Author: bugman
Date: Sun Mar 14 12:13:15 2010
New Revision: 10990
URL: http://svn.gna.org/viewcvs/relax?rev=10990&view=rev
Log:
Added a series of new cone types to generic_fns.structure.cones.
Modified:
1.3/generic_fns/structure/cones.py
Modified: 1.3/generic_fns/structure/cones.py
URL:
http://svn.gna.org/viewcvs/relax/1.3/generic_fns/structure/cones.py?rev=10990&r1=10989&r2=10990&view=diff
==============================================================================
--- 1.3/generic_fns/structure/cones.py (original)
+++ 1.3/generic_fns/structure/cones.py Sun Mar 14 12:13:15 2010
@@ -24,77 +24,11 @@
"""Module containing all the different cone type classes."""
# Python module imports.
-from math import acos, cos, pi, sqrt, sin
-
-
-class Iso_cone:
- """The class for the isotropic cone."""
-
- def __init__(self, angle):
- """Set up the cone object.
-
- @param angle: The cone angle.
- @type angle: float
- """
-
- # Store the cone angle.
- self._angle = angle
-
-
- def limit_check(self, phi, theta):
- """Determine if the point is within the cone.
-
- @param phi: The polar angle.
- @type phi: float
- @param theta: The azimuthal angle.
- @type phi: float
- @return: True if the point is within the cone, False
otherwise.
- @rtype: bool
- """
-
- # Outside.
- if phi > self._angle:
- return False
-
- # Else inside.
- return True
-
-
- def phi_max(self, theta):
- """Return the maximum polar angle phi for the given azimuthal angle
theta.
-
- @param theta: The azimuthal angle.
- @type theta: float
- @return: The maximum polar angle phi for the value of theta.
- @rtype: float
- """
-
- # The polar angle is fixed!
- return self._angle
-
-
- def theta_max(self, phi):
- """Return the maximum azimuthal angle theta for the given polar
angle phi.
-
- @param phi: The polar angle.
- @type phi: float
- @return: The maximum azimuthal angle theta for the value of
phi.
- @rtype: float
- """
-
- # The polar angle is fixed, so return zero.
- return 0.0
-
-
-class Pseudo_elliptic:
- """The class for the pseudo-elliptic cone.
-
- This is not an elliptic cone! The pseudo-ellipse is defined by::
-
- phi_max^2 = phi_x^2 * cos(theta)^2 + phi_y^2 * sin(theta)^2,
-
- where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis.
- """
+from math import acos, asin, cos, pi, sqrt, sin
+
+
+class Base:
+ """A base class for all the cone objects."""
def __init__(self, phi_x, phi_y):
"""Set up the cone object.
@@ -129,6 +63,37 @@
return True
+
+class Cosine(Base):
+ """The class for the cosine cone.
+
+ The ellipse is defined by::
+
+ phi_max = cos(theta) * phi_x + sin(theta) * phi_y,
+
+ where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis. The
maximum cone opening angle allowed is pi/2.
+ """
+
+ def __init__(self, phi_x, phi_y):
+ """Set up the cone object.
+
+ @param phi_x: The maximum cone angle along the x-eigenvector.
+ @type phi_x: float
+ @param phi_y: The maximum cone angle along the y-eigenvector.
+ @type phi_y: float
+ """
+
+ # Store the cone limits.
+ self._phi_x = phi_x
+ self._phi_y = phi_y
+
+ # The scaling factor.
+ self._scale = (phi_x - phi_y)/2
+
+ # The shift.
+ self._shift = (phi_x + phi_y)/2
+
+
def phi_max(self, theta):
"""Return the maximum polar angle phi for the given azimuthal angle
theta.
@@ -139,7 +104,7 @@
"""
# Determine phi_max.
- phi_max = sqrt((self._phi_x * cos(theta))**2 + (self._phi_y *
sin(theta))**2)
+ phi_max = self._scale * cos(theta*2) + self._shift
# Return the limit.
return phi_max
@@ -159,6 +124,161 @@
"""
# The factor.
+ b = (phi - self._shift)/self._scale
+
+ # The 4 quadrants.
+ if theta_max < pi/2:
+ theta = 0.5*acos(b)
+ elif theta_max < pi:
+ theta = 0.5*acos(-b) + pi/2
+ elif theta_max < 3*pi/2:
+ theta = 0.5*acos(b) + pi
+ elif theta_max < 2*pi:
+ theta = 0.5*acos(-b) + 3*pi/2
+
+ # Return the azimuthal angle.
+ return theta
+
+
+
+class Elliptic(Base):
+ """The class for the elliptic cone.
