()).times(input)).get(0, 0);
return 1 / (1 + exp(-z));
}
private void RunSPKF() {
// SPKF Steps:
// 1) Generate Test Points
// 2) Propagate Test Points
// 3) Compute Predicted Mean and Covariance
// 4) Compute Measurements
// 5) Compute Innovations and Cross Covariance
// 6) Compute corrections and update
// Line up initial variables from the controller!
Double dAlpha = dGreek.get(0);
Double dBeta = dGreek.get(1);
cController.setAlpha(dAlpha);
cController.setBeta(dBeta);
cController.setKappa(dGreek.get(2));
Double dGamma = cController.getGamma();
Double dLambda = cController.getLambda();
// // DEBUG - Print the Greeks
// System.out.println("Greeks!");
// System.out.println("Alpha - " + dAlpha);
// System.out.println("Beta - " + dBeta);
// System.out.println("Kappa - " + dGreek.get(2));
// System.out.println("Lambda - " + dLambda);
// System.out.println("Gamma - " + dGamma);
// Let's get started:
// Step 1: Generate Test Points
Vector<Matrix> Chi = new Vector<Matrix>();
Vector<Matrix> UpChi = new Vector<Matrix>();
Vector<Matrix> UpY = new Vector<Matrix>();
Matrix UpPx = new Matrix(3, 3, 0.0);
Matrix UpPy = new Matrix(3, 3, 0.0);
Matrix UpPxy = new Matrix(3, 3, 0.0);
Matrix K;
Vector<Double> wc = new Vector<Double>();
Vector<Double> wm = new Vector<Double>();
Chi.add(X); // Add Chi_0 - the current state estimate (X, Y, Z)
// Big P Matrix is LxL diagonal
Matrix SqrtP = SqrtSPKF(P);
SqrtP = SqrtP.times(dGamma);
// Set up Sigma Points
for (int i = 0; i <= 8; i++) {
Matrix tempVec = SqrtP.getMatrix(0, 8, i, i);
Matrix tempX = X;
Matrix tempPlus = tempX.plus(tempVec);
// System.out.println("TempPlus");
// tempPlus.print(3, 2);
Matrix tempMinu = tempX.minus(tempVec);
// System.out.println("TempMinus");
// tempMinu.print(3, 2);
// tempX = X.copy();
// tempX.setMatrix(i, i, 0, 2, tempPlus);
Chi.add(tempPlus);
// tempX = X.copy();
// tempX.setMatrix(i, i, 0, 2, tempMinu);
Chi.add(tempMinu);
}
// DEBUG Print the lines inside the Chi Matrix (2L x L)
// for (int i = 0; i<=(2*L); i++){
// System.out.println("Chi Matrix Set: "+i);
// Chi.get(i).print(5, 2);
// }
// Generate weights
Double WeightZero = (dLambda / (L + dLambda));
Double OtherWeight = (1 / (2 * (L + dLambda)));
Double TotalWeight = WeightZero;
wm.add(WeightZero);
wc.add(WeightZero + (1 - (dAlpha * dAlpha) + dBeta));
for (int i = 1; i <= (2 * L); i++) {
TotalWeight = TotalWeight + OtherWeight;
wm.add(OtherWeight);
wc.add(OtherWeight);
}
// Weights MUST BE 1 in total
for (int i = 0; i <= (2 * L); i++) {
wm.set(i, wm.get(i) / TotalWeight);
wc.set(i, wc.get(i) / TotalWeight);
}
// //DEBUG Print the weights
// System.out.println("Total Weight:");
// System.out.println(TotalWeight);
// for (int i = 0; i<=(2*L); i++){
// System.out.println("Weight M for "+i+" Entry");
// System.out.println(wm.get(i));
// System.out.println("Weight C for "+i+" Entry");
// System.out.println(wc.get(i));
// }
// Step 2: Propagate Test Points
// This will also handle computing the mean
Double ux = dControl.elementAt(0);
Double uy = dControl.elementAt(1);
Double uz = dControl.elementAt(2);
Matrix XhatMean = new Matrix(3, 1, 0.0);
for (int i = 0; i < Chi.size(); i++) {
Matrix ChiOne = Chi.get(i);
Matrix Chixminus = new Matrix(3, 1, 0.0);
Double Xhat = ChiOne.get(0, 0);
Double Yhat = ChiOne.get(1, 0);
Double Zhat = ChiOne.get(2, 0);
Double Xerr = ChiOne.get(3, 0);
Double Yerr = ChiOne.get(4, 0);
Double Zerr = ChiOne.get(5, 0);
Xhat = Xhat + ux + Xerr;
Yhat = Yhat + uy + Yerr;
Zhat = Zhat + uz + Zerr;
Chixminus.set(0, 0, Xhat);
Chixminus.set(1, 0, Yhat);
Chixminus.set(2, 0, Zhat);
// System.out.println("ChixMinus:");
// Chixminus.print(3, 2);
UpChi.add(Chixminus);
XhatMean = XhatMean.plus(Chixminus.times(wm.get(i)));
}
// Mean is right!
// System.out.println("XhatMean: ");
// XhatMean.print(3, 2);
// Step 3: Compute Predicted Mean and Covariance
// Welp, we already solved the mean - let's do the covariance now
for (int i = 0; i <= (2 * L); i++) {
Matrix tempP = UpChi.get(i).minus(XhatMean);
Matrix tempPw = tempP.times(wc.get(i));
tempP = tempPw.times(tempP.transpose());
UpPx = UpPx.plus(tempP);
}
// New Steps!
