Example usage for org.apache.commons.math3.linear RealMatrix transpose

Introduction

In this page you can find the example usage for org.apache.commons.math3.linear RealMatrix transpose.

Prototype

RealMatrix transpose();

Source Link

Document

Returns the transpose of this matrix.

Usage

From source file:io.github.malapert.jwcs.coordsystem.Utility.java

/**
 * Creates a rotation matrix for a precession based on IAU 2000/2006
 * expressions, see `IAU2006precangles`.
 * //from w w  w  . jav a  2  s  .  com
 * Reference:
 * ----------
 * Capitaine N. et al.: IAU 2000 precession A and A 412, 567-586 (2003)
 * 
 * Notes:     
 * ------
 * Note that we apply this precession only to equatorial
 * coordinates in the system of dynamical J2000 coordinates.
 * When converting from ICRS coordinates this means applying 
 * a frame bias. 
 * Therefore the angles differ from the precession 
 * Fukushima-Williams angles (IAU 2006)     
 * The precession matrix is: M = rotZ(-z).rotY(+theta).rotZ(-zeta)
 * 
 * @param epoch1 Julian start epoch
 * @param epoch2 Julian epoch to precess to
 * @return Matrix to transform equatorial coordinates from epoch1 to 
 * epoch2 as in XYZepoch2 = M * XYZepoch1
 */
public final static RealMatrix IAU2006MatrixEpoch12Epoch2(float epoch1, float epoch2) {
    RealMatrix result;
    if (epoch1 == epoch2) {
        result = MatrixUtils.createRealIdentityMatrix(3);
    } else if (epoch1 == 2000.0) {
        double[] precessionAngles = IAU2006PrecAngles(epoch2);
        result = precessionMatrix(precessionAngles[0], precessionAngles[1], precessionAngles[2]);
    } else { // If both epochs are not J2000.0
        double[] precessionAngles = IAU2006PrecAngles(epoch1);
        RealMatrix m1 = precessionMatrix(precessionAngles[0], precessionAngles[1], precessionAngles[2]);
        m1 = m1.transpose();
        precessionAngles = IAU2006PrecAngles(epoch2);
        RealMatrix m2 = precessionMatrix(precessionAngles[0], precessionAngles[1], precessionAngles[2]);
        result = m1.multiply(m2);
    }
    return result;
}

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From source file:edu.cudenver.bios.matrix.GramSchmidtOrthonormalization.java

/**
 * Perform Gram Schmidt Orthonormalization on the specified 
 * matrix. The matrix A (mxn) is decomposed into two matrices 
 * Q (mxn), R (nxn) such that//  w w w . j av  a  2s.c  o  m
 * <ul>
 * <li>A = QR
 * <li>Q'Q = Identity
 * <li>R is upper triangular
 * </ul> 
 * The resulting Q, R matrices can be retrieved with the getQ()
 * and getR() functions.
 * 
 * @param matrix
 */
public GramSchmidtOrthonormalization(RealMatrix matrix) {
    if (matrix == null)
        throw new IllegalArgumentException("Null matrix");

    // create the Q, R matrices
    int m = matrix.getRowDimension();
    int n = matrix.getColumnDimension();
    Q = MatrixUtils.createRealMatrix(m, n);
    R = MatrixUtils.createRealMatrix(n, n);

    // perform Gram Schmidt process using the following algorithm
    // let w<n> be the resulting orthonormal column vectors
    // let v<n> be the columns of the incoming matrix
    // w1 = (1/norm(v1))*v1
    // ...
    // wj = 1/norm(vj - projectionVj-1Vj)*[vj - projectionVj-1Vj]
    // where projectionVj-1Vj = (w1 * vj) * w1 + (w2 * vj) * w2 + ... + (wj-1 * vj) * wj-1
    //
    for (int i = 0; i < n; i++) {
        RealMatrix v = matrix.getColumnMatrix(i);
        for (int j = 0; j < i; j++) {
            RealMatrix Qj = Q.getColumnMatrix(j);
            double value = Qj.transpose().multiply(v).getEntry(0, 0);
            R.setEntry(j, i, value);
            v = v.subtract(Qj.scalarMultiply(value));
        }
        double norm = v.getFrobeniusNorm();
        R.setEntry(i, i, norm);
        Q.setColumnMatrix(i, v.scalarMultiply(1 / norm));
    }
}

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From source file:edu.cudenver.bios.matrix.test.TestMatrixOrthonormalization.java

