Java Code Examples for org.apache.commons.math3.util.FastMath#tan()
The following examples show how to use
org.apache.commons.math3.util.FastMath#tan() .
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Example 1
| Source File: SparseGradientTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testTrigo() {
double epsilon = 2.0e-12;
for (double x = 0.1; x < 1.2; x += 0.1) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0.1; y < 1.2; y += 0.1) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
for (double z = 0.1; z < 1.2; z += 0.1) {
SparseGradient sgZ = SparseGradient.createVariable(2, z);
SparseGradient f = sgX.divide(sgY.cos().add(sgZ.tan())).sin();
double a = FastMath.cos(y) + FastMath.tan(z);
double f0 = FastMath.sin(x / a);
Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
double dfdx = FastMath.cos(x / a) / a;
Assert.assertEquals(dfdx, f.getDerivative(0), FastMath.abs(epsilon * dfdx));
double dfdy = x * FastMath.sin(y) * dfdx / a;
Assert.assertEquals(dfdy, f.getDerivative(1), FastMath.abs(epsilon * dfdy));
double cz = FastMath.cos(z);
double cz2 = cz * cz;
double dfdz = -x * dfdx / (a * cz2);
Assert.assertEquals(dfdz, f.getDerivative(2), FastMath.abs(epsilon * dfdz));
}
}
}
}
Example 2
| Source File: Tan.java From astor with GNU General Public License v2.0 | 5 votes |
|
/** {@inheritDoc} */
public UnivariateFunction derivative() {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
final double tanX = FastMath.tan(x);
return 1 + tanX * tanX;
}
};
}
Example 3
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Create a new generator.
*
* @param generator underlying random generator to use
* @param alpha Stability parameter. Must be in range (0, 2]
* @param beta Skewness parameter. Must be in range [-1, 1]
* @throws NullArgumentException if generator is null
* @throws OutOfRangeException if {@code alpha <= 0} or {@code alpha > 2}
* or {@code beta < -1} or {@code beta > 1}
*/
public StableRandomGenerator(final RandomGenerator generator,
final double alpha, final double beta)
throws NullArgumentException, OutOfRangeException {
if (generator == null) {
throw new NullArgumentException();
}
if (!(alpha > 0d && alpha <= 2d)) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_LEFT,
alpha, 0, 2);
}
if (!(beta >= -1d && beta <= 1d)) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_SIMPLE,
beta, -1, 1);
}
this.generator = generator;
this.alpha = alpha;
this.beta = beta;
if (alpha < 2d && beta != 0d) {
zeta = beta * FastMath.tan(FastMath.PI * alpha / 2);
} else {
zeta = 0d;
}
}
Example 4
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* Create a new generator.
*
* @param generator underlying random generator to use
* @param alpha Stability parameter. Must be in range (0, 2]
* @param beta Skewness parameter. Must be in range [-1, 1]
* @throws NullArgumentException if generator is null
* @throws OutOfRangeException if {@code alpha <= 0} or {@code alpha > 2}
* or {@code beta < -1} or {@code beta > 1}
*/
public StableRandomGenerator(final RandomGenerator generator,
final double alpha, final double beta)
throws NullArgumentException, OutOfRangeException {
if (generator == null) {
throw new NullArgumentException();
}
if (!(alpha > 0d && alpha <= 2d)) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_LEFT,
alpha, 0, 2);
}
if (!(beta >= -1d && beta <= 1d)) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_SIMPLE,
beta, -1, 1);
}
this.generator = generator;
this.alpha = alpha;
this.beta = beta;
if (alpha < 2d && beta != 0d) {
zeta = beta * FastMath.tan(FastMath.PI * alpha / 2);
} else {
zeta = 0d;
}
}
Example 5
| Source File: CauchyDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* {@inheritDoc}
*
* Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
* and {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
double ret;
if (p < 0 || p > 1) {
throw new OutOfRangeException(p, 0, 1);
} else if (p == 0) {
ret = Double.NEGATIVE_INFINITY;
} else if (p == 1) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
}
return ret;
}
Example 6
| Source File: CauchyDistribution.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* {@inheritDoc}
*
* Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
* and {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
double ret;
if (p < 0 || p > 1) {
throw new OutOfRangeException(p, 0, 1);
} else if (p == 0) {
ret = Double.NEGATIVE_INFINITY;
} else if (p == 1) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
}
return ret;
}
Example 7
| Source File: LibSpoofPrimitives.java From systemds with Apache License 2.0 | 4 votes |
|
public static double[] vectTanWrite(double[] a, int ai, int len) {
double[] c = allocVector(len, false);
for( int j = 0; j < len; j++, ai++)
c[j] = FastMath.tan(a[ai]);
return c;
}
Example 8
| Source File: Tan.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double value(double x) {
return FastMath.tan(x);
}
Example 9
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Generate a random scalar with zero location and unit scale.