// Step 4: Compute Measurements! (and Y mean!)
Matrix YhatMean = new Matrix(3, 1, 0.0);
for (int i = 0; i <= (2 * L); i++) {
Matrix ChiOne = Chi.get(i);
Matrix Chiyminus = new Matrix(3, 1, 0.0);
Double Xhat = UpChi.get(i).get(0, 0);
Double Yhat = UpChi.get(i).get(1, 0);
Double Zhat = UpChi.get(i).get(2, 0);
Double Xerr = ChiOne.get(6, 0);
Double Yerr = ChiOne.get(7, 0);
Double Zerr = ChiOne.get(8, 0);
Xhat = Xhat + Xerr;
Yhat = Yhat + Yerr;
Zhat = Zhat + Zerr;
Chiyminus.set(0, 0, Xhat);
Chiyminus.set(1, 0, Yhat);
Chiyminus.set(2, 0, Zhat);
UpY.add(Chiyminus);
YhatMean = YhatMean.plus(Chiyminus.times(wm.get(i)));
}
// // Welp, we already solved the mean - let's do the covariances
// now
// System.out.println("XHatMean and YHatMean = ");
// XhatMean.print(3, 2);
// YhatMean.print(3, 2);
for (int i = 0; i <= (2 * L); i++) {
Matrix tempPx = UpChi.get(i).minus(XhatMean);
Matrix tempPy = UpY.get(i).minus(YhatMean);
// System.out.println("ChiX - XhatMean and ChiY-YhatMean");
// tempPx.print(3, 2);
// tempPy.print(3, 2);
Matrix tempPxw = tempPx.times(wc.get(i));
Matrix tempPyw = tempPy.times(wc.get(i));
tempPx = tempPxw.times(tempPy.transpose());
tempPy = tempPyw.times(tempPy.transpose());
UpPy = UpPy.plus(tempPy);
UpPxy = UpPxy.plus(tempPx);
}
// Step 6: Compute Corrections and Update
// Compute Kalman Gain!
// System.out.println("Updated Px");
// UpPx.print(5, 2);
// System.out.println("Updated Py");
// UpPy.print(5, 2);
// System.out.println("Updated Pxy");
// UpPxy.print(5, 2);
K = UpPxy.times(UpPy.inverse());
// System.out.println("Kalman");
// K.print(5, 2);
Matrix Mea = new Matrix(3, 1, 0.0);
Mea.set(0, 0, dMeasure.get(0));
Mea.set(1, 0, dMeasure.get(1));
Mea.set(2, 0, dMeasure.get(2));
Matrix Out = K.times(Mea.minus(YhatMean));
Out = Out.plus(XhatMean);
// System.out.println("Out:");
// Out.print(3, 2);
Matrix Px = UpPx.minus(K.times(UpPy.times(K.transpose())));
// Update Stuff!
// Push the P to the controller
Matrix OutP = P.copy();
OutP.setMatrix(0, 2, 0, 2, Px);
X.setMatrix(0, 2, 0, 0, Out);
Residual = XhatMean.minus(Out);
cController.inputState(OutP, Residual);
// cController.setL(L);
cController.startProcess();
while (!cController.finishedProcess()) {
try {
Thread.sleep(10);
} catch (InterruptedException e) {
e.printStackTrace();
}
}
// System.out.println("Post Greeks: " + cController.getAlpha() + " ,
// "+ cController.getBeta());
dGreek.set(0, cController.getAlpha());
dGreek.set(1, cController.getBeta());
dGreek.set(2, cController.getKappa());
P = cController.getP();
// System.out.println("P is post Process:");
// P.print(3, 2);
StepDone = true;
}
public static void main(String[] args) throws IOException {
String train_file_name = "150(1000)-100-train.csv",
test_file_name = "test-1000-100.csv",
train_data,
test_data,
output_file;
int training_rows = 0, training_cols = 0, testing_rows = 0, testing_cols = 0;
BufferedReader CSVTrain = new BufferedReader(new FileReader(train_file_name));
train_data = CSVTrain.readLine();
BufferedReader CSVTest = new BufferedReader(new FileReader(test_file_name));
test_data = CSVTest.readLine();
ArrayList<String[]> train_array_list = new ArrayList<String[]>();
ArrayList<String[]> test_array_list = new ArrayList<String[]>();
training_cols = countColumns(train_data, training_cols);
testing_cols = countColumns(test_data, testing_cols);
training_rows = readData(CSVTrain, train_array_list, training_rows, training_cols);
testing_rows = readData(CSVTest, test_array_list, testing_rows, testing_cols);
double X_train[][] = new double[training_rows][training_cols];
double Y_train[][] = new double[training_rows][1];
double X_test[][] = new double[testing_rows][testing_cols];
double Y_test[][] = new double[testing_rows][1];
insertX0(training_rows, X_train);
insertX0(testing_rows, X_test);
createXYarray(train_array_list, training_cols, X_train, Y_train);
createXYarray(test_array_list, testing_cols, X_test, Y_test);
Matrix mx_train = Matrix.constructWithCopy(X_train);
Matrix my_train = Matrix.constructWithCopy(Y_train);
Matrix mx_test = Matrix.constructWithCopy(X_test);
Matrix my_test = Matrix.constructWithCopy(Y_test);
double minimum_error = (double) 1000;
int optimal_lambda = 0;
output_file = "output-" + train_file_name;
PrintStream output = new PrintStream(new File(output_file));
for (int lambda = 0; lambda <= 150; lambda++) {
Matrix w =
((((mx_train.transpose().times(mx_train))
.plus(Matrix.identity(training_cols, training_cols).times((double) lambda)))
.inverse())
.times((mx_train.transpose()).times(my_train)));
Matrix E_train = calculateMSE(training_rows, mx_train, my_train, w);
Matrix E_test = calculateMSE(testing_rows, mx_test, my_test, w);
output.append(Double.toString(E_train.get(0, 0)) + ",");
output.append(Double.toString(E_test.get(0, 0)) + ",");
output.append(Integer.toString(lambda) + ",");
output.println();
if (E_test.get(0, 0) < minimum_error) {
minimum_error = E_test.get(0, 0);
optimal_lambda = lambda;
}
}
System.out.println("Minimum Error:" + minimum_error);
System.out.println("Optimal Lambda:" + optimal_lambda);
output.close();
}
public static void main(String argv[]) {
Matrix A, B, C, Z, O, I, R, S, X, SUB, M, T, SQ, DEF, SOL;
// Uncomment this to test IO in a different locale.
