/usr/lib/python2.7/dist-packages/PySPH-1.0a4.dev0-py2.7-linux-x86_64.egg/pysph/base/c_kernels.pyx is in python-pysph 0~20160514.git91867dc-4build1.
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from libc.math cimport *
import numpy as np
cdef class CubicSpline:
cdef public long dim
cdef public double radius_scale
cdef public double fac
def __init__(self, **kwargs):
for key, value in kwargs.iteritems():
setattr(self, key, value)
cdef inline double get_deltap(self):
return 2./3
cpdef double py_get_deltap(self):
return self.get_deltap()
cdef inline void gradient(self, double* xij, double rij, double h, double* grad):
cdef double tmp
cdef double val
cdef double h1
cdef double q
cdef double fac
cdef double tmp2
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# compute the gradient.
tmp2 = 2. - q
if (rij > 1e-12):
if (q > 2.0):
val = 0.0
elif ( q > 1.0 ):
val = -0.75 * tmp2*tmp2 * h1/rij
else:
val = -3.0*q * (1 - 0.75*q) * h1/rij
else:
val = 0.0
tmp = val * fac
grad[0] = tmp * xij[0]
grad[1] = tmp * xij[1]
grad[2] = tmp * xij[2]
cpdef py_gradient(self, double[:] xij, double rij, double h, double[:] grad):
self.gradient(&xij[0], rij, h, &grad[0])
cdef inline double gradient_h(self, double* xij, double rij, double h):
cdef double h1
cdef double q
cdef double w
cdef double fac
cdef double dw
cdef double tmp2
h1 = 1./h; q = rij * h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# kernel and gradient evaluated at q
tmp2 = 2. - q
if ( q > 2.0 ):
w = 0.0
dw = 0.0
elif ( q > 1.0 ):
w = 0.25 * tmp2 * tmp2 * tmp2
dw = -0.75 * tmp2 * tmp2
else:
w = 1 - 1.5 * q * q * (1 - 0.5 * q)
dw = -3.0*q * (1 - 0.75*q)
return -fac * h1 * ( dw*q + w*self.dim )
cpdef double py_gradient_h(self, double[:] xij, double rij, double h):
return self.gradient_h(&xij[0], rij, h)
cdef inline double kernel(self, double* xij, double rij, double h):
cdef double q
cdef double fac
cdef double h1
cdef double val
cdef double tmp2
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
tmp2 = 2. - q
if ( q > 2.0 ):
val = 0.0
elif ( q > 1.0 ):
val = 0.25 * tmp2 * tmp2 * tmp2
else:
val = 1 - 1.5 * q * q * (1 - 0.5 * q)
return val * fac
cpdef double py_kernel(self, double[:] xij, double rij, double h):
return self.kernel(&xij[0], rij, h)
cdef class CubicSplineWrapper:
"""Reasonably high-performance convenience wrapper for Kernels.
"""
cdef public CubicSpline kern
cdef double[3] xij, grad
cdef public double radius_scale
cdef public double fac
def __init__(self, kern):
self.kern = kern
self.radius_scale = kern.radius_scale
self.fac = kern.fac
cpdef double kernel(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
return self.kern.kernel(xij, rij, h)
cpdef gradient(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
cdef double* grad = self.grad
self.kern.gradient(xij, rij, h, grad)
return grad[0], grad[1], grad[2]
cdef class WendlandQuintic:
cdef public long dim
cdef public double radius_scale
cdef public double fac
def __init__(self, **kwargs):
for key, value in kwargs.iteritems():
setattr(self, key, value)
cdef inline double get_deltap(self):
return 0.5
cpdef double py_get_deltap(self):
return self.get_deltap()
cdef inline void gradient(self, double* xij, double rij, double h, double* grad):
cdef double tmp
cdef double q
cdef double h1
cdef double val
cdef double fac
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# compute the gradient
val = 0.0
tmp = 1.0 - 0.5*q
if ( q < 2.0 ):
if (rij > 1e-12):
val = -5.0 * q * tmp * tmp * tmp * h1/rij
tmp = val * fac
grad[0] = tmp * xij[0]
grad[1] = tmp * xij[1]
grad[2] = tmp * xij[2]
cpdef py_gradient(self, double[:] xij, double rij, double h, double[:] grad):
self.gradient(&xij[0], rij, h, &grad[0])
cdef inline double gradient_h(self, double* xij, double rij, double h):
cdef double tmp
cdef double h1
cdef double q
cdef double w
cdef double fac
cdef double dw
h1 = 1./h; q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# compute the kernel and gradient at q
w = 0.0; dw = 0.0
tmp = 1.0 - 0.5*q
if ( q < 2.0 ):
w = tmp * tmp * tmp * tmp * (2.0*q + 1.0)
dw = -5.0 * q * tmp * tmp * tmp
return -fac * h1 * ( dw*q + w*self.dim )
cpdef double py_gradient_h(self, double[:] xij, double rij, double h):
return self.gradient_h(&xij[0], rij, h)
cdef inline double kernel(self, double* xij, double rij, double h):
cdef double q
cdef double fac
cdef double h1
cdef double val
cdef double tmp
h1 = 1.0/h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
val = 0.0
tmp = 1. - 0.5 * q
if ( q < 2.0 ):
val = tmp * tmp * tmp * tmp * (2.0*q + 1.0)
return val * fac
cpdef double py_kernel(self, double[:] xij, double rij, double h):
return self.kernel(&xij[0], rij, h)
cdef class WendlandQuinticWrapper:
"""Reasonably high-performance convenience wrapper for Kernels.