*
* @return a random scalar with zero location and unit scale
*/
public double nextNormalizedDouble() {
// we need 2 uniform random numbers to calculate omega and phi
double omega = -FastMath.log(generator.nextDouble());
double phi = FastMath.PI * (generator.nextDouble() - 0.5);
// Normal distribution case (Box-Muller algorithm)
if (alpha == 2d) {
return FastMath.sqrt(2d * omega) * FastMath.sin(phi);
}
double x;
// when beta = 0, zeta is zero as well
// Thus we can exclude it from the formula
if (beta == 0d) {
// Cauchy distribution case
if (alpha == 1d) {
x = FastMath.tan(phi);
} else {
x = FastMath.pow(omega * FastMath.cos((1 - alpha) * phi),
1d / alpha - 1d) *
FastMath.sin(alpha * phi) /
FastMath.pow(FastMath.cos(phi), 1d / alpha);
}
} else {
// Generic stable distribution
double cosPhi = FastMath.cos(phi);
// to avoid rounding errors around alpha = 1
if (FastMath.abs(alpha - 1d) > 1e-8) {
double alphaPhi = alpha * phi;
double invAlphaPhi = phi - alphaPhi;
x = (FastMath.sin(alphaPhi) + zeta * FastMath.cos(alphaPhi)) / cosPhi *
(FastMath.cos(invAlphaPhi) + zeta * FastMath.sin(invAlphaPhi)) /
FastMath.pow(omega * cosPhi, (1 - alpha) / alpha);
} else {
double betaPhi = FastMath.PI / 2 + beta * phi;
x = 2d / FastMath.PI * (betaPhi * FastMath.tan(phi) - beta *
FastMath.log(FastMath.PI / 2d * omega * cosPhi / betaPhi));
if (alpha != 1d) {
x = x + beta * FastMath.tan(FastMath.PI * alpha / 2);
}
}
}
return x;
}
Example 10
| Source File: DSCompiler.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** Compute tangent of a derivative structure.
* @param operand array holding the operand
* @param operandOffset offset of the operand in its array
* @param result array where result must be stored (for
* tangent the result array <em>cannot</em> be the input
* array)
* @param resultOffset offset of the result in its array
*/
public void tan(final double[] operand, final int operandOffset,
final double[] result, final int resultOffset) {
// create the function value and derivatives
final double[] function = new double[1 + order];
final double t = FastMath.tan(operand[operandOffset]);
function[0] = t;
if (order > 0) {
// the nth order derivative of tan has the form:
// dn(tan(x)/dxn = P_n(tan(x))
// where P_n(t) is a degree n+1 polynomial with same parity as n+1
// P_0(t) = t, P_1(t) = 1 + t^2, P_2(t) = 2 t (1 + t^2) ...