+
+ The ellipse is defined by::
+
+ 1 / sin(phi_max)^2 = cos(theta)^2 / sin(phi_x)^2 + sin(theta)^2 /
sin(phi_y)^2,
+
+ where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis. The
maximum cone opening angle allowed is pi/2.
+ """
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # Determine phi_max.
+ phi_max = asin(1.0/sqrt((cos(theta) / sin(self._phi_x))**2 +
(sin(theta) / sin(self._phi_y))**2))
+
+ # Return the limit.
+ return phi_max
+
+
+ def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @keyword theta_min: The lower limit of the azimuthal angle range for
complex distributions.
+ @type theta_min: float
+ @keyword theta_max: The upper limit of the azimuthal angle range for
complex distributions.
+ @type theta_max: float
+ @return: The maximum azimuthal angle theta for the value
of phi.
+ @rtype: float
+ """
+
+ # The factor.
+ b = sqrt((1.0/sin(phi)**2 -
1.0/sin(self._phi_y)**2)/(1.0/sin(self._phi_x)**2 - 1.0/sin(self._phi_y)**2))
+
+ # The 4 quadrants.
+ if theta_max < pi/2:
+ theta = acos(b)
+ elif theta_max < pi:
+ theta = acos(-b)
+ elif theta_max < 3*pi/2:
+ theta = -acos(-b)
+ elif theta_max < 2*pi:
+ theta = -acos(b)
+
+ # Return the azimuthal angle.
+ return theta
+
+
+
+class Iso_cone(Base):
+ """The class for the isotropic cone."""
+
+ def __init__(self, angle):
+ """Set up the cone object.
+
+ @param angle: The cone angle.
+ @type angle: float
+ """
+
+ # Store the cone angle.
+ self._angle = angle
+
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # The polar angle is fixed!
+ return self._angle
+
+
+ def theta_max(self, phi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @return: The maximum azimuthal angle theta for the value of
phi.
+ @rtype: float
+ """
+
+ # The polar angle is fixed, so return zero.
+ return 0.0
+
+
+
+class Pseudo_elliptic(Base):
+ """The class for the pseudo-elliptic cone.
+
+ This is not an elliptic cone! The pseudo-ellipse is defined by::
+
+ phi_max^2 = phi_x^2 * cos(theta)^2 + phi_y^2 * sin(theta)^2,
+
+ where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis.
+ """
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # Determine phi_max.
+ phi_max = sqrt((self._phi_x * cos(theta))**2 + (self._phi_y *
sin(theta))**2)
+
+ # Return the limit.
+ return phi_max
+
+
+ def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @keyword theta_min: The lower limit of the azimuthal angle range for
complex distributions.
+ @type theta_min: float
+ @keyword theta_max: The upper limit of the azimuthal angle range for
complex distributions.
+ @type theta_max: float
+ @return: The maximum azimuthal angle theta for the value
of phi.
+ @rtype: float
+ """
+
+ # The factor.
b = sqrt((phi**2 - self._phi_y**2)/(self._phi_x**2 - self._phi_y**2))
# The 4 quadrants.
@@ -173,3 +293,224 @@
# Return the polar angle.
return phi
+
+
+
+class Pseudo_elliptic2(Base):
+ """The class for another pseudo-elliptic cone.
+
+ The pseudo-ellipse is defined by::
+
+ 1/phi_max^2 = 1/phi_x^2 * cos(theta)^2 + 1/phi_y^2 * sin(theta)^2,
+
+ where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis.
+ """
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # Determine phi_max.
+ phi_max = 1.0/sqrt(((1.0/self._phi_x) * cos(theta))**2 +
((1.0/self._phi_y) * sin(theta))**2)
+
+ # Return the limit.
+ return phi_max
+
+
+ def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @keyword theta_min: The lower limit of the azimuthal angle range for
complex distributions.
+ @type theta_min: float
+ @keyword theta_max: The upper limit of the azimuthal angle range for
complex distributions.
+ @type theta_max: float
+ @return: The maximum azimuthal angle theta for the value
of phi.
+ @rtype: float
+ """
+
+ # The factor.
+ b = sqrt(((1.0/phi)**2 - (1.0/self._phi_y)**2) /
((1.0/self._phi_x)**2 - (1.0/self._phi_y)**2))
+
+ # The 4 quadrants.
+ if theta_max < pi/2:
+ phi = acos(b)
+ elif theta_max < pi:
+ phi = acos(-b)
+ elif theta_max < 3*pi/2:
+ phi = -acos(-b)
+ elif theta_max < 2*pi:
+ phi = -acos(b)
+
+ # Return the polar angle.
+ return phi
+
+
+
+class Square(Base):
+ """The class for the square cone.