/**
 * Verify that the Q'Q = I for the Q matrix produced by the
 * orthonormalization/*from  w  ww  .j  av a  2  s . co m*/
 */
public void testQQisIdentity() {
    RealMatrix Q = norm.getQ();

    // verify that Q'Q = identity
    RealMatrix shouldBeIdentityMatrix = Q.transpose().multiply(Q);
    // make sure the matrix is sqaure
    if (!shouldBeIdentityMatrix.isSquare()) {
        fail();
    }
    // make sure the diagonal elements are one (within tolerance), and off diagonals
    // are zero (within tolerance)
    for (int r = 0; r < shouldBeIdentityMatrix.getRowDimension(); r++) {
        for (int c = 0; c < shouldBeIdentityMatrix.getColumnDimension(); c++) {
            double shouldBeValue = (r == c) ? 1 : 0;
            if (Precision.compareTo(shouldBeIdentityMatrix.getEntry(r, c), shouldBeValue, TOLERANCE) != 0)
                fail();
        }
    }
    assertTrue(true);
}

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From source file:edu.cmu.tetrad.search.EstimateRank.java

public double[] CanCor(double[][] A, double[][] B) {
    this.A = A;/* ww w.  j  av  a  2s  . c  o  m*/
    this.B = B;
    RealMatrix Ua = new SingularValueDecomposition(new BlockRealMatrix(A)).getU();
    RealMatrix UTa = Ua.transpose();
    RealMatrix Ub = new SingularValueDecomposition(new BlockRealMatrix(B)).getU();
    return new SingularValueDecomposition(UTa.multiply(Ub)).getSingularValues();
}

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From source file:com.itemanalysis.psychometrics.mixture.MvNormalComponentDistribution.java

/**
 *
 * @param x a matrix of dimension 1 x k, where k is the number of variables
 * @return//from w  ww  . ja v a 2 s  .c o  m
 */
public double density(RealMatrix x) throws SingularMatrixException {
    double prob = 0.0;
    RealMatrix xTran = x.transpose();
    int d = xTran.getRowDimension();
    double det = new LUDecomposition(sigma).getDeterminant();
    double nconst = 1.0 / Math.sqrt(det * Math.pow(2.0 * Math.PI, d));
    RealMatrix Sinv = new LUDecomposition(sigma).getSolver().getInverse();
    RealMatrix delta = xTran.subtract(mu);
    RealMatrix dist = (delta.transpose().multiply(Sinv).multiply(delta));
    prob = nconst * Math.exp(-0.5 * dist.getEntry(0, 0));
    return prob;
}

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From source file:edu.ucdenver.bios.designcalculator.DesignCalculator.java

/**
 * Calculate the sum of squares error matrix (the E matrix)
 * /*from  w ww .j a  v  a2s .  c om*/
 * @param params matrices input by the user
 * @return error sum of squares
 */
public RealMatrix getErrorSumOfSquares(RealMatrix U, RealMatrix sigmaError, double nuError) {
    return U.transpose().multiply(sigmaError.multiply(U)).scalarMultiply(nuError);
}

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From source file:com.itemanalysis.psychometrics.factoranalysis.FactorAnalysisTest.java

@Test
public void eigenValues() {
    RealMatrix R = new Array2DRowRealMatrix(readHarman74Data());

    int nFactors = 2;
    int nVariables = 24;
    double[] x = new double[nVariables];
    for (int i = 0; i < nVariables; i++) {
        x[i] = .5;/*from ww  w  .  j  av a 2s .  c om*/
    }

    for (int i = 0; i < nVariables; i++) {
        R.setEntry(i, i, 1.0 - x[i]);
    }

    EigenDecomposition eigen = new EigenDecomposition(R);
    RealMatrix eigenVectors = eigen.getV().getSubMatrix(0, nVariables - 1, 0, nFactors - 1);

    double[] ev = new double[nFactors];
    for (int i = 0; i < nFactors; i++) {
        ev[i] = Math.sqrt(eigen.getRealEigenvalue(i));
    }
    DiagonalMatrix evMatrix = new DiagonalMatrix(ev);// USE Apache version
    // of Diagonal
    // matrix when
    // upgrade to
    // version 3.2
    RealMatrix LAMBDA = eigenVectors.multiply(evMatrix);
    RealMatrix SIGMA = (LAMBDA.multiply(LAMBDA.transpose()));
    RealMatrix RESID = R.subtract(SIGMA);

    double sum = 0.0;
    double squared = 0.0;
    for (int i = 0; i < RESID.getRowDimension(); i++) {
        for (int j = 0; j < RESID.getColumnDimension(); j++) {
            if (i != j) {
                sum += Math.pow(RESID.getEntry(i, j), 2);
            }
        }
    }