// the general recurrence relation for P_n is:
// P_n(x) = (1+t^2) P_(n-1)'(t)
// as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
final double[] p = new double[order + 2];
p[1] = 1;
final double t2 = t * t;
for (int n = 1; n <= order; ++n) {
// update and evaluate polynomial P_n(t)
double v = 0;
p[n + 1] = n * p[n];
for (int k = n + 1; k >= 0; k -= 2) {
v = v * t2 + p[k];
if (k > 2) {
p[k - 2] = (k - 1) * p[k - 1] + (k - 3) * p[k - 3];
} else if (k == 2) {
p[0] = p[1];
}
}
if ((n & 0x1) == 0) {
v *= t;
}
function[n] = v;
}
}
// apply function composition
compose(operand, operandOffset, function, result, resultOffset);
}
Example 11
| Source File: Tan.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double value(double x) {
return FastMath.tan(x);
}
Example 12
| Source File: DSCompiler.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** Compute tangent of a derivative structure.
* @param operand array holding the operand
* @param operandOffset offset of the operand in its array
* @param result array where result must be stored (for
* tangent the result array <em>cannot</em> be the input
* array)
* @param resultOffset offset of the result in its array
*/
public void tan(final double[] operand, final int operandOffset,
final double[] result, final int resultOffset) {
// create the function value and derivatives
final double[] function = new double[1 + order];
final double t = FastMath.tan(operand[operandOffset]);
function[0] = t;
if (order > 0) {
// the nth order derivative of tan has the form:
// dn(tan(x)/dxn = P_n(tan(x))
// where P_n(t) is a degree n+1 polynomial with same parity as n+1
// P_0(t) = t, P_1(t) = 1 + t^2, P_2(t) = 2 t (1 + t^2) ...
// the general recurrence relation for P_n is:
// P_n(x) = (1+t^2) P_(n-1)'(t)
// as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
final double[] p = new double[order + 2];
p[1] = 1;
final double t2 = t * t;
for (int n = 1; n <= order; ++n) {
// update and evaluate polynomial P_n(t)
double v = 0;
p[n + 1] = n * p[n];
for (int k = n + 1; k >= 0; k -= 2) {
v = v * t2 + p[k];
if (k > 2) {
p[k - 2] = (k - 1) * p[k - 1] + (k - 3) * p[k - 3];
} else if (k == 2) {
p[0] = p[1];
}
}
if ((n & 0x1) == 0) {
v *= t;
}
function[n] = v;
}
}
// apply function composition
compose(operand, operandOffset, function, result, resultOffset);
}
Example 13
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Generate a random scalar with zero location and unit scale.
*
* @return a random scalar with zero location and unit scale
*/
public double nextNormalizedDouble() {
// we need 2 uniform random numbers to calculate omega and phi
double omega = -FastMath.log(generator.nextDouble());
double phi = FastMath.PI * (generator.nextDouble() - 0.5);
// Normal distribution case (Box-Muller algorithm)
if (alpha == 2d) {
return FastMath.sqrt(2d * omega) * FastMath.sin(phi);
}
double x;
// when beta = 0, zeta is zero as well
// Thus we can exclude it from the formula
if (beta == 0d) {
// Cauchy distribution case