// Locale.setDefault(Locale.GERMAN);
int errorCount = 0;
int warningCount = 0;
double tmp, s;
double[] columnwise = {1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.};
double[] rowwise = {1., 4., 7., 10., 2., 5., 8., 11., 3., 6., 9., 12.};
double[][] avals = {{1., 4., 7., 10.}, {2., 5., 8., 11.}, {3., 6., 9., 12.}};
double[][] rankdef = avals;
double[][] tvals = {{1., 2., 3.}, {4., 5., 6.}, {7., 8., 9.}, {10., 11., 12.}};
double[][] subavals = {{5., 8., 11.}, {6., 9., 12.}};
double[][] rvals = {{1., 4., 7.}, {2., 5., 8., 11.}, {3., 6., 9., 12.}};
double[][] pvals = {{4., 1., 1.}, {1., 2., 3.}, {1., 3., 6.}};
double[][] ivals = {{1., 0., 0., 0.}, {0., 1., 0., 0.}, {0., 0., 1., 0.}};
double[][] evals = {
{0., 1., 0., 0.}, {1., 0., 2.e-7, 0.}, {0., -2.e-7, 0., 1.}, {0., 0., 1., 0.}
};
double[][] square = {{166., 188., 210.}, {188., 214., 240.}, {210., 240., 270.}};
double[][] sqSolution = {{13.}, {15.}};
double[][] condmat = {{1., 3.}, {7., 9.}};
double[][] badeigs = {
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 1, 0}, {1, 1, 0, 0, 1}, {1, 0, 1, 0, 1}
};
int rows = 3, cols = 4;
int invalidld = 5; /* should trigger bad shape for construction with val */
int raggedr = 0; /* (raggedr,raggedc) should be out of bounds in ragged array */
int raggedc = 4;
int validld = 3; /* leading dimension of intended test Matrices */
int nonconformld = 4; /* leading dimension which is valid, but nonconforming */
int ib = 1, ie = 2, jb = 1, je = 3; /* index ranges for sub Matrix */
int[] rowindexset = {1, 2};
int[] badrowindexset = {1, 3};
int[] columnindexset = {1, 2, 3};
int[] badcolumnindexset = {1, 2, 4};
double columnsummax = 33.;
double rowsummax = 30.;
double sumofdiagonals = 15;
double sumofsquares = 650;
/**
* Constructors and constructor-like methods: double[], int double[][] int, int int, int, double
* int, int, double[][] constructWithCopy(double[][]) random(int,int) identity(int)
*/
print("\nTesting constructors and constructor-like methods...\n");
try {
/** check that exception is thrown in packed constructor with invalid length * */
A = new Matrix(columnwise, invalidld);
errorCount =
try_failure(
errorCount,
"Catch invalid length in packed constructor... ",
"exception not thrown for invalid input");
} catch (IllegalArgumentException e) {
try_success("Catch invalid length in packed constructor... ", e.getMessage());
}
try {
/** check that exception is thrown in default constructor if input array is 'ragged' * */
A = new Matrix(rvals);
tmp = A.get(raggedr, raggedc);
} catch (IllegalArgumentException e) {
try_success("Catch ragged input to default constructor... ", e.getMessage());
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"Catch ragged input to constructor... ",
"exception not thrown in construction...ArrayIndexOutOfBoundsException thrown later");
}
try {
/** check that exception is thrown in constructWithCopy if input array is 'ragged' * */
A = Matrix.constructWithCopy(rvals);
tmp = A.get(raggedr, raggedc);
} catch (IllegalArgumentException e) {
try_success("Catch ragged input to constructWithCopy... ", e.getMessage());
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"Catch ragged input to constructWithCopy... ",
"exception not thrown in construction...ArrayIndexOutOfBoundsException thrown later");
}
A = new Matrix(columnwise, validld);
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;
if ((tmp - B.get(0, 0)) != 0.0) {
/** check that constructWithCopy behaves properly * */
errorCount =
try_failure(
errorCount, "constructWithCopy... ", "copy not effected... data visible outside");
} else {
try_success("constructWithCopy... ", "");
}
avals[0][0] = columnwise[0];
I = new Matrix(ivals);
try {
check(I, Matrix.identity(3, 4));
try_success("identity... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
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("\nTesting access methods...\n");
/** Various get methods: */
B = new Matrix(avals);
if (B.getRowDimension() != rows) {
errorCount = try_failure(errorCount, "getRowDimension... ", "");
} else {
try_success("getRowDimension... ", "");
}
if (B.getColumnDimension() != cols) {
errorCount = try_failure(errorCount, "getColumnDimension... ", "");
} else {
try_success("getColumnDimension... ", "");
}
B = new Matrix(avals);
double[][] barray = B.getArray();
if (barray != avals) {
errorCount = try_failure(errorCount, "getArray... ", "");
} else {
try_success("getArray... ", "");
}
barray = B.getArrayCopy();
if (barray == avals) {
errorCount = try_failure(errorCount, "getArrayCopy... ", "data not (deep) copied");
}
try {
check(barray, avals);
try_success("getArrayCopy... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(errorCount, "getArrayCopy... ", "data not successfully (deep) copied");
}
double[] bpacked = B.getColumnPackedCopy();
try {
check(bpacked, columnwise);
try_success("getColumnPackedCopy... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"getColumnPackedCopy... ",
"data not successfully (deep) copied by columns");
}
bpacked = B.getRowPackedCopy();
try {
check(bpacked, rowwise);
try_success("getRowPackedCopy... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "getRowPackedCopy... ", "data not successfully (deep) copied by rows");
}
try {
tmp = B.get(B.getRowDimension(), B.getColumnDimension() - 1);
errorCount =