+
+ The cone is defined by::
+
+ / phi_y, if 0 <= theta < pi/2,
+ |
+ phi_max = < phi_x, if pi/2 <= theta < 3*pi/3,
+ |
+ \ phi_y, if 3*pi/2 <= theta < 2*pi,
+
+ where phi_max is the maximum polar angle for the given azimuthal angle
theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is
that of the y-eigenvector. The cone axis is assumed to be the z-axis. The
maximum cone opening angle allowed is pi/2.
+ """
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # The 4 quadrants.
+ if theta < pi/2:
+ phi_max = self._phi_y
+ elif theta < 3*pi/2:
+ phi_max = self._phi_x
+ elif theta < 2*pi:
+ phi_max = self._phi_y
+
+ # Return the limit.
+ print phi_max
+ return phi_max
+
+
+ def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @keyword theta_min: The lower limit of the azimuthal angle range for
complex distributions.
+ @type theta_min: float
+ @keyword theta_max: The upper limit of the azimuthal angle range for
complex distributions.
+ @type theta_max: float
+ @return: The maximum azimuthal angle theta for the value
of phi.
+ @rtype: float
+ """
+
+ # The factor.
+ return 0
+ b = (phi - self._shift)/self._scale
+
+ # The 4 quadrants.
+ if theta_max < pi/2:
+ theta = pi/4 *(1 - b)
+ elif theta_max < pi:
+ theta = pi/4 *(3 + b)
+ elif theta_max < 3*pi/2:
+ theta = pi/4 *(5 - b)
+ elif theta_max < 2*pi:
+ theta = pi/4 *(7 + b)
+
+ # Return the azimuthal angle.
+ return theta
+
+
+
+class Zig_zag(Base):
+ """The class for the zig-zag cone.
+
+ The cone is defined by::
+
+ phi_max = c * asin(cos(theta*2)) + a,
+
+ where::
+
+ c = (phi_x - phi_y)/2,
+
+ a = (phi_x + phi_y)/2,
+
+ and where phi_max is the maximum polar angle for the given azimuthal
angle theta, phi_x is the maximum cone angle along the x-eigenvector, and
phi_y is that of the y-eigenvector. The cone axis is assumed to be the
z-axis. The maximum cone opening angle allowed is pi/2.
+ """
+
+ def __init__(self, phi_x, phi_y):
+ """Set up the cone object.
+
+ @param phi_x: The maximum cone angle along the x-eigenvector.
+ @type phi_x: float
+ @param phi_y: The maximum cone angle along the y-eigenvector.
+ @type phi_y: float
+ """
+
+ # Store the cone limits.
+ self._phi_x = phi_x
+ self._phi_y = phi_y
+
+ # The scaling factor.
+ self._scale = (phi_x - phi_y)/2
+
+ # The shift.
+ self._shift = (phi_x + phi_y)/2
+
+
+ def phi_max(self, theta):
+ """Return the maximum polar angle phi for the given azimuthal angle
theta.
+
+ @param theta: The azimuthal angle.
+ @type theta: float
+ @return: The maximum polar angle phi for the value of theta.
+ @rtype: float
+ """
+
+ # The factor.
+ b = 4.0 * theta / pi
+
+ # The 4 quadrants.
+ if theta < pi/2:
+ phi_max = 1 - b
+ elif theta < pi:
+ phi_max = b - 3
+ elif theta < 3*pi/2:
+ phi_max = 5 - b
+ elif theta < 2*pi:
+ phi_max = b - 7
+
+ # Determine phi_max.
+ phi_max = self._scale * phi_max + self._shift
+
+ # Return the limit.
+ return phi_max
+
+
+ def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):
+ """Return the maximum azimuthal angle theta for the given polar
angle phi.
+
+ @param phi: The polar angle.
+ @type phi: float
+ @keyword theta_min: The lower limit of the azimuthal angle range for
complex distributions.
+ @type theta_min: float
+ @keyword theta_max: The upper limit of the azimuthal angle range for
complex distributions.
+ @type theta_max: float
+ @return: The maximum azimuthal angle theta for the value
of phi.
+ @rtype: float
+ """
+
+ # The factor.
+ b = (phi - self._shift)/self._scale
+
+ # The 4 quadrants.
+ if theta_max < pi/2:
+ theta = pi/4 *(1 - b)
+ elif theta_max < pi:
+ theta = pi/4 *(3 + b)
+ elif theta_max < 3*pi/2:
+ theta = pi/4 *(5 - b)
+ elif theta_max < 2*pi:
+ theta = pi/4 *(7 + b)
+
+ # Return the azimuthal angle.
+ return theta
r10990 - /1.3/generic_fns/structure/cones.py