Example #1
0
  private void costantiniUnwrap() throws LPException {

    final int ny = wrappedPhase.rows - 1; // start from Zero!
    final int nx = wrappedPhase.columns - 1; // start from Zero!

    if (wrappedPhase.isVector()) throw new IllegalArgumentException("Input must be 2D array");
    if (wrappedPhase.rows < 2 || wrappedPhase.columns < 2)
      throw new IllegalArgumentException("Size of input must be larger than 2");

    // Default weight
    DoubleMatrix w1 = DoubleMatrix.ones(ny + 1, 1);
    w1.put(0, 0.5);
    w1.put(w1.length - 1, 0.5);
    DoubleMatrix w2 = DoubleMatrix.ones(1, nx + 1);
    w2.put(0, 0.5);
    w2.put(w2.length - 1, 0.5);
    DoubleMatrix weight = w1.mmul(w2);

    DoubleMatrix i, j, I_J, IP1_J, I_JP1;
    DoubleMatrix Psi1, Psi2;
    DoubleMatrix[] ROWS;

    // Compute partial derivative Psi1, eqt (1,3)
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1]);
    IP1_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0].add(1), ROWS[1]);
    Psi1 =
        JblasUtils.getMatrixFromIdx(wrappedPhase, IP1_J)
            .sub(JblasUtils.getMatrixFromIdx(wrappedPhase, I_J));
    Psi1 = UnwrapUtils.wrapDoubleMatrix(Psi1);

    // Compute partial derivative Psi2, eqt (2,4)
    i = intRangeDoubleMatrix(0, ny);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1].add(1));
    Psi2 =
        JblasUtils.getMatrixFromIdx(wrappedPhase, I_JP1)
            .sub(JblasUtils.getMatrixFromIdx(wrappedPhase, I_J));
    Psi2 = UnwrapUtils.wrapDoubleMatrix(Psi2);

    // Compute beq
    DoubleMatrix beq = DoubleMatrix.zeros(ny, nx);
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(Psi1.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(Psi1.rows, ROWS[0], ROWS[1].add(1));
    beq.addi(JblasUtils.getMatrixFromIdx(Psi1, I_JP1).sub(JblasUtils.getMatrixFromIdx(Psi1, I_J)));
    I_J = JblasUtils.sub2ind(Psi2.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(Psi2.rows, ROWS[0].add(1), ROWS[1]);
    beq.subi(JblasUtils.getMatrixFromIdx(Psi2, I_JP1).sub(JblasUtils.getMatrixFromIdx(Psi2, I_J)));
    beq.muli(-1 / (2 * Constants._PI));
    for (int k = 0; k < beq.length; k++) {
      beq.put(k, Math.round(beq.get(k)));
    }
    beq.reshape(beq.length, 1);

    logger.debug("Constraint matrix");
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    DoubleMatrix ROW_I_J = JblasUtils.sub2ind(i.length, ROWS[0], ROWS[1]);
    int nS0 = nx * ny;

    // Use by S1p, S1m
    DoubleMatrix[] COLS;
    COLS = grid2D(i, j);
    DoubleMatrix COL_IJ_1 = JblasUtils.sub2ind(i.length, COLS[0], COLS[1]);
    COLS = grid2D(i, j.add(1));
    DoubleMatrix COL_I_JP1 = JblasUtils.sub2ind(i.length, COLS[0], COLS[1]);
    int nS1 = (nx + 1) * (ny);

    // SOAPBinding.Use by S2p, S2m
    COLS = grid2D(i, j);
    DoubleMatrix COL_IJ_2 = JblasUtils.sub2ind(i.length + 1, COLS[0], COLS[1]);
    COLS = grid2D(i.add(1), j);
    DoubleMatrix COL_IP1_J = JblasUtils.sub2ind(i.length + 1, COLS[0], COLS[1]);
    int nS2 = nx * (ny + 1);

    // Equality constraint matrix (Aeq)
    /*
        S1p = + sparse(ROW_I_J, COL_I_JP1,1,nS0,nS1) ...
              - sparse(ROW_I_J, COL_IJ_1,1,nS0,nS1);
        S1m = -S1p;