    System.out.println(sum);

    // RealMatrix SIGMA = (LAMBDA.multiply(LAMBDA.transpose()));
    //
    // System.out.println("SIGMA");
    // for(int i=0;i<SIGMA.getRowDimension();i++){
    // for(int j=0;j<SIGMA.getColumnDimension();j++){
    // System.out.print(SIGMA.getEntry(i, j) + " ");
    // }
    // System.out.println();
    // }
}

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From source file:com.joptimizer.algebra.CholeskyRCFactorizationTest.java

public void testInvert1() throws Exception {
    log.debug("testInvert1");
    double[][] QData = new double[][] { { 1, .12, .13, .14, .15 }, { .12, 2, .23, .24, .25 },
            { .13, .23, 3, 0, 0 }, { .14, .24, 0, 4, 0 }, { .15, .25, 0, 0, 5 } };
    RealMatrix Q = MatrixUtils.createRealMatrix(QData);

    CholeskyRCFactorization myc = new CholeskyRCFactorization(DoubleFactory2D.dense.make(QData));
    myc.factorize();/*www . j a va 2s.c om*/
    RealMatrix L = new Array2DRowRealMatrix(myc.getL().toArray());
    RealMatrix LT = new Array2DRowRealMatrix(myc.getLT().toArray());
    log.debug("L: " + ArrayUtils.toString(L.getData()));
    log.debug("LT: " + ArrayUtils.toString(LT.getData()));
    log.debug("L.LT: " + ArrayUtils.toString(L.multiply(LT).getData()));
    log.debug("LT.L: " + ArrayUtils.toString(LT.multiply(L).getData()));

    // check Q = L.LT
    double norm = L.multiply(LT).subtract(Q).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);

    RealMatrix LInv = new SingularValueDecomposition(L).getSolver().getInverse();
    log.debug("LInv: " + ArrayUtils.toString(LInv.getData()));
    RealMatrix LInvT = LInv.transpose();
    log.debug("LInvT: " + ArrayUtils.toString(LInvT.getData()));
    RealMatrix LTInv = new SingularValueDecomposition(LT).getSolver().getInverse();
    log.debug("LTInv: " + ArrayUtils.toString(LTInv.getData()));
    RealMatrix LTInvT = LTInv.transpose();
    log.debug("LTInvT: " + ArrayUtils.toString(LTInvT.getData()));
    log.debug("LInv.LInvT: " + ArrayUtils.toString(LInv.multiply(LInvT).getData()));
    log.debug("LTInv.LTInvT: " + ArrayUtils.toString(LTInv.multiply(LTInvT).getData()));

    RealMatrix Id = MatrixUtils.createRealIdentityMatrix(Q.getRowDimension());
    //check Q.(LTInv * LInv) = 1
    norm = Q.multiply(LTInv.multiply(LInv)).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 5.E-15);

    // check Q.QInv = 1
    RealMatrix QInv = MatrixUtils.createRealMatrix(myc.getInverse().toArray());
    norm = Q.multiply(QInv).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);
}

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From source file:com.joptimizer.algebra.CholeskyRCTFactorizationTest.java

public void testInvert1() throws Exception {
    log.debug("testInvert1");
    double[][] QData = new double[][] { { 1, .12, .13, .14, .15 }, { .12, 2, .23, .24, .25 },
            { .13, .23, 3, 0, 0 }, { .14, .24, 0, 4, 0 }, { .15, .25, 0, 0, 5 } };
    RealMatrix Q = MatrixUtils.createRealMatrix(QData);

    CholeskyRCTFactorization myc = new CholeskyRCTFactorization(DoubleFactory2D.dense.make(QData));
    myc.factorize();//from  w ww .ja  v a2s  .  co  m
    RealMatrix L = new Array2DRowRealMatrix(myc.getL().toArray());
    RealMatrix LT = new Array2DRowRealMatrix(myc.getLT().toArray());
    log.debug("L: " + ArrayUtils.toString(L.getData()));
    log.debug("LT: " + ArrayUtils.toString(LT.getData()));
    log.debug("L.LT: " + ArrayUtils.toString(L.multiply(LT).getData()));
    log.debug("LT.L: " + ArrayUtils.toString(LT.multiply(L).getData()));