"""
cdef public WendlandQuintic kern
cdef double[3] xij, grad
cdef public double radius_scale
cdef public double fac
def __init__(self, kern):
self.kern = kern
self.radius_scale = kern.radius_scale
self.fac = kern.fac
cpdef double kernel(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
return self.kern.kernel(xij, rij, h)
cpdef gradient(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
cdef double* grad = self.grad
self.kern.gradient(xij, rij, h, grad)
return grad[0], grad[1], grad[2]
cdef class Gaussian:
cdef public long dim
cdef public double radius_scale
cdef public double fac
def __init__(self, **kwargs):
for key, value in kwargs.iteritems():
setattr(self, key, value)
cdef inline double get_deltap(self):
# The inflection point is at q=1/sqrt(2)
# the deltap values for some standard kernels
# have been tabulated in sec 3.2 of
# http://cfd.mace.manchester.ac.uk/sph/SPH_PhDs/2008/crespo_thesis.pdf
return 0.70710678118654746
cpdef double py_get_deltap(self):
return self.get_deltap()
cdef inline void gradient(self, double* xij, double rij, double h, double* grad):
cdef double tmp
cdef double q
cdef double h1
cdef double val
cdef double fac
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# compute the gradient
val = 0.0
if (q < 3.0):
if (rij > 1e-12):
val = -2.0* q * exp(-q*q) * h1/rij
tmp = val * fac
grad[0] = tmp * xij[0]
grad[1] = tmp * xij[1]
grad[2] = tmp * xij[2]
cpdef py_gradient(self, double[:] xij, double rij, double h, double[:] grad):
self.gradient(&xij[0], rij, h, &grad[0])
cdef inline double gradient_h(self, double* xij, double rij, double h):
cdef double q
cdef double fac
cdef double h1
cdef double w
cdef double dw
h1 = 1./h; q= rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
# kernel and gradient evaluated at q
w = 0.0; dw = 0.0
if ( q < 3.0 ):
w = exp(-q*q)
dw = -2.0 * q * w
return -fac * h1 * ( dw*q + w*self.dim )
cpdef double py_gradient_h(self, double[:] xij, double rij, double h):
return self.gradient_h(&xij[0], rij, h)
cdef inline double kernel(self, double* xij, double rij, double h):
cdef double q
cdef double fac
cdef double h1
cdef double val
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
val = 0.0
if ( q < 3.0 ):
val = exp(-q*q) * fac
return val
cpdef double py_kernel(self, double[:] xij, double rij, double h):
return self.kernel(&xij[0], rij, h)
cdef class GaussianWrapper:
"""Reasonably high-performance convenience wrapper for Kernels.
