Exemplo n.º 1
0
 /**
  * Multiply by Hessian <code> H = F'NF + M </code>
  *
  * @param x Vector to be multiplied and modified
  */
 public void multiplyHessian(Vect x) {
   Vect data = _data.clone();
   _transform.forwardLinearized(data, x, _referenceModel); // data is Fx
   data.multiplyInverseCovariance(); // data is NFx
   x.multiplyInverseCovariance(); // x is Mx
   _transform.addTranspose(data, x, _referenceModel); // x is (F'NF +M)x
   data.dispose();
 }
Exemplo n.º 2
0
 /**
  * Return gradient term of quadratic. This instance will be in the vector space of the
  * perturbModel, if provided. Otherwise, uses an instance of the referenceModel.
  *
  * @return Value of <code> b = -F' N [data - f(m)] + Mm  </code> if dampOnlyPerturbation is false,
  *     and <code> b = -F' N [data - f(m)] </code> if dampOnlyPerturbation is true.
  */
 public Vect getB() {
   Vect data = VectUtil.cloneZero(_data); // data is data with zeros
   _transform.forwardNonlinear(data, _referenceModel); // data is f(m)
   data.add(1., -1., _data); // data is -e = -(d - f(m))
   _transform.adjustRobustErrors(data); // (remove outliers from e)
   data.multiplyInverseCovariance(); // data is -Ne
   Vect b = null;
   if (_dampOnlyPerturbation) {
     if (_perturbModel != null) {
       b = VectUtil.cloneZero(_perturbModel); // b is 0
     } else {
       b = VectUtil.cloneZero(_referenceModel); // b is 0
     }
   } else {
     if (_perturbModel != null) {
       b = _perturbModel.clone();
       b.project(0., 1., _referenceModel); // b is m
     } else {
       b = _referenceModel.clone(); // b is m
     }
     b.multiplyInverseCovariance(); // b is M m
   }
   _transform.addTranspose(data, b, _referenceModel); // b is -F'Ne [+ Mm]
   data.dispose();
   return b;
 }
Exemplo n.º 3
0
  /**
   * Evaluate the full objective function without approximation. Provide a model in the vector space
   * of the referenceModel. perturbModel is unused. Useful for line-search of best scale factor. If
   * dampedPerturbation, evaluates
   *
   * <pre>
   * [f(m)-data]'N[f(m)-data] + (m-m0)'M(m-m0)
   * </pre>
   *
   * where m0 is the reference model. Otherwise evaluates
   *
   * <pre>
   * [f(m)-data]'N[f(m)-data] + m'M m
   * </pre>
   *
   * @param m Model to be evaluated.
   * @return Value of objective function.
   */
  public double evalFullObjectiveFunction(VectConst m) {

    Vect data = VectUtil.cloneZero(_data); // data is zeros

    Vect model = m.clone(); // model is m
    model.constrain(); // may have been done already

    _transform.forwardNonlinear(data, model); // data is f(m)
    data.add(1., -1., _data); // data is e = f(m) - data
    _transform.adjustRobustErrors(data);
    double eNe = data.magnitude(); // eNe is e'Ne
    checkNaN(eNe);
    data.dispose();

    // damp perturbation if requested
    if (_dampOnlyPerturbation) {
      model.add(1., -1., _referenceModel); // model is (m-m0)
    }

    double mMm = model.magnitude(); // mMm is (m-m0)'M(m-m0)
    checkNaN(mMm);
    model.dispose();
    return (eNe + mMm);
  }
Exemplo n.º 4
0
  /**
   * Run a few tests to ensure that transpose satisfies definition. This is expensive and intended
   * only for test code.
   *
   * @return number of sigficant digits of precision in transpose. Expect 5 or 6. Unacceptable if
   *     not 3 or more. A value of 3 or 4 probably indicates a subtle error.
   */
  public int getTransposePrecision() {
    VectConst d = _data; // arbitrary nonzero data
    Vect b = this.getB(); // arbitrary nonzero model
    double bb = b.dot(b);
    checkNaN(bb);
    assert !Almost.FLOAT.zero(bb) : "Cannot test with zero-magnitude b";

    // Get forward transform of b
    Vect Fb = VectUtil.cloneZero(d);
    Vect bSave = b.clone();
    _transform.forwardLinearized(Fb, b, _referenceModel);

    // make sure didn't step on wrong vector
    assert VectUtil.areSame(b, bSave) : "model was changed by forward model";
    bSave.dispose();

    // check that forward zeros output data.
    Vect test = d.clone();
    _transform.forwardLinearized(test, b, _referenceModel);
    assert VectUtil.areSame(test, Fb) : "forwardLinearized should zero data";
    test.dispose();

    // Get transpose of d
    Vect Ad = VectUtil.cloneZero(b);
    Vect dSave = d.clone();
    _transform.addTranspose(d, Ad, _referenceModel);
    double transposeMagnitude = Ad.dot(Ad);
    checkNaN(transposeMagnitude);

    // make sure didn't step on wrong vector
    assert VectUtil.areSame(d, dSave) : "data was changed by transpose";
    dSave.dispose();

    // ensure that transpose adds to existing model
    test = b.clone(); // make initial size comparable to transpose
    double scaleTest = 1.1 * Math.sqrt(transposeMagnitude / bb);
    VectUtil.scale(test, scaleTest);
    _transform.addTranspose(d, test, _referenceModel);
    assert !VectUtil.areSame(Ad, test)
        : "Transpose should not zero model.  "
            + "Magnitude: b="
            + bb
            + "trans="
            + transposeMagnitude
            + " test="
            + test.dot(test);
    test.add(1., -1., Ad);
    VectUtil.scale(test, 1. / scaleTest);
    assert VectUtil.areSame(test, b) : "Transpose did not add to model vector";
    test.dispose();

    // get dot products that should be equal
    double dFb = d.dot(Fb);
    double Adb = Ad.dot(b);
    assert !Almost.FLOAT.zero(dFb) : "zero magnitude test: dFb is zero";
    assert !Almost.FLOAT.zero(Adb) : "zero magnitude test: Adb is zero";
    checkNaN(dFb);
    checkNaN(Adb);

    int significantDigits = 10;
    boolean matches = false;
    while (!matches && significantDigits > 0) {
      Almost almost = new Almost(significantDigits);
      matches = almost.equal(dFb, Adb);
      if (!matches) {
        --significantDigits;
      }
    }
    if (significantDigits < 3) {
      LOG.severe("Transpose precision is unacceptable: dFb=" + dFb + " Adb=" + Adb);
    }
    Ad.dispose();
    Fb.dispose();
    b.dispose();
    return significantDigits;
  }