Java Code Examples for org.apache.commons.math3.exception.util.LocalizedFormats#CONTINUED_FRACTION_NAN_DIVERGENCE
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org.apache.commons.math3.exception.util.LocalizedFormats#CONTINUED_FRACTION_NAN_DIVERGENCE .
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Example 1
| Source File: Math_31_ContinuedFraction_t.java From coming with MIT License | 4 votes |
|
/**
* <p>
* Evaluates the continued fraction at the value x.
* </p>
*
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* Note: the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction / MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
*/
public double evaluate(double x, double epsilon, int maxIterations) {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 2
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 3
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 4
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* <p>
* Evaluates the continued fraction at the value x.
* </p>
*
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* Note: the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction / MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
*/
public double evaluate(double x, double epsilon, int maxIterations) {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 5
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 6
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 7
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
Example 8
| Source File: ContinuedFraction.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Evaluates the continued fraction at the value x.
* <p>
* The implementation of this method is based on the modified Lentz algorithm as described
* on page 18 ff. in:
* <ul>
* <li>
* I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
* <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
* http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
* </li>
* </ul>
* <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
* <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
* </p>
*
* @param x the evaluation point.
* @param epsilon maximum error allowed.
* @param maxIterations maximum number of convergents
* @return the value of the continued fraction evaluated at x.
* @throws ConvergenceException if the algorithm fails to converge.
* @throws MaxCountExceededException if maximal number of iterations is reached
*/
public double evaluate(double x, double epsilon, int maxIterations)
throws ConvergenceException, MaxCountExceededException {
final double small = 1e-50;
double hPrev = getA(0, x);
// use the value of small as epsilon criteria for zero checks
if (Precision.equals(hPrev, 0.0, small)) {
hPrev = small;
}
int n = 1;
double dPrev = 0.0;
double cPrev = hPrev;
double hN = hPrev;
while (n < maxIterations) {
final double a = getA(n, x);
final double b = getB(n, x);
double dN = a + b * dPrev;
if (Precision.equals(dN, 0.0, small)) {
dN = small;
}
double cN = a + b / cPrev;
if (Precision.equals(cN, 0.0, small)) {
cN = small;
}
dN = 1 / dN;
final double deltaN = cN * dN;
hN = hPrev * deltaN;
if (Double.isInfinite(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
x);
}
if (Double.isNaN(hN)) {
throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
x);
}
if (FastMath.abs(deltaN - 1.0) < epsilon) {
break;
}
dPrev = dN;
cPrev = cN;
hPrev = hN;
n++;
}
if (n >= maxIterations) {
throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
maxIterations, x);
}
return hN;
}