"""
cdef public Gaussian kern
cdef double[3] xij, grad
cdef public double radius_scale
cdef public double fac
def __init__(self, kern):
self.kern = kern
self.radius_scale = kern.radius_scale
self.fac = kern.fac
cpdef double kernel(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
return self.kern.kernel(xij, rij, h)
cpdef gradient(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
cdef double* grad = self.grad
self.kern.gradient(xij, rij, h, grad)
return grad[0], grad[1], grad[2]
cdef class QuinticSpline:
cdef public long dim
cdef public double radius_scale
cdef public double fac
def __init__(self, **kwargs):
for key, value in kwargs.iteritems():
setattr(self, key, value)
cdef inline double get_deltap(self):
# The inflection points for the polynomial are obtained as
# http://www.wolframalpha.com/input/?i=%28%283-x%29%5E5+-+6*%282-x%29%5E5+%2B+15*%281-x%29%5E5%29%27%27
# the only permissible value is taken
return 0.759298480738450
cpdef double py_get_deltap(self):
return self.get_deltap()
cdef inline void gradient(self, double* xij, double rij, double h, double* grad):
cdef double tmp
cdef double val
cdef double h1
cdef double q
cdef double fac
cdef double tmp1
cdef double tmp3
cdef double tmp2
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
tmp3 = 3. - q
tmp2 = 2. - q
tmp1 = 1. - q
# compute the gradient
if (rij > 1e-12):
if ( q > 3.0 ):
val = 0.0
elif ( q > 2.0 ):
val = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
val *= h1/rij
elif ( q > 1.0 ):
val = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
val += 30.0 * tmp2 * tmp2 * tmp2 * tmp2
val *= h1/rij
else:
val = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
val += 30.0 * tmp2 * tmp2 * tmp2 * tmp2
val -= 75.0 * tmp1 * tmp1 * tmp1 * tmp1
val *= h1/rij
else:
val = 0.0
tmp = val * fac
grad[0] = tmp * xij[0]
grad[1] = tmp * xij[1]
grad[2] = tmp * xij[2]
cpdef py_gradient(self, double[:] xij, double rij, double h, double[:] grad):
self.gradient(&xij[0], rij, h, &grad[0])
cdef inline double gradient_h(self, double* xij, double rij, double h):
cdef double h1
cdef double q
cdef double w
cdef double fac
cdef double dw
cdef double tmp1
cdef double tmp3
cdef double tmp2
h1 = 1./h; q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
tmp3 = 3. - q
tmp2 = 2. - q
tmp1 = 1. - q
# compute the kernel & gradient at q
if ( q > 3.0 ):
w = 0.0
dw = 0.0
elif ( q > 2.0 ):
w = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
dw = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
elif ( q > 1.0 ):
w = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
w -= 6.0 * tmp2 * tmp2 * tmp2 * tmp2 * tmp2
dw = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
dw += 30.0 * tmp2 * tmp2 * tmp2 * tmp2
else:
w = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
w -= 6.0 * tmp2 * tmp2 * tmp2 * tmp2 * tmp2
w += 15. * tmp1 * tmp1 * tmp1 * tmp1 * tmp1
dw = -5.0 * tmp3 * tmp3 * tmp3 * tmp3
dw += 30.0 * tmp2 * tmp2 * tmp2 * tmp2
dw -= 75.0 * tmp1 * tmp1 * tmp1 * tmp1
return -fac * h1 * ( dw*q + w*self.dim )
cpdef double py_gradient_h(self, double[:] xij, double rij, double h):
return self.gradient_h(&xij[0], rij, h)
cdef inline double kernel(self, double* xij, double rij, double h):
cdef double val
cdef double h1
cdef double q
cdef double fac
cdef double tmp1
cdef double tmp3
cdef double tmp2
h1 = 1./h
q = rij*h1
# get the kernel normalizing factor
if self.dim == 1:
fac = self.fac * h1
elif self.dim == 2:
fac = self.fac * h1 * h1
elif self.dim == 3:
fac = self.fac * h1 * h1 * h1
tmp3 = 3. - q
tmp2 = 2. - q
tmp1 = 1. - q
if ( q > 3.0 ):
val = 0.0
elif ( q > 2.0 ):
val = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
elif ( q > 1.0 ):
val = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
val -= 6.0 * tmp2 * tmp2 * tmp2 * tmp2 * tmp2
else:
val = tmp3 * tmp3 * tmp3 * tmp3 * tmp3
val -= 6.0 * tmp2 * tmp2 * tmp2 * tmp2 * tmp2
val += 15. * tmp1 * tmp1 * tmp1 * tmp1 * tmp1
return val * fac
cpdef double py_kernel(self, double[:] xij, double rij, double h):
return self.kernel(&xij[0], rij, h)
cdef class QuinticSplineWrapper:
"""Reasonably high-performance convenience wrapper for Kernels.
"""
cdef public QuinticSpline kern
cdef double[3] xij, grad
cdef public double radius_scale
cdef public double fac
def __init__(self, kern):
self.kern = kern
self.radius_scale = kern.radius_scale
self.fac = kern.fac
cpdef double kernel(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
return self.kern.kernel(xij, rij, h)
cpdef gradient(self, double xi, double yi, double zi, double xj, double yj, double zj, double h):
cdef double* xij = self.xij
xij[0] = xi-xj
xij[1] = yi-yj
xij[2] = zi-zj
cdef double rij = sqrt(xij[0]*xij[0] + xij[1]*xij[1] +xij[2]*xij[2])
cdef double* grad = self.grad
self.kern.gradient(xij, rij, h, grad)
return grad[0], grad[1], grad[2]
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