if (alpha == 1d) {
x = FastMath.tan(phi);
} else {
x = FastMath.pow(omega * FastMath.cos((1 - alpha) * phi),
1d / alpha - 1d) *
FastMath.sin(alpha * phi) /
FastMath.pow(FastMath.cos(phi), 1d / alpha);
}
} else {
// Generic stable distribution
double cosPhi = FastMath.cos(phi);
// to avoid rounding errors around alpha = 1
if (FastMath.abs(alpha - 1d) > 1e-8) {
double alphaPhi = alpha * phi;
double invAlphaPhi = phi - alphaPhi;
x = (FastMath.sin(alphaPhi) + zeta * FastMath.cos(alphaPhi)) / cosPhi *
(FastMath.cos(invAlphaPhi) + zeta * FastMath.sin(invAlphaPhi)) /
FastMath.pow(omega * cosPhi, (1 - alpha) / alpha);
} else {
double betaPhi = FastMath.PI / 2 + beta * phi;
x = 2d / FastMath.PI * (betaPhi * FastMath.tan(phi) - beta *
FastMath.log(FastMath.PI / 2d * omega * cosPhi / betaPhi));
if (alpha != 1d) {
x = x + beta * FastMath.tan(FastMath.PI * alpha / 2);
}
}
}
return x;
}
Example 14
| Source File: DerivativeStructureTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testTrigo() {
double epsilon = 2.0e-12;
for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {
for (double x = 0.1; x < 1.2; x += 0.1) {
DerivativeStructure dsX = new DerivativeStructure(3, maxOrder, 0, x);
for (double y = 0.1; y < 1.2; y += 0.1) {
DerivativeStructure dsY = new DerivativeStructure(3, maxOrder, 1, y);
for (double z = 0.1; z < 1.2; z += 0.1) {
DerivativeStructure dsZ = new DerivativeStructure(3, maxOrder, 2, z);
DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();
double a = FastMath.cos(y) + FastMath.tan(z);
double f0 = FastMath.sin(x / a);
Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
if (f.getOrder() > 0) {
double dfdx = FastMath.cos(x / a) / a;
Assert.assertEquals(dfdx, f.getPartialDerivative(1, 0, 0), FastMath.abs(epsilon * dfdx));
double dfdy = x * FastMath.sin(y) * dfdx / a;
Assert.assertEquals(dfdy, f.getPartialDerivative(0, 1, 0), FastMath.abs(epsilon * dfdy));
double cz = FastMath.cos(z);
double cz2 = cz * cz;
double dfdz = -x * dfdx / (a * cz2);
Assert.assertEquals(dfdz, f.getPartialDerivative(0, 0, 1), FastMath.abs(epsilon * dfdz));
if (f.getOrder() > 1) {
double df2dx2 = -(f0 / (a * a));
Assert.assertEquals(df2dx2, f.getPartialDerivative(2, 0, 0), FastMath.abs(epsilon * df2dx2));
double df2dy2 = x * FastMath.cos(y) * dfdx / a -
x * x * FastMath.sin(y) * FastMath.sin(y) * f0 / (a * a * a * a) +
2 * FastMath.sin(y) * dfdy / a;
Assert.assertEquals(df2dy2, f.getPartialDerivative(0, 2, 0), FastMath.abs(epsilon * df2dy2));
double c4 = cz2 * cz2;
double df2dz2 = x * (2 * a * (1 - a * cz * FastMath.sin(z)) * dfdx - x * f0 / a ) / (a * a * a * c4);
Assert.assertEquals(df2dz2, f.getPartialDerivative(0, 0, 2), FastMath.abs(epsilon * df2dz2));
double df2dxdy = dfdy / x - x * FastMath.sin(y) * f0 / (a * a * a);
Assert.assertEquals(df2dxdy, f.getPartialDerivative(1, 1, 0), FastMath.abs(epsilon * df2dxdy));
}
}
}
}
}
}
}
Example 15
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Generate a random scalar with zero location and unit scale.