    // check Q = L.LT
    double norm = L.multiply(LT).subtract(Q).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);

    RealMatrix LInv = new SingularValueDecomposition(L).getSolver().getInverse();
    log.debug("LInv: " + ArrayUtils.toString(LInv.getData()));
    RealMatrix LInvT = LInv.transpose();
    log.debug("LInvT: " + ArrayUtils.toString(LInvT.getData()));
    RealMatrix LTInv = new SingularValueDecomposition(LT).getSolver().getInverse();
    log.debug("LTInv: " + ArrayUtils.toString(LTInv.getData()));
    RealMatrix LTInvT = LTInv.transpose();
    log.debug("LTInvT: " + ArrayUtils.toString(LTInvT.getData()));
    log.debug("LInv.LInvT: " + ArrayUtils.toString(LInv.multiply(LInvT).getData()));
    log.debug("LTInv.LTInvT: " + ArrayUtils.toString(LTInv.multiply(LTInvT).getData()));

    RealMatrix Id = MatrixUtils.createRealIdentityMatrix(Q.getRowDimension());
    //check Q.(LTInv * LInv) = 1
    norm = Q.multiply(LTInv.multiply(LInv)).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 5.E-15);

    // check Q.QInv = 1
    RealMatrix QInv = MatrixUtils.createRealMatrix(myc.getInverse().toArray());
    norm = Q.multiply(QInv).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);
}

---

From source file:com.joptimizer.util.CholeskyFactorizationTest.java

public void testInvert1() throws Exception {
    log.debug("testInvert1");
    double[][] QData = new double[][] { { 1, .12, .13, .14, .15 }, { .12, 2, .23, .24, .25 },
            { .13, .23, 3, 0, 0 }, { .14, .24, 0, 4, 0 }, { .15, .25, 0, 0, 5 } };
    RealMatrix Q = MatrixUtils.createRealMatrix(QData);

    CholeskyFactorization myc = new CholeskyFactorization(QData);
    RealMatrix L = new Array2DRowRealMatrix(myc.getL());
    RealMatrix LT = new Array2DRowRealMatrix(myc.getLT());
    log.debug("L: " + L);
    log.debug("LT: " + LT);
    log.debug("L.LT: " + L.multiply(LT));
    log.debug("LT.L: " + LT.multiply(L));

    // check Q = L.LT
    double norm = L.multiply(LT).subtract(Q).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);//  www.  ja va  2s.co m

    RealMatrix LInv = new SingularValueDecomposition(L).getSolver().getInverse();
    log.debug("LInv: " + ArrayUtils.toString(LInv.getData()));
    RealMatrix LInvT = LInv.transpose();
    log.debug("LInvT: " + ArrayUtils.toString(LInvT.getData()));
    RealMatrix LTInv = new SingularValueDecomposition(LT).getSolver().getInverse();
    log.debug("LTInv: " + ArrayUtils.toString(LTInv.getData()));
    RealMatrix LTInvT = LTInv.transpose();
    log.debug("LTInvT: " + ArrayUtils.toString(LTInvT.getData()));
    log.debug("LInv.LInvT: " + ArrayUtils.toString(LInv.multiply(LInvT).getData()));
    log.debug("LTInv.LTInvT: " + ArrayUtils.toString(LTInv.multiply(LTInvT).getData()));

    RealMatrix Id = MatrixUtils.createRealIdentityMatrix(Q.getRowDimension());
    //check Q.(LTInv * LInv) = 1
    norm = Q.multiply(LTInv.multiply(LInv)).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 5.E-15);

    // check Q.QInv = 1
    RealMatrix QInv = MatrixUtils.createRealMatrix(myc.getInverse());
    norm = Q.multiply(QInv).subtract(Id).getNorm();
    log.debug("norm: " + norm);
    assertTrue(norm < 1.E-15);

    //check eigenvalues
    double det1 = Utils.calculateDeterminant(QData, QData.length);
    double det2 = 1;
    List<Double> eigenvalues = myc.getEigenvalues();
    for (double ev : eigenvalues) {
        det2 = det2 * ev;
    }
    log.debug("det1: " + det1);
    log.debug("det2: " + det2);
    assertEquals(det1, det2, 1.E-13);
}

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