try_failure(
errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
tmp = B.get(B.getRowDimension() - 1, B.getColumnDimension());
errorCount =
try_failure(
errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("get(int,int)... OutofBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
}
try {
if (B.get(B.getRowDimension() - 1, B.getColumnDimension() - 1)
!= avals[B.getRowDimension() - 1][B.getColumnDimension() - 1]) {
errorCount =
try_failure(
errorCount, "get(int,int)... ", "Matrix entry (i,j) not successfully retreived");
} else {
try_success("get(int,int)... ", "");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(errorCount, "get(int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
}
SUB = new Matrix(subavals);
try {
M = B.getMatrix(ib, ie + B.getRowDimension() + 1, jb, je);
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
M = B.getMatrix(ib, ie, jb, je + B.getColumnDimension() + 1);
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("getMatrix(int,int,int,int)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
M = B.getMatrix(ib, ie, jb, je);
try {
check(SUB, M);
try_success("getMatrix(int,int,int,int)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int,int)... ",
"submatrix not successfully retreived");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int,int)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
M = B.getMatrix(ib, ie, badcolumnindexset);
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
M = B.getMatrix(ib, ie + B.getRowDimension() + 1, columnindexset);
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("getMatrix(int,int,int[])... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
M = B.getMatrix(ib, ie, columnindexset);
try {
check(SUB, M);
try_success("getMatrix(int,int,int[])... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "getMatrix(int,int,int[])... ", "submatrix not successfully retreived");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"getMatrix(int,int,int[])... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
M = B.getMatrix(badrowindexset, jb, je);
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
M = B.getMatrix(rowindexset, jb, je + B.getColumnDimension() + 1);
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("getMatrix(int[],int,int)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int,int)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
M = B.getMatrix(rowindexset, jb, je);
try {
check(SUB, M);
try_success("getMatrix(int[],int,int)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "getMatrix(int[],int,int)... ", "submatrix not successfully retreived");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int,int)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
M = B.getMatrix(badrowindexset, columnindexset);
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
M = B.getMatrix(rowindexset, badcolumnindexset);
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("getMatrix(int[],int[])... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int[])... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
M = B.getMatrix(rowindexset, columnindexset);
try {
check(SUB, M);
try_success("getMatrix(int[],int[])... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "getMatrix(int[],int[])... ", "submatrix not successfully retreived");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
errorCount =
try_failure(
errorCount,
"getMatrix(int[],int[])... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
/** Various set methods: */
try {
B.set(B.getRowDimension(), B.getColumnDimension() - 1, 0.);
errorCount =
try_failure(
errorCount,
"set(int,int,double)... ",
"OutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
B.set(B.getRowDimension() - 1, B.getColumnDimension(), 0.);
errorCount =
try_failure(
errorCount,
"set(int,int,double)... ",
"OutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("set(int,int,double)... OutofBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"set(int,int,double)... ",
"OutOfBoundsException expected but not thrown");
}
try {
B.set(ib, jb, 0.);
tmp = B.get(ib, jb);
try {
check(tmp, 0.);
try_success("set(int,int,double)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "set(int,int,double)... ", "Matrix element not successfully set");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
errorCount =
try_failure(
errorCount, "set(int,int,double)... ", "Unexpected ArrayIndexOutOfBoundsException");
}
M = new Matrix(2, 3, 0.);
try {
B.setMatrix(ib, ie + B.getRowDimension() + 1, jb, je, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
B.setMatrix(ib, ie, jb, je + B.getColumnDimension() + 1, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("setMatrix(int,int,int,int,Matrix)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
B.setMatrix(ib, ie, jb, je, M);
try {
check(M.minus(B.getMatrix(ib, ie, jb, je)), M);
try_success("setMatrix(int,int,int,int,Matrix)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int,int,Matrix)... ",
"submatrix not successfully set");
}
B.setMatrix(ib, ie, jb, je, SUB);
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int,int,Matrix)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
B.setMatrix(ib, ie + B.getRowDimension() + 1, columnindexset, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