        S2p = - sparse(ROW_I_J, COL_IP1_J,1,nS0,nS2) ...
              + sparse(ROW_I_J, COL_IJ_2,1,nS0,nS2);
        S2m = -S2p;
    */

    // ToDo: Aeq matrix should be sparse from it's initialization, look into JblasMatrix factory for
    // howto
    // ...otherwise even a data set of eg 40x40 pixels will exhaust heap:
    // ...    dimension of Aeq (equality constraints) matrix for 30x30 input is 1521x6240 matrix
    // ...    dimension of Aeq (                    ) matrix for 50x50 input is 2401x9800
    // ...    dimension of Aeq (                    ) matrix for 512x512 input is 261121x1046528
    DoubleMatrix S1p =
        JblasUtils.setUpMatrixFromIdx(nS0, nS1, ROW_I_J, COL_I_JP1)
            .sub(JblasUtils.setUpMatrixFromIdx(nS0, nS1, ROW_I_J, COL_IJ_1));
    DoubleMatrix S1m = S1p.neg();

    DoubleMatrix S2p =
        JblasUtils.setUpMatrixFromIdx(nS0, nS2, ROW_I_J, COL_IP1_J)
            .neg()
            .add(JblasUtils.setUpMatrixFromIdx(nS0, nS2, ROW_I_J, COL_IJ_2));
    DoubleMatrix S2m = S2p.neg();

    DoubleMatrix Aeq =
        concatHorizontally(concatHorizontally(S1p, S1m), concatHorizontally(S2p, S2m));

    final int nObs = Aeq.columns;
    final int nUnkn = Aeq.rows;

    DoubleMatrix c1 = JblasUtils.getMatrixFromRange(0, ny, 0, weight.columns, weight);
    DoubleMatrix c2 = JblasUtils.getMatrixFromRange(0, weight.rows, 0, nx, weight);

    c1.reshape(c1.length, 1);
    c2.reshape(c2.length, 1);

    DoubleMatrix cost =
        DoubleMatrix.concatVertically(
            DoubleMatrix.concatVertically(c1, c1), DoubleMatrix.concatVertically(c2, c2));

    logger.debug("Minimum network flow resolution");

    StopWatch clockLP = new StopWatch();
    LinearProgram lp = new LinearProgram(cost.data);
    lp.setMinProblem(true);

    boolean[] integerBool = new boolean[nObs];
    double[] lowerBound = new double[nObs];
    double[] upperBound = new double[nObs];

    for (int k = 0; k < nUnkn; k++) {
      lp.addConstraint(new LinearEqualsConstraint(Aeq.getRow(k).toArray(), beq.get(k), "cost"));
    }

    for (int k = 0; k < nObs; k++) {
      integerBool[k] = true;
      lowerBound[k] = 0;
      upperBound[k] = 99999;
    }

    // setup bounds and integer nature
    lp.setIsinteger(integerBool);
    lp.setUpperbound(upperBound);
    lp.setLowerbound(lowerBound);
    LinearProgramSolver solver = SolverFactory.newDefault();

    //        double[] solution;
    //        solution = solver.solve(lp);
    DoubleMatrix solution = new DoubleMatrix(solver.solve(lp));

    clockLP.stop();
    logger.debug("Total GLPK time: {} [sec]", (double) (clockLP.getElapsedTime()) / 1000);

    // Displatch the LP solution
    int offset;

    int[] idx1p = JblasUtils.intRangeIntArray(0, nS1 - 1);
    DoubleMatrix x1p = solution.get(idx1p);
    x1p.reshape(ny, nx + 1);
    offset = idx1p[nS1 - 1] + 1;

    int[] idx1m = JblasUtils.intRangeIntArray(offset, offset + nS1 - 1);
    DoubleMatrix x1m = solution.get(idx1m);
    x1m.reshape(ny, nx + 1);
    offset = idx1m[idx1m.length - 1] + 1;

    int[] idx2p = JblasUtils.intRangeIntArray(offset, offset + nS2 - 1);
    DoubleMatrix x2p = solution.get(idx2p);
    x2p.reshape(ny + 1, nx);
    offset = idx2p[idx2p.length - 1] + 1;

    int[] idx2m = JblasUtils.intRangeIntArray(offset, offset + nS2 - 1);
    DoubleMatrix x2m = solution.get(idx2m);
    x2m.reshape(ny + 1, nx);

