public class SphericalCoordinates
extends java.lang.Object
implements java.io.Serializable
The conventions used here are the mathematical ones, i.e. spherical coordinates are related to Cartesian coordinates as follows:
r is the radius, θ is the azimuthal angle in the x-y plane and Φ is the polar (co-latitude) angle. These conventions are different from the conventions used in physics (and in particular in spherical harmonics) where the meanings of θ and Φ are reversed.
This class provides conversion of coordinates and also of gradient and Hessian between spherical and Cartesian coordinates.
Modifier and Type | Class and Description |
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private static class |
SphericalCoordinates.DataTransferObject
Internal class used only for serialization.
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Modifier and Type | Field and Description |
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private double[][] |
jacobian
Jacobian of (r, θ &Phi).
|
private double |
phi
Polar angle (co-latitude) Φ.
|
private double[][] |
phiHessian
Hessian of polar (co-latitude) angle Φ.
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private double |
r
Radius.
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private double[][] |
rHessian
Hessian of radius.
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private static long |
serialVersionUID
Serializable UID.
|
private double |
theta
Azimuthal angle in the x-y plane θ.
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private double[][] |
thetaHessian
Hessian of azimuthal angle in the x-y plane θ.
|
private Vector3D |
v
Cartesian coordinates.
|
Constructor and Description |
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SphericalCoordinates(double r,
double theta,
double phi)
Build a spherical coordinates transformer from spherical coordinates.
|
SphericalCoordinates(Vector3D v)
Build a spherical coordinates transformer from Cartesian coordinates.
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Modifier and Type | Method and Description |
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private void |
computeHessians()
Lazy evaluation of Hessians.
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private void |
computeJacobian()
Lazy evaluation of (r, θ, φ) Jacobian.
|
Vector3D |
getCartesian()
Get the Cartesian coordinates.
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double |
getPhi()
Get the polar (co-latitude) angle.
|
double |
getR()
Get the radius.
|
double |
getTheta()
Get the azimuthal angle in x-y plane.
|
double[] |
toCartesianGradient(double[] sGradient)
Convert a gradient with respect to spherical coordinates into a gradient
with respect to Cartesian coordinates.
|
double[][] |
toCartesianHessian(double[][] sHessian,
double[] sGradient)
Convert a Hessian with respect to spherical coordinates into a Hessian
with respect to Cartesian coordinates.
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private java.lang.Object |
writeReplace()
Replace the instance with a data transfer object for serialization.
|
private static final long serialVersionUID
private final Vector3D v
private final double r
private final double theta
private final double phi
private double[][] jacobian
private double[][] rHessian
private double[][] thetaHessian
private double[][] phiHessian
public SphericalCoordinates(Vector3D v)
v
- Cartesian coordinatespublic SphericalCoordinates(double r, double theta, double phi)
r
- radiustheta
- azimuthal angle in x-y planephi
- polar (co-latitude) anglepublic Vector3D getCartesian()
public double getR()
getTheta()
,
getPhi()
public double getTheta()
public double getPhi()
getR()
,
getTheta()
public double[] toCartesianGradient(double[] sGradient)
sGradient
- gradient with respect to spherical coordinates
{df/dr, df/dθ, df/dΦ}public double[][] toCartesianHessian(double[][] sHessian, double[] sGradient)
As Hessian are always symmetric, we use only the lower left part of the provided spherical Hessian, so the upper part may not be initialized. However, we still do fill up the complete array we create, with guaranteed symmetry.
sHessian
- Hessian with respect to spherical coordinates
{{d2f/dr2, d2f/drdθ, d2f/drdΦ},
{d2f/drdθ, d2f/dθ2, d2f/dθdΦ},
{d2f/drdΦ, d2f/dθdΦ, d2f/dΦ2}sGradient
- gradient with respect to spherical coordinates
{df/dr, df/dθ, df/dΦ}private void computeJacobian()
private void computeHessians()
private java.lang.Object writeReplace()