B.setMatrix(ib, ie, badcolumnindexset, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("setMatrix(int,int,int[],Matrix)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
B.setMatrix(ib, ie, columnindexset, M);
try {
check(M.minus(B.getMatrix(ib, ie, columnindexset)), M);
try_success("setMatrix(int,int,int[],Matrix)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int[],Matrix)... ",
"submatrix not successfully set");
}
B.setMatrix(ib, ie, jb, je, SUB);
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int,int,int[],Matrix)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
B.setMatrix(rowindexset, jb, je + B.getColumnDimension() + 1, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
B.setMatrix(badrowindexset, jb, je, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("setMatrix(int[],int,int,Matrix)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int,int,Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
B.setMatrix(rowindexset, jb, je, M);
try {
check(M.minus(B.getMatrix(rowindexset, jb, je)), M);
try_success("setMatrix(int[],int,int,Matrix)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int,int,Matrix)... ",
"submatrix not successfully set");
}
B.setMatrix(ib, ie, jb, je, SUB);
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int,int,Matrix)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
try {
B.setMatrix(rowindexset, badcolumnindexset, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e) {
try {
B.setMatrix(badrowindexset, columnindexset, M);
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
try_success("setMatrix(int[],int[],Matrix)... ArrayIndexOutOfBoundsException... ", "");
}
} catch (java.lang.IllegalArgumentException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int[],Matrix)... ",
"ArrayIndexOutOfBoundsException expected but not thrown");
}
try {
B.setMatrix(rowindexset, columnindexset, M);
try {
check(M.minus(B.getMatrix(rowindexset, columnindexset)), M);
try_success("setMatrix(int[],int[],Matrix)... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "setMatrix(int[],int[],Matrix)... ", "submatrix not successfully set");
}
} catch (java.lang.ArrayIndexOutOfBoundsException e1) {
errorCount =
try_failure(
errorCount,
"setMatrix(int[],int[],Matrix)... ",
"Unexpected ArrayIndexOutOfBoundsException");
}
/**
* Array-like methods: minus minusEquals plus plusEquals arrayLeftDivide arrayLeftDivideEquals
* arrayRightDivide arrayRightDivideEquals arrayTimes arrayTimesEquals uminus
*/
print("\nTesting array-like methods...\n");
S = new Matrix(columnwise, nonconformld);
R = Matrix.random(A.getRowDimension(), A.getColumnDimension());
A = R;
try {
S = A.minus(S);
errorCount =
try_failure(errorCount, "minus conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("minus conformance check... ", "");
}
if (A.minus(R).norm1() != 0.) {
errorCount =
try_failure(
errorCount,
"minus... ",
"(difference of identical Matrices is nonzero,\nSubsequent use of minus should be suspect)");
} else {
try_success("minus... ", "");
}
A = R.copy();
A.minusEquals(R);
Z = new Matrix(A.getRowDimension(), A.getColumnDimension());
try {
A.minusEquals(S);
errorCount =
try_failure(errorCount, "minusEquals conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("minusEquals conformance check... ", "");
}
if (A.minus(Z).norm1() != 0.) {
errorCount =
try_failure(
errorCount,
"minusEquals... ",
"(difference of identical Matrices is nonzero,\nSubsequent use of minus should be suspect)");
} else {
try_success("minusEquals... ", "");
}
A = R.copy();
B = Matrix.random(A.getRowDimension(), A.getColumnDimension());
C = A.minus(B);
try {
S = A.plus(S);
errorCount =
try_failure(errorCount, "plus conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("plus conformance check... ", "");
}
try {
check(C.plus(B), A);
try_success("plus... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "plus... ", "(C = A - B, but C + B != A)");
}
C = A.minus(B);
C.plusEquals(B);
try {
A.plusEquals(S);
errorCount =
try_failure(errorCount, "plusEquals conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("plusEquals conformance check... ", "");
}
try {
check(C, A);
try_success("plusEquals... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "plusEquals... ", "(C = A - B, but C = C + B != A)");
}
A = R.uminus();
try {
check(A.plus(R), Z);
try_success("uminus... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "uminus... ", "(-A + A != zeros)");
}
A = R.copy();
O = new Matrix(A.getRowDimension(), A.getColumnDimension(), 1.0);
C = A.arrayLeftDivide(R);
try {
S = A.arrayLeftDivide(S);
errorCount =
try_failure(
errorCount, "arrayLeftDivide conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayLeftDivide conformance check... ", "");
}
try {
check(C, O);
try_success("arrayLeftDivide... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "arrayLeftDivide... ", "(M.\\M != ones)");
}
try {
A.arrayLeftDivideEquals(S);
errorCount =
try_failure(
errorCount,
"arrayLeftDivideEquals conformance check... ",
"nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayLeftDivideEquals conformance check... ", "");
}
A.arrayLeftDivideEquals(R);
try {
check(A, O);
try_success("arrayLeftDivideEquals... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "arrayLeftDivideEquals... ", "(M.\\M != ones)");
}
A = R.copy();
try {