*
* @return a random scalar with zero location and unit scale
*/
public double nextNormalizedDouble() {
// we need 2 uniform random numbers to calculate omega and phi
double omega = -FastMath.log(generator.nextDouble());
double phi = FastMath.PI * (generator.nextDouble() - 0.5);
// Normal distribution case (Box-Muller algorithm)
if (alpha == 2d) {
return FastMath.sqrt(2d * omega) * FastMath.sin(phi);
}
double x;
// when beta = 0, zeta is zero as well
// Thus we can exclude it from the formula
if (beta == 0d) {
// Cauchy distribution case
if (alpha == 1d) {
x = FastMath.tan(phi);
} else {
x = FastMath.pow(omega * FastMath.cos((1 - alpha) * phi),
1d / alpha - 1d) *
FastMath.sin(alpha * phi) /
FastMath.pow(FastMath.cos(phi), 1d / alpha);
}
} else {
// Generic stable distribution
double cosPhi = FastMath.cos(phi);
// to avoid rounding errors around alpha = 1
if (FastMath.abs(alpha - 1d) > 1e-8) {
double alphaPhi = alpha * phi;
double invAlphaPhi = phi - alphaPhi;
x = (FastMath.sin(alphaPhi) + zeta * FastMath.cos(alphaPhi)) / cosPhi *
(FastMath.cos(invAlphaPhi) + zeta * FastMath.sin(invAlphaPhi)) /
FastMath.pow(omega * cosPhi, (1 - alpha) / alpha);
} else {
double betaPhi = FastMath.PI / 2 + beta * phi;
x = 2d / FastMath.PI * (betaPhi * FastMath.tan(phi) - beta *
FastMath.log(FastMath.PI / 2d * omega * cosPhi / betaPhi));
if (alpha != 1d) {
x = x + beta * FastMath.tan(FastMath.PI * alpha / 2);
}
}
}
return x;
}
Example 16
| Source File: DerivativeStructureTest.java From astor with GNU General Public License v2.0 | 4 votes |
|
@Test
public void testTrigo() {
double epsilon = 2.0e-12;
for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {
for (double x = 0.1; x < 1.2; x += 0.1) {
DerivativeStructure dsX = new DerivativeStructure(3, maxOrder, 0, x);
for (double y = 0.1; y < 1.2; y += 0.1) {
DerivativeStructure dsY = new DerivativeStructure(3, maxOrder, 1, y);
for (double z = 0.1; z < 1.2; z += 0.1) {
DerivativeStructure dsZ = new DerivativeStructure(3, maxOrder, 2, z);
DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();
double a = FastMath.cos(y) + FastMath.tan(z);
double f0 = FastMath.sin(x / a);
Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
if (f.getOrder() > 0) {
double dfdx = FastMath.cos(x / a) / a;
Assert.assertEquals(dfdx, f.getPartialDerivative(1, 0, 0), FastMath.abs(epsilon * dfdx));
double dfdy = x * FastMath.sin(y) * dfdx / a;
Assert.assertEquals(dfdy, f.getPartialDerivative(0, 1, 0), FastMath.abs(epsilon * dfdy));
double cz = FastMath.cos(z);
double cz2 = cz * cz;
double dfdz = -x * dfdx / (a * cz2);
Assert.assertEquals(dfdz, f.getPartialDerivative(0, 0, 1), FastMath.abs(epsilon * dfdz));
if (f.getOrder() > 1) {
double df2dx2 = -(f0 / (a * a));
Assert.assertEquals(df2dx2, f.getPartialDerivative(2, 0, 0), FastMath.abs(epsilon * df2dx2));
double df2dy2 = x * FastMath.cos(y) * dfdx / a -
x * x * FastMath.sin(y) * FastMath.sin(y) * f0 / (a * a * a * a) +
2 * FastMath.sin(y) * dfdy / a;
Assert.assertEquals(df2dy2, f.getPartialDerivative(0, 2, 0), FastMath.abs(epsilon * df2dy2));
double c4 = cz2 * cz2;
double df2dz2 = x * (2 * a * (1 - a * cz * FastMath.sin(z)) * dfdx - x * f0 / a ) / (a * a * a * c4);
Assert.assertEquals(df2dz2, f.getPartialDerivative(0, 0, 2), FastMath.abs(epsilon * df2dz2));
double df2dxdy = dfdy / x - x * FastMath.sin(y) * f0 / (a * a * a);
Assert.assertEquals(df2dxdy, f.getPartialDerivative(1, 1, 0), FastMath.abs(epsilon * df2dxdy));
}
}
}
}
}
}
}
Example 17
| Source File: StableRandomGenerator.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* Generate a random scalar with zero location and unit scale.
