/**
* 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();
}
/**
* 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;
}
/**
* 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);
}
/**
* 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;
}