    // Compute the derivative jumps, eqt (20,21)
    DoubleMatrix k1 = x1p.sub(x1m);
    DoubleMatrix k2 = x2p.sub(x2m);

    // (?) Round to integer solution
    if (roundK == true) {
      for (int idx = 0; idx < k1.length; idx++) {
        k1.put(idx, FastMath.floor(k1.get(idx)));
      }
      for (int idx = 0; idx < k2.length; idx++) {
        k2.put(idx, FastMath.floor(k2.get(idx)));
      }
    }

    // Sum the jumps with the wrapped partial derivatives, eqt (10,11)
    k1.reshape(ny, nx + 1);
    k2.reshape(ny + 1, nx);
    k1.addi(Psi1.div(Constants._TWO_PI));
    k2.addi(Psi2.div(Constants._TWO_PI));

    // Integrate the partial derivatives, eqt (6)
    // cumsum() method in JblasTester -> see cumsum_demo() in JblasTester.cumsum_demo()
    DoubleMatrix k2_temp = DoubleMatrix.concatHorizontally(DoubleMatrix.zeros(1), k2.getRow(0));
    k2_temp = JblasUtils.cumsum(k2_temp, 1);
    DoubleMatrix k = DoubleMatrix.concatVertically(k2_temp, k1);
    k = JblasUtils.cumsum(k, 1);

    // Unwrap - final solution
    unwrappedPhase = k.mul(Constants._TWO_PI);
  }
 // align input so it can be used in training
 protected DoubleMatrix preProcessInput(DoubleMatrix input) {
   if (concatBiases)
     return DoubleMatrix.concatHorizontally(input, DoubleMatrix.ones(input.rows, 1));
   return input;
 }
Example #3
0
  public static double[] polyFit2D(
      final DoubleMatrix x, final DoubleMatrix y, final DoubleMatrix z, final int degree)
      throws IllegalArgumentException {

    logger.setLevel(Level.INFO);

    if (x.length != y.length || !x.isVector() || !y.isVector()) {
      logger.error("polyfit: require same size vectors.");
      throw new IllegalArgumentException("polyfit: require same size vectors.");
    }

    final int numOfObs = x.length;
    final int numOfUnkn = numberOfCoefficients(degree) + 1;

    DoubleMatrix A = new DoubleMatrix(numOfObs, numOfUnkn); // designmatrix

    DoubleMatrix mul;

    /** Set up design-matrix */
    for (int p = 0; p <= degree; p++) {
      for (int q = 0; q <= p; q++) {
        mul = pow(y, (p - q)).mul(pow(x, q));
        if (q == 0 && p == 0) {
          A = mul;
        } else {
          A = DoubleMatrix.concatHorizontally(A, mul);
        }
      }
    }

    // Fit polynomial
    logger.debug("Solving lin. system of equations with Cholesky.");
    DoubleMatrix N = A.transpose().mmul(A);
    DoubleMatrix rhs = A.transpose().mmul(z);

    // solution seems to be OK up to 10^-09!
    rhs = Solve.solveSymmetric(N, rhs);

    DoubleMatrix Qx_hat = Solve.solveSymmetric(N, DoubleMatrix.eye(N.getRows()));

    double maxDeviation = (N.mmul(Qx_hat).sub(DoubleMatrix.eye(Qx_hat.rows))).normmax();
    logger.debug("polyfit orbit: max(abs(N*inv(N)-I)) = " + maxDeviation);

    // ___ report max error... (seems sometimes this can be extremely large) ___
    if (maxDeviation > 1e-6) {
      logger.warn("polyfit orbit: max(abs(N*inv(N)-I)) = {}", maxDeviation);
      logger.warn("polyfit orbit interpolation unstable!");
    }