A.arrayRightDivide(S);
errorCount =
try_failure(
errorCount, "arrayRightDivide conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayRightDivide conformance check... ", "");
}
C = A.arrayRightDivide(R);
try {
check(C, O);
try_success("arrayRightDivide... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "arrayRightDivide... ", "(M./M != ones)");
}
try {
A.arrayRightDivideEquals(S);
errorCount =
try_failure(
errorCount,
"arrayRightDivideEquals conformance check... ",
"nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayRightDivideEquals conformance check... ", "");
}
A.arrayRightDivideEquals(R);
try {
check(A, O);
try_success("arrayRightDivideEquals... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "arrayRightDivideEquals... ", "(M./M != ones)");
}
A = R.copy();
B = Matrix.random(A.getRowDimension(), A.getColumnDimension());
try {
S = A.arrayTimes(S);
errorCount =
try_failure(errorCount, "arrayTimes conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayTimes conformance check... ", "");
}
C = A.arrayTimes(B);
try {
check(C.arrayRightDivideEquals(B), A);
try_success("arrayTimes... ", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "arrayTimes... ", "(A = R, C = A.*B, but C./B != A)");
}
try {
A.arrayTimesEquals(S);
errorCount =
try_failure(
errorCount, "arrayTimesEquals conformance check... ", "nonconformance not raised");
} catch (IllegalArgumentException e) {
try_success("arrayTimesEquals conformance check... ", "");
}
A.arrayTimesEquals(B);
try {
check(A.arrayRightDivideEquals(B), R);
try_success("arrayTimesEquals... ", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(errorCount, "arrayTimesEquals... ", "(A = R, A = A.*B, but A./B != R)");
}
/** I/O methods: read print serializable: writeObject readObject */
print("\nTesting I/O methods...\n");
try {
DecimalFormat fmt = new DecimalFormat("0.0000E00");
fmt.setDecimalFormatSymbols(new DecimalFormatSymbols(Locale.US));
PrintWriter FILE = new PrintWriter(new FileOutputStream("JamaTestMatrix.out"));
A.print(FILE, fmt, 10);
FILE.close();
R = Matrix.read(new BufferedReader(new FileReader("JamaTestMatrix.out")));
if (A.minus(R).norm1() < .001) {
try_success("print()/read()...", "");
} else {
errorCount =
try_failure(
errorCount,
"print()/read()...",
"Matrix read from file does not match Matrix printed to file");
}
} catch (java.io.IOException ioe) {
warningCount =
try_warning(
warningCount,
"print()/read()...",
"unexpected I/O error, unable to run print/read test; check write permission in current directory and retry");
} catch (Exception e) {
try {
e.printStackTrace(System.out);
warningCount =
try_warning(
warningCount,
"print()/read()...",
"Formatting error... will try JDK1.1 reformulation...");
DecimalFormat fmt = new DecimalFormat("0.0000");
PrintWriter FILE = new PrintWriter(new FileOutputStream("JamaTestMatrix.out"));
A.print(FILE, fmt, 10);
FILE.close();
R = Matrix.read(new BufferedReader(new FileReader("JamaTestMatrix.out")));
if (A.minus(R).norm1() < .001) {
try_success("print()/read()...", "");
} else {
errorCount =
try_failure(
errorCount,
"print()/read() (2nd attempt) ...",
"Matrix read from file does not match Matrix printed to file");
}
} catch (java.io.IOException ioe) {
warningCount =
try_warning(
warningCount,
"print()/read()...",
"unexpected I/O error, unable to run print/read test; check write permission in current directory and retry");
}
}
R = Matrix.random(A.getRowDimension(), A.getColumnDimension());
String tmpname = "TMPMATRIX.serial";
try {
@SuppressWarnings("resource")
ObjectOutputStream out = new ObjectOutputStream(new FileOutputStream(tmpname));
out.writeObject(R);
@SuppressWarnings("resource")
ObjectInputStream sin = new ObjectInputStream(new FileInputStream(tmpname));
A = (Matrix) sin.readObject();
try {
check(A, R);
try_success("writeObject(Matrix)/readObject(Matrix)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"writeObject(Matrix)/readObject(Matrix)...",
"Matrix not serialized correctly");
}
} catch (java.io.IOException ioe) {
warningCount =
try_warning(
warningCount,
"writeObject()/readObject()...",
"unexpected I/O error, unable to run serialization test; check write permission in current directory and retry");
} catch (Exception e) {
errorCount =
try_failure(
errorCount,
"writeObject(Matrix)/readObject(Matrix)...",
"unexpected error in serialization test");
}
/**
* LA methods: transpose times cond rank det trace norm1 norm2 normF normInf solve
* solveTranspose inverse chol eig lu qr svd
*/
print("\nTesting linear algebra methods...\n");
A = new Matrix(columnwise, 3);
T = new Matrix(tvals);
T = A.transpose();
try {
check(A.transpose(), T);
try_success("transpose...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "transpose()...", "transpose unsuccessful");
}
A.transpose();
try {
check(A.norm1(), columnsummax);
try_success("norm1...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "norm1()...", "incorrect norm calculation");
}
try {
check(A.normInf(), rowsummax);
try_success("normInf()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "normInf()...", "incorrect norm calculation");
}
try {
check(A.normF(), Math.sqrt(sumofsquares));
try_success("normF...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "normF()...", "incorrect norm calculation");
}
try {
check(A.trace(), sumofdiagonals);