*
* @return a random scalar with zero location and unit scale
*/
public double nextNormalizedDouble() {
// we need 2 uniform random numbers to calculate omega and phi
double omega = -FastMath.log(generator.nextDouble());
double phi = FastMath.PI * (generator.nextDouble() - 0.5);
// Normal distribution case (Box-Muller algorithm)
if (alpha == 2d) {
return FastMath.sqrt(2d * omega) * FastMath.sin(phi);
}
double x;
// when beta = 0, zeta is zero as well
// Thus we can exclude it from the formula
if (beta == 0d) {
// Cauchy distribution case
if (alpha == 1d) {
x = FastMath.tan(phi);
} else {
x = FastMath.pow(omega * FastMath.cos((1 - alpha) * phi),
1d / alpha - 1d) *
FastMath.sin(alpha * phi) /
FastMath.pow(FastMath.cos(phi), 1d / alpha);
}
} else {
// Generic stable distribution
double cosPhi = FastMath.cos(phi);
// to avoid rounding errors around alpha = 1
if (FastMath.abs(alpha - 1d) > 1e-8) {
double alphaPhi = alpha * phi;
double invAlphaPhi = phi - alphaPhi;
x = (FastMath.sin(alphaPhi) + zeta * FastMath.cos(alphaPhi)) / cosPhi *
(FastMath.cos(invAlphaPhi) + zeta * FastMath.sin(invAlphaPhi)) /
FastMath.pow(omega * cosPhi, (1 - alpha) / alpha);
} else {
double betaPhi = FastMath.PI / 2 + beta * phi;
x = 2d / FastMath.PI * (betaPhi * FastMath.tan(phi) - beta *
FastMath.log(FastMath.PI / 2d * omega * cosPhi / betaPhi));
if (alpha != 1d) {
x = x + beta * FastMath.tan(FastMath.PI * alpha / 2);
}
}
}
return x;
}
Example 18
| Source File: Tan.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** {@inheritDoc} */
public double value(double x) {
return FastMath.tan(x);
}
Example 19
| Source File: LibSpoofPrimitives.java From systemds with Apache License 2.0 | 4 votes |
|
public static double[] vectTanWrite(double[] a, int ai, int len) {
double[] c = allocVector(len, false);
for( int j = 0; j < len; j++, ai++)
c[j] = FastMath.tan(a[ai]);
return c;
}
Example 20
| Source File: DSCompiler.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** Compute tangent of a derivative structure.
* @param operand array holding the operand
* @param operandOffset offset of the operand in its array
* @param result array where result must be stored (for
* tangent the result array <em>cannot</em> be the input
* array)
* @param resultOffset offset of the result in its array
*/
public void tan(final double[] operand, final int operandOffset,
final double[] result, final int resultOffset) {
// create the function value and derivatives
final double[] function = new double[1 + order];
final double t = FastMath.tan(operand[operandOffset]);
function[0] = t;
if (order > 0) {
// the nth order derivative of tan has the form:
// dn(tan(x)/dxn = P_n(tan(x))
// where P_n(t) is a degree n+1 polynomial with same parity as n+1
// P_0(t) = t, P_1(t) = 1 + t^2, P_2(t) = 2 t (1 + t^2) ...
// the general recurrence relation for P_n is:
// P_n(x) = (1+t^2) P_(n-1)'(t)
// as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
final double[] p = new double[order + 2];
p[1] = 1;
final double t2 = t * t;
for (int n = 1; n <= order; ++n) {
// update and evaluate polynomial P_n(t)
double v = 0;
p[n + 1] = n * p[n];
for (int k = n + 1; k >= 0; k -= 2) {
v = v * t2 + p[k];
if (k > 2) {
p[k - 2] = (k - 1) * p[k - 1] + (k - 3) * p[k - 3];
} else if (k == 2) {
p[0] = p[1];
}
}
if ((n & 0x1) == 0) {
v *= t;
}
function[n] = v;
}
}
// apply function composition
compose(operand, operandOffset, function, result, resultOffset);
}