    // work out residuals
    DoubleMatrix y_hat = A.mmul(rhs);
    DoubleMatrix e_hat = y.sub(y_hat);

    if (e_hat.normmax() > 0.02) {
      logger.warn(
          "WARNING: Max. polyFit2D approximation error at datapoints (x,y,or z?): {}",
          e_hat.normmax());
    } else {
      logger.info(
          "Max. polyFit2D approximation error at datapoints (x,y,or z?): {}", e_hat.normmax());
    }

    if (logger.isDebugEnabled()) {
      logger.debug("REPORTING POLYFIT LEAST SQUARES ERRORS");
      logger.debug(" time \t\t\t y \t\t\t yhat  \t\t\t ehat");
      for (int i = 0; i < numOfObs; i++) {
        logger.debug(
            " ("
                + x.get(i)
                + ","
                + y.get(i)
                + ") :"
                + "\t"
                + y.get(i)
                + "\t"
                + y_hat.get(i)
                + "\t"
                + e_hat.get(i));
      }
    }
    return rhs.toArray();
  }
    // TODO: DOUBLECHECK EVERYTHING
    @Override
    public void map(Text key, jBLASArrayWritable input, GibbsSampling.Context context)
        throws IOException, InterruptedException {
      /* *******************************************************************/
      /* initialize all memory we're going to use during the process		 */
      long start_time = System.nanoTime();
      ArrayList<DoubleMatrix> data = input.getData();
      label = data.get(4);
      v_data = data.get(5);

      // check to see if we are in the first layer or there are layers beneath us we must sample
      // from
      if (data.size() > 6) {
        int prelayer = (data.size() - 6) / 3;
        DoubleMatrix[] preWeights = new DoubleMatrix[prelayer],
            preHbias = new DoubleMatrix[prelayer],
            preVbias = new DoubleMatrix[prelayer];
        for (int i = 0; i < prelayer; i++) {
          preWeights[i] = data.get(6 + i * 3);
          preHbias[i] = data.get(7 + i * 3);
          preVbias[i] = data.get(8 + i * 3);
        }
        DoubleMatrix vnew = null;
        for (int i = 0; i < prelayer; i++) {
          weights = preWeights[i];
          vbias = preVbias[i];
          hbias = preHbias[i];
          vnew = sample_h_from_v(i == 0 ? v_data : vnew);
        }
        v_data = vnew;
      }

      weights = data.get(0);
      hbias = data.get(1);
      hiddenChain = data.get(2);
      vbias = data.get(3);

      // check if we need to attach labels to the observed variables
      if (vbias.columns != v_data.columns) {
        DoubleMatrix labels = DoubleMatrix.zeros(1, classCount);
        int labelNum = (new Double(label.get(0))).intValue();
        labels.put(labelNum, 1.0);
        v_data = DoubleMatrix.concatHorizontally(v_data, labels);
      }

      w1 = DoubleMatrix.zeros(weights.rows, weights.columns);
      hb1 = DoubleMatrix.zeros(hbias.rows, hbias.columns);
      vb1 = DoubleMatrix.zeros(vbias.rows, vbias.columns);

      /* ********************************************************************/
      // sample hidden state to get positive phase
      // if empty, use it as the start of the chain
      // or use persistent hidden state from pCD

      DoubleMatrix phaseSample = sample_h_from_v(v_data);
      h1_data = new DoubleMatrix();
      v1_data = new DoubleMatrix();

      if (hiddenChain == null) {
        data.set(2, new DoubleMatrix(hbias.rows, hbias.columns));
        hiddenChain = data.get(2);
        hiddenChain.copy(phaseSample);
        h1_data.copy(phaseSample);
      } else {
        h1_data.copy(hiddenChain);
      }
      // run Gibbs chain for k steps
      for (int j = 0; j < gibbsSteps; j++) {
        v1_data.copy(sample_v_from_h(h1_data));
        h1_data.copy(sample_h_from_v(v1_data));
      }
      DoubleMatrix hprob = propup(v1_data);
      weight_contribution(hiddenChain, v_data, hprob, v1_data);
      hiddenChain.copy(h1_data);

      data.get(0).copy(w1);
      data.get(1).copy(hb1);
      data.get(2).copy(hiddenChain);
      data.get(3).copy(vb1);

      jBLASArrayWritable outputmatrix = new jBLASArrayWritable(data);
      context.write(key, outputmatrix);
      log.info("Job completed in: " + (System.nanoTime() - start_time) / (1E6) + " ms");
    }