try_success("trace()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "trace()...", "incorrect trace calculation");
}
try {
check(A.getMatrix(0, A.getRowDimension() - 1, 0, A.getRowDimension() - 1).det(), 0.);
try_success("det()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "det()...", "incorrect determinant calculation");
}
SQ = new Matrix(square);
try {
check(A.times(A.transpose()), SQ);
try_success("times(Matrix)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "times(Matrix)...", "incorrect Matrix-Matrix product calculation");
}
try {
check(A.times(0.), Z);
try_success("times(double)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount, "times(double)...", "incorrect Matrix-scalar product calculation");
}
A = new Matrix(columnwise, 4);
QRDecomposition QR = A.qr();
R = QR.getR();
try {
check(A, QR.getQ().times(R));
try_success("QRDecomposition...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(errorCount, "QRDecomposition...", "incorrect QR decomposition calculation");
}
SingularValueDecomposition SVD = A.svd();
try {
check(A, SVD.getU().times(SVD.getS().times(SVD.getV().transpose())));
try_success("SingularValueDecomposition...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"SingularValueDecomposition...",
"incorrect singular value decomposition calculation");
}
DEF = new Matrix(rankdef);
try {
check(DEF.rank(), Math.min(DEF.getRowDimension(), DEF.getColumnDimension()) - 1);
try_success("rank()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "rank()...", "incorrect rank calculation");
}
B = new Matrix(condmat);
SVD = B.svd();
double[] singularvalues = SVD.getSingularValues();
try {
check(
B.cond(),
singularvalues[0]
/ singularvalues[Math.min(B.getRowDimension(), B.getColumnDimension()) - 1]);
try_success("cond()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "cond()...", "incorrect condition number calculation");
}
int n = A.getColumnDimension();
A = A.getMatrix(0, n - 1, 0, n - 1);
A.set(0, 0, 0.);
LUDecomposition LU = A.lu();
try {
check(A.getMatrix(LU.getPivot(), 0, n - 1), LU.getL().times(LU.getU()));
try_success("LUDecomposition...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(errorCount, "LUDecomposition...", "incorrect LU decomposition calculation");
}
X = A.inverse();
try {
check(A.times(X), Matrix.identity(3, 3));
try_success("inverse()...", "");
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "inverse()...", "incorrect inverse calculation");
}
O = new Matrix(SUB.getRowDimension(), 1, 1.0);
SOL = new Matrix(sqSolution);
SQ = SUB.getMatrix(0, SUB.getRowDimension() - 1, 0, SUB.getRowDimension() - 1);
try {
check(SQ.solve(SOL), O);
try_success("solve()...", "");
} catch (java.lang.IllegalArgumentException e1) {
errorCount = try_failure(errorCount, "solve()...", e1.getMessage());
} catch (java.lang.RuntimeException e) {
errorCount = try_failure(errorCount, "solve()...", e.getMessage());
}
A = new Matrix(pvals);
CholeskyDecomposition Chol = A.chol();
Matrix L = Chol.getL();
try {
check(A, L.times(L.transpose()));
try_success("CholeskyDecomposition...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"CholeskyDecomposition...",
"incorrect Cholesky decomposition calculation");
}
X = Chol.solve(Matrix.identity(3, 3));
try {
check(A.times(X), Matrix.identity(3, 3));
try_success("CholeskyDecomposition solve()...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"CholeskyDecomposition solve()...",
"incorrect Choleskydecomposition solve calculation");
}
EigenvalueDecomposition Eig = A.eig();
Matrix D = Eig.getD();
Matrix V = Eig.getV();
try {
check(A.times(V), V.times(D));
try_success("EigenvalueDecomposition (symmetric)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"EigenvalueDecomposition (symmetric)...",
"incorrect symmetric Eigenvalue decomposition calculation");
}
A = new Matrix(evals);
Eig = A.eig();
D = Eig.getD();
V = Eig.getV();
try {
check(A.times(V), V.times(D));
try_success("EigenvalueDecomposition (nonsymmetric)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(
errorCount,
"EigenvalueDecomposition (nonsymmetric)...",
"incorrect nonsymmetric Eigenvalue decomposition calculation");
}
try {
print("\nTesting Eigenvalue; If this hangs, we've failed\n");
Matrix bA = new Matrix(badeigs);
EigenvalueDecomposition bEig = bA.eig();
try_success("EigenvalueDecomposition (hang)...", "");
} catch (java.lang.RuntimeException e) {
errorCount =
try_failure(errorCount, "EigenvalueDecomposition (hang)...", "incorrect termination");
}
print("\nTestMatrix completed.\n");
print("Total errors reported: " + Integer.toString(errorCount) + "\n");
print("Total warnings reported: " + Integer.toString(warningCount) + "\n");
}
public MyMatrix transpose() {
return new MyMatrix(a.transpose());
}
/**
* Assume une relation linéaire entre les angles et la longueur, les moments faisant office de
* "rayons". En normalisant, on peut oublier ce moment.
*
* @param angles (in rad)
* @return normalized length of muscle.
*/
public Matrix computeLength(Matrix angles) {
Matrix l = _minL0.minus(_k.arrayTimes((angles.minus(_minA)).times(_mom.transpose())));
return l;
}
/**
* Assume une relation linéaire entre les angles et la longueur, les moments faisant office de
* "rayons". En normalisant, on peut oublier ce moment. Ici, les angles sont inutiles...
