public void ParametricHessianTest()
{
// function is null
{
string parameterName = "function";
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Hessian(
function: null,
argument: EngineFailureModel.EstimatedParameters,
parameter: EngineFailureModel.Data);
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// argument is null
{
string parameterName = "argument";
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Hessian(
function: EngineFailureModel.LogLikelihood,
argument: null,
parameter: EngineFailureModel.Data);
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// valid input
{
var expected =
EngineFailureModel.LogLikelihoodHessian(
argument: EngineFailureModel.EstimatedParameters,
parameter: EngineFailureModel.Data);
var actual =
NumericalDifferentiation.Hessian(
function: EngineFailureModel.LogLikelihood,
argument: EngineFailureModel.EstimatedParameters,
parameter: EngineFailureModel.Data);
DoubleMatrixAssert.AreEqual(
expected: expected,
actual: actual,
delta: DoubleMatrixTest.Accuracy);
}
}
public void testDerivativeWeightsOnNonUniformGrids()
{
Fdm1dMesher mesherX =
new Concentrating1dMesher(-2.0, 3.0, 50, new Pair <double?, double?>(0.5, 0.01));
Fdm1dMesher mesherY =
new Concentrating1dMesher(0.5, 5.0, 25, new Pair <double?, double?>(0.5, 0.1));
Fdm1dMesher mesherZ =
new Concentrating1dMesher(-1.0, 2.0, 31, new Pair <double?, double?>(1.5, 0.01));
FdmMesher meshers =
new FdmMesherComposite(mesherX, mesherY, mesherZ);
FdmLinearOpLayout layout = meshers.layout();
FdmLinearOpIterator endIter = layout.end();
double tol = 1e-13;
for (int direction = 0; direction < 3; ++direction)
{
SparseMatrix dfdx
= new FirstDerivativeOp(direction, meshers).toMatrix();
SparseMatrix d2fdx2
= new SecondDerivativeOp(direction, meshers).toMatrix();
Vector gridPoints = meshers.locations(direction);
for (FdmLinearOpIterator iter = layout.begin();
iter != endIter; ++iter)
{
int c = iter.coordinates()[direction];
int index = iter.index();
int indexM1 = layout.neighbourhood(iter, direction, -1);
int indexP1 = layout.neighbourhood(iter, direction, +1);
// test only if not on the boundary
if (c == 0)
{
Vector twoPoints = new Vector(2);
twoPoints[0] = 0.0;
twoPoints[1] = gridPoints[indexP1] - gridPoints[index];
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, twoPoints).weights();
double beta1 = dfdx[index, index];
double gamma1 = dfdx[index, indexP1];
if (Math.Abs((beta1 - ndWeights1st[0]) / beta1) > tol ||
Math.Abs((gamma1 - ndWeights1st[1]) / gamma1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator "
+ "on the lower boundary"
+ "\n expected beta: " + ndWeights1st[0]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[0])
+ "\n expected gamma: " + ndWeights1st[1]
+ "\n calculated gamma: " + gamma1
+ "\n difference gamma: "
+ (gamma1 - ndWeights1st[1]));
}
// free boundary condition by default
double beta2 = d2fdx2[index, index];
double gamma2 = d2fdx2[index, indexP1];
if (Math.Abs(beta2) > Const.QL_EPSILON ||
Math.Abs(gamma2) > Const.QL_EPSILON)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator "
+ "on the lower boundary"
+ "\n expected beta: " + 0.0
+ "\n calculated beta: " + beta2
+ "\n expected gamma: " + 0.0
+ "\n calculated gamma: " + gamma2);
}
}
else if (c == layout.dim()[direction] - 1)
{
Vector twoPoints = new Vector(2);
twoPoints[0] = gridPoints[indexM1] - gridPoints[index];
twoPoints[1] = 0.0;
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, twoPoints).weights();
double alpha1 = dfdx[index, indexM1];
double beta1 = dfdx[index, index];
if (Math.Abs((alpha1 - ndWeights1st[0]) / alpha1) > tol ||
Math.Abs((beta1 - ndWeights1st[1]) / beta1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator "
+ "on the upper boundary"
+ "\n expected alpha: " + ndWeights1st[0]
+ "\n calculated alpha: " + alpha1
+ "\n difference alpha: "
+ (alpha1 - ndWeights1st[0])
+ "\n expected beta: " + ndWeights1st[1]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[1]));
}
// free boundary condition by default
double alpha2 = d2fdx2[index, indexM1];
double beta2 = d2fdx2[index, index];
if (Math.Abs(alpha2) > Const.QL_EPSILON ||
Math.Abs(beta2) > Const.QL_EPSILON)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator "
+ "on the upper boundary"
+ "\n expected alpha: " + 0.0
+ "\n calculated alpha: " + alpha2
+ "\n expected beta: " + 0.0
+ "\n calculated beta: " + beta2);
}
}
else
{
Vector threePoints = new Vector(3);
threePoints[0] = gridPoints[indexM1] - gridPoints[index];
threePoints[1] = 0.0;
threePoints[2] = gridPoints[indexP1] - gridPoints[index];
Vector ndWeights1st = new NumericalDifferentiation(x => x, 1, threePoints).weights();
double alpha1 = dfdx[index, indexM1];
double beta1 = dfdx[index, index];
double gamma1 = dfdx[index, indexP1];
if (Math.Abs((alpha1 - ndWeights1st[0]) / alpha1) > tol ||
Math.Abs((beta1 - ndWeights1st[1]) / beta1) > tol ||
