示例#1
0
  public static DoubleMatrix conv2d(DoubleMatrix input, DoubleMatrix kernel, Type type) {

    DoubleMatrix xShape = new DoubleMatrix(1, 2);
    xShape.put(0, input.rows);
    xShape.put(1, input.columns);

    DoubleMatrix yShape = new DoubleMatrix(1, 2);
    yShape.put(0, kernel.rows);
    yShape.put(1, kernel.columns);

    DoubleMatrix zShape = xShape.addi(yShape).subi(1);
    int retRows = (int) zShape.get(0);
    int retCols = (int) zShape.get(1);

    ComplexDoubleMatrix fftInput = complexDisceteFourierTransform(input, retRows, retCols);
    ComplexDoubleMatrix fftKernel = complexDisceteFourierTransform(kernel, retRows, retCols);
    ComplexDoubleMatrix mul = fftKernel.muli(fftInput);
    ComplexDoubleMatrix retComplex = complexInverseDisceteFourierTransform(mul);
    DoubleMatrix ret = retComplex.getReal();

    if (type == Type.VALID) {

      DoubleMatrix validShape = xShape.subi(yShape).addi(1);

      DoubleMatrix start = zShape.subi(validShape).divi(2);
      DoubleMatrix end = start.addi(validShape);
      if (start.get(0) < 1 || start.get(1) < 1)
        throw new IllegalStateException("Illegal row index " + start);
      if (end.get(0) < 1 || end.get(1) < 1)
        throw new IllegalStateException("Illegal column index " + end);

      ret =
          ret.get(
              RangeUtils.interval((int) start.get(0), (int) end.get(0)),
              RangeUtils.interval((int) start.get(1), (int) end.get(1)));
    }

    return ret;
  }
示例#2
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);
  }
  /**
   * Update the gradient according to the configuration such as adagrad, momentum, and sparsity
   *
   * @param gradient the gradient to modify
   * @param iteration the current iteration
   * @param learningRate the learning rate for the current iteration
   */
  protected void updateGradientAccordingToParams(
      NeuralNetworkGradient gradient, int iteration, double learningRate) {
    DoubleMatrix wGradient = gradient.getwGradient();

    DoubleMatrix hBiasGradient = gradient.gethBiasGradient();
    DoubleMatrix vBiasGradient = gradient.getvBiasGradient();

    // reset adagrad history
    if (iteration != 0 && resetAdaGradIterations > 0 && iteration % resetAdaGradIterations == 0) {
      wAdaGrad.historicalGradient = null;
      hBiasAdaGrad.historicalGradient = null;
      vBiasAdaGrad.historicalGradient = null;
      if (this.W != null && this.wAdaGrad == null)
        this.wAdaGrad = new AdaGrad(this.W.rows, this.W.columns);

      if (this.vBias != null && this.vBiasAdaGrad == null)
        this.vBiasAdaGrad = new AdaGrad(this.vBias.rows, this.vBias.columns);

      if (this.hBias != null && this.hBiasAdaGrad == null)
        this.hBiasAdaGrad = new AdaGrad(this.hBias.rows, this.hBias.columns);

      log.info("Resetting adagrad");
    }

    DoubleMatrix wLearningRates = wAdaGrad.getLearningRates(wGradient);
    // change up momentum after so many iterations if specified
    double momentum = this.momentum;
    if (momentumAfter != null && !momentumAfter.isEmpty()) {
      int key = momentumAfter.keySet().iterator().next();
      if (iteration >= key) {
        momentum = momentumAfter.get(key);
      }
    }

    if (useAdaGrad) wGradient.muli(wLearningRates);
    else wGradient.muli(learningRate);

    if (useAdaGrad) hBiasGradient = hBiasGradient.mul(hBiasAdaGrad.getLearningRates(hBiasGradient));
    else hBiasGradient = hBiasGradient.mul(learningRate);

    if (useAdaGrad) vBiasGradient = vBiasGradient.mul(vBiasAdaGrad.getLearningRates(vBiasGradient));
    else vBiasGradient = vBiasGradient.mul(learningRate);

    // only do this with binary hidden layers
    if (applySparsity && this.hBiasGradient != null) applySparsity(hBiasGradient, learningRate);

    if (momentum != 0 && this.wGradient != null)
      wGradient.addi(this.wGradient.mul(momentum).add(wGradient.mul(1 - momentum)));

    if (momentum != 0 && this.vBiasGradient != null)
      vBiasGradient.addi(this.vBiasGradient.mul(momentum).add(vBiasGradient.mul(1 - momentum)));

    if (momentum != 0 && this.hBiasGradient != null)
      hBiasGradient.addi(this.hBiasGradient.mul(momentum).add(hBiasGradient.mul(1 - momentum)));

    if (normalizeByInputRows) {
      wGradient.divi(lastMiniBatchSize);
      vBiasGradient.divi(lastMiniBatchSize);
      hBiasGradient.divi(lastMiniBatchSize);
    }

    // simulate post gradient application  and apply the difference to the gradient to decrease the
    // change the gradient has
    if (useRegularization && l2 > 0) {
      if (useAdaGrad) wGradient.subi(W.mul(l2).mul(wLearningRates));
      else wGradient.subi(W.mul(l2 * learningRate));
    }

    if (constrainGradientToUnitNorm) {
      wGradient.divi(wGradient.norm2());
      vBiasGradient.divi(vBiasGradient.norm2());
      hBiasGradient.divi(hBiasGradient.norm2());
    }

    this.wGradient = wGradient;
    this.vBiasGradient = vBiasGradient;
    this.hBiasGradient = hBiasGradient;
  }