*
* @param angles (in rad)
* @param angSpeed (in rad/s)
* @return normalized speed on muscle.
*/
public Matrix computeSpeed(Matrix angles, Matrix angSpeed) {
Matrix v = _k.arrayTimes(angSpeed.times(_mom.transpose()));
return v;
}
public static Matrix find(Stack<?> from, Stack<?> to) {
// System.out.println("Homographie:");
// System.out.println("From:");
// System.out.println(" "+from);
// System.out.println("To:");
// System.out.println(" "+to);
Stack fromC = new Stack(), toC = new Stack();
for (Object p : from) {
fromC.push(p);
}
for (Object p : to) {
toC.push(p);
}
int n = from.size();
if (n < 4) {
throw new Error("Homographie.find: Not enought point");
}
if (n != to.size()) {
throw new Error("Homographie.find: The 2 args don't have the same number of point");
}
if (!((from.peek() instanceof Pt2 && from.peek() instanceof Pt2)
|| (from.peek() instanceof Pt3 && from.peek() instanceof Pt3))) {
throw new Error("Homographie.find: The 2 args don't have the same class, among Pt or Vect");
}
boolean typeIsPt = from.peek() instanceof Pt2;
// On definit la matrice A et Q
double[][] A_array = new double[2 * n][8];
double[][] Q_array = new double[2 * n][1];
int i = 0;
while (!fromC.isEmpty()) {
Pt2 p = (typeIsPt) ? (Pt2) fromC.pop() : new Pt2((Pt3) fromC.pop());
Pt2 q = (typeIsPt) ? (Pt2) toC.pop() : new Pt2((Pt3) toC.pop());
// while (!from.isEmpty()) {
// Pt2 p = (typeIsPt) ? (Pt2) from.pop() : new Pt2((Pt3) from.pop());
// Pt2 q = (typeIsPt) ? (Pt2) to.pop() : new Pt2((Pt3) to.pop());
double[] l1 = {p.x, p.y, 1, 0, 0, 0, -p.x * q.x, -p.y * q.x};
double[] l2 = {0, 0, 0, p.x, p.y, 1, -p.x * q.y, -p.y * q.y};
A_array[i] = l1;
A_array[i + 1] = l2;
Q_array[i][0] = q.x;
Q_array[i + 1][0] = q.y;
i += 2;
}
Matrix A = new Matrix(A_array);
Matrix Q = new Matrix(Q_array);
// On calcule son inverse ou son pseudo-inverse B
Matrix B;
if (n == 4) {
B = A.inverse();
} else {
Matrix At = A.transpose();
B = At.times(A).inverse().times(At);
}
// On calcule l'homographie
Matrix h_vert = B.times(Q);
double[][] H_array = {
{h_vert.get(0, 0), h_vert.get(1, 0), h_vert.get(2, 0)},
{h_vert.get(3, 0), h_vert.get(4, 0), h_vert.get(5, 0)},
{h_vert.get(6, 0), h_vert.get(7, 0), 1}
};
Matrix H = new Matrix(H_array);
return (typeIsPt) ? H : H.inverse().transpose();
}
public boolean calcNearPD(Matrix x) {
int n = x.getRowDimension();
Matrix X;
// Init local variables
double[] diagX0 = new double[n];
double[] d = new double[n];
Matrix D_S = new Matrix(n, n);
Matrix R = new Matrix(n, n);
Matrix Y = new Matrix(n, n);
EigenvalueDecomposition eig;
Matrix D_plus = new Matrix(n, n);
Matrix Q = new Matrix(n, n);
if (keepDiag) {
for (int i = 0; i < n; i++) {
diagX0[i] = x.get(i, i);
}
}
X = x.copy();
// Set iteration, convergence criteria
int iter = 0;
boolean converged = false;
double conv = Double.POSITIVE_INFINITY;
// Loop
while ((iter < maxit) & !converged) {
Y = X.copy();
// Dykstra correction
if (doDykstra) {
R = Y.minus(D_S);
}
// project onto PSD matrices X_k = P_S (R_k)
if (doDykstra) {
eig = R.eig();
} else {
eig = Y.eig();
}
d = eig.getRealEigenvalues();
Q = eig.getV();
// Get the maximum eigenvalue
double eigMax = Double.NEGATIVE_INFINITY;
for (int i = 0; i < n; i++) {
if (d[i] > eigMax) eigMax = d[i];
}
// compute the D_plus diagonal matricies
for (int i = 0; i < n; i++) {
double d_plus = Math.max(d[i], eigTol * eigMax);
D_plus.set(i, i, d_plus);
}
X = (Q.times(D_plus)).times(Q.transpose());
// Update Dykstra correction
if (doDykstra) D_S = X.minus(R);
// project onto symmetric and possibly 'given diag' matrices:
if (keepDiag) {
for (int i = 0; i < n; i++) {
X.set(i, i, diagX0[i]);
}
}
// update convergence and iteration values
conv = (Y.minus(X)).normInf() / Y.normInf();
iter = iter + 1;
// check convergence criteria
if (conv <= convTol) converged = true;
}
// Set solution local variables as globals
this.X = X;
this.conv = conv;
this.normF = (x.minus(X)).normF();
this.iter = iter;
this.eigVals = d;
return converged;
}