Math.Abs((gamma1 - ndWeights1st[2]) / gamma1) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "first order derivative operator"
+ "\n expected alpha: " + ndWeights1st[0]
+ "\n calculated alpha: " + alpha1
+ "\n difference alpha: "
+ (alpha1 - ndWeights1st[0])
+ "\n expected beta: " + ndWeights1st[1]
+ "\n calculated beta: " + beta1
+ "\n difference beta: "
+ (beta1 - ndWeights1st[1])
+ "\n expected gamma: " + ndWeights1st[2]
+ "\n calculated gamma: " + gamma1
+ "\n difference gamma: "
+ (gamma1 - ndWeights1st[2]));
}
Vector ndWeights2nd = new NumericalDifferentiation(x => x, 2, threePoints).weights();
double alpha2 = d2fdx2[index, indexM1];
double beta2 = d2fdx2[index, index];
double gamma2 = d2fdx2[index, indexP1];
if (Math.Abs((alpha2 - ndWeights2nd[0]) / alpha2) > tol ||
Math.Abs((beta2 - ndWeights2nd[1]) / beta2) > tol ||
Math.Abs((gamma2 - ndWeights2nd[2]) / gamma2) > tol)
{
QAssert.Fail("can not reproduce the weights of the "
+ "second order derivative operator"
+ "\n expected alpha: " + ndWeights2nd[0]
+ "\n calculated alpha: " + alpha2
+ "\n difference alpha: "
+ (alpha2 - ndWeights2nd[0])
+ "\n expected beta: " + ndWeights2nd[1]
+ "\n calculated beta: " + beta2
+ "\n difference beta: "
+ (beta2 - ndWeights2nd[1])
+ "\n expected gamma: " + ndWeights2nd[2]
+ "\n calculated gamma: " + gamma2
+ "\n difference gamma: "
+ (gamma2 - ndWeights2nd[2]));
}
}
}
}
}
public void TestInitialize()
{
library = new NumericalDifferentiation();
}
public void NonparametricHessianTest()
{
// function is null
{
string parameterName = "function";
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Hessian(
function: null,
argument: DoubleMatrix.Dense(2, 1));
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// argument is null
{
string parameterName = "argument";
double function(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
double f = x * x * y + Math.Exp(y);
return(f);
};
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Hessian(
function: function,
argument: null);
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// valid input
{
double function(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
double f = x * x * y + Math.Exp(y);
return(f);
};
DoubleMatrix hessian(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
DoubleMatrix h = DoubleMatrix.Dense(2, 2);
h[0, 0] = 2.0 * y;
h[0, 1] = 2.0 * x;
h[1, 0] = h[0, 1];
h[1, 1] = Math.Exp(y);
return(h);
}
var arg = DoubleMatrix.Dense(2, 1, new double[2]
{
9.0, -2.1
});
var expected =
hessian(
argument: arg);
var actual =
NumericalDifferentiation.Hessian(
function: function,
argument: arg);
DoubleMatrixAssert.AreEqual(
expected: expected,
actual: actual,
delta: DoubleMatrixTest.Accuracy);
}
}
public void NonparametricGradientTest()
{
// function is null
{
string parameterName = "function";
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Gradient(
function: null,
argument: DoubleMatrix.Dense(2, 1));
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// argument is null
{
string parameterName = "argument";
double function(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
double f = x * x * y + Math.Exp(y);
return(f);
};
ArgumentExceptionAssert.Throw(
() =>
{
NumericalDifferentiation.Gradient(
function: function,
argument: null);
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// valid input - Non zero arguments
{
double function(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
double f = x * x * y + Math.Exp(y);
return(f);
};
DoubleMatrix gradient(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
DoubleMatrix g = DoubleMatrix.Dense(2, 1);
g[0] = 2.0 * x * y;
g[1] = x * x + Math.Exp(y);
return(g);
};
var arg = DoubleMatrix.Dense(2, 1, new double[2]
{
9.0, -2.1
});
var expected =
gradient(
argument: arg);
var actual =
NumericalDifferentiation.Gradient(
function: function,
argument: arg);
DoubleMatrixAssert.AreEqual(
expected: expected,
actual: actual,
delta: DoubleMatrixTest.Accuracy);
}
// valid input - Some zero arguments
{
double function(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
double f = x * x * y + Math.Exp(y);
return(f);
};
DoubleMatrix gradient(DoubleMatrix argument)
{
double x, y;
x = argument[0];
y = argument[1];
DoubleMatrix g = DoubleMatrix.Dense(2, 1);
g[0] = 2.0 * x * y;
g[1] = x * x + Math.Exp(y);
return(g);
};
var arg = DoubleMatrix.Dense(2, 1, new double[2]
{
0.0, -2.1
});
var expected =
gradient(
argument: arg);
var actual =
NumericalDifferentiation.Gradient(
function: function,
argument: arg);
DoubleMatrixAssert.AreEqual(
expected: expected,
actual: actual,
delta: DoubleMatrixTest.Accuracy);
arg = DoubleMatrix.Dense(2, 1, new double[2]
{
9.0, 0.0
});
expected =
gradient(
argument: arg);
actual =
NumericalDifferentiation.Gradient(
function: function,
argument: arg);
DoubleMatrixAssert.AreEqual(
expected: expected,
actual: actual,
delta: DoubleMatrixTest.Accuracy);
}
}
