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eosinterx.pyx
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eosinterx.pyx
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# -*- coding: utf-8 -*-
"""
Created on Wed Nov 30 14:21:59 2016
@author: René Georg Salhab
"""
from __future__ import division, print_function
import numpy as np
from cython.parallel import prange
cimport cython
cimport numpy as np
from libc.math cimport exp, log10, log
DTYPE = np.int32
DTYPEf = np.float32
DTYPEf64 = np.float64
ctypedef np.int32_t DTYPE_t
ctypedef np.float32_t DTYPEf_t
ctypedef np.float64_t DTYPEf64_t
cdef inline DTYPE_t int_max(DTYPE_t a, DTYPE_t b): return a if a >= b else b
cdef inline DTYPE_t int_min(DTYPE_t a, DTYPE_t b): return a if a <= b else b
cdef inline DTYPEf_t float_max(DTYPEf_t a, DTYPEf_t b): return a if a >= b else b
cdef inline DTYPEf_t float_min(DTYPEf_t a, DTYPEf_t b): return a if a <= b else b
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef STP3D(np.ndarray[DTYPEf_t, ndim=3] C, np.ndarray[DTYPE_t, ndim=3] i1, np.ndarray[DTYPE_t, ndim=3] i2,
np.ndarray[DTYPEf_t, ndim=3] x1ta, np.ndarray[DTYPEf_t, ndim=3] x2ta):
"""
Description:
Computes the entropy, pressure, or temperature with the help of the eos-file.
inputs:
:param rho: numpy-ndarray, 3D, shape of simulation box, density-field
:param ei: numpy-ndarray, 3D, shape of simulation box, internal energy-field
:param C: ndarray, interpolation coefficients of eos-file
:param i1: numpy-ndarray, 3D, indices for pressure-dimension of C
:param i2: numpy-ndarray, 3D, indices for temperature-dimension of C
:param x1ta: numpy-ndarray, 3D, interpolation-factors along pressure-dimension
:param x2ta: numpy-ndarray, 3D, interpolation-factors along temperature-dimension
output:
:return: ndarray, shape of simulation box, values of :param quantity:. The function returns entropy, or
log(P), or log(T)
"""
cdef DTYPE_t i, j, k, ti1, ti2
cdef DTYPE_t nx = i1.shape[0]
cdef DTYPE_t ny = i1.shape[1]
cdef DTYPE_t nz = i1.shape[2]
cdef np.ndarray[DTYPEf_t, ndim=3] out = np.empty((nx, ny, nz), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(nz):
ti1 = i1[i, j, k]
ti2 = i2[i, j, k]
out[i,j,k] = C[0,ti1,ti2] + x1ta[i,j,k] * (C[1,ti1,ti2] + x1ta[i,j,k] * (C[2,ti1,ti2] + x1ta[i,j,k] *
C[3,ti1,ti2])) + x2ta[i,j,k] * (C[4,ti1,ti2] + x1ta[i,j,k] * (C[5,ti1, ti2] + x1ta[i,j,k] *
(C[6,ti1,ti2] + x1ta[i,j,k] * C[7,ti1,ti2])) + x2ta[i,j,k] * (C[8,ti1,ti2] + x1ta[i,j,k] *
(C[9,ti1, ti2] + x1ta[i,j,k] * (C[10,ti1,ti2] + x1ta[i,j,k] * C[11,ti1, ti2])) + x2ta[i,j,k] *
(C[12,ti1,ti2] + x1ta[i,j,k] * (C[13,ti1,ti2] + x1ta[i,j,k] * (C[14,ti1, ti2] + x1ta[i,j,k] *
C[15,ti1,ti2])))))
return out
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef STP4D(np.ndarray[DTYPEf_t, ndim=3] C, np.ndarray[DTYPE_t, ndim=4] i1, np.ndarray[DTYPE_t, ndim=4] i2,
np.ndarray[DTYPEf_t, ndim=4] x1ta, np.ndarray[DTYPEf_t, ndim=4] x2ta):
"""
Description:
Computes the entropy, pressure, or temperature with the hekp of the eos-file.
inputs:
:param rho: ndarray, shape of simulation box, density-field
:param ei: ndarray, shape of simulation box, internal energy-field
:param quantity: string, the demanded quantity
output:
:return: ndarray, shape of simulation box, values of :param quantity:. The function returns entropy, or
log(P), or log(T)
"""
cdef DTYPE_t i, j, k, l, ti1, ti2
cdef DTYPE_t nt = i1.shape[0]
cdef DTYPE_t nx = i1.shape[1]
cdef DTYPE_t ny = i1.shape[2]
cdef DTYPE_t nz = i1.shape[3]
cdef np.ndarray[DTYPEf_t, ndim = 4] out = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(nz):
ti1 = i1[i, j, k, l]
ti2 = i2[i, j, k, l]
out[i,j,k,l] = C[0,ti1,ti2] + x1ta[i, j, k, l] * (C[1, ti1, ti2] + x1ta[i, j, k, l] *
(C[2, ti1, ti2] + x1ta[i, j, k, l] * C[3, ti1, ti2])) + x2ta[i, j, k, l] * (C[4, ti1, ti2] +
x1ta[i, j, k, l] * (C[5, ti1, ti2] + x1ta[i, j, k, l] * (C[6, ti1, ti2] + x1ta[i, j, k, l] *
C[7, ti1, i2[i, j, k ,l]])) + x2ta[i, j, k, l] * (C[8, ti1, ti2] + x1ta[i, j, k, l] *
(C[9, ti1, ti2] + x1ta[i, j, k, l] * (C[10, ti1, ti2] + x1ta[i, j, k, l] * C[11, ti1, ti2])) +
x2ta[i, j, k ,l] * (C[12, ti1, ti2] + x1ta[i, j, k, l] * (C[13, ti1, ti2] + x1ta[i, j, k, l] *
(C[14, ti1, ti2] + x1ta[i, j, k, l] * C[15, ti1, ti2])))))
return out
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef PandT3D(np.ndarray[DTYPEf_t, ndim=3] CP, np.ndarray[DTYPEf_t, ndim=3] CT, np.ndarray[DTYPE_t, ndim=3] i1,
np.ndarray[DTYPE_t, ndim=3] i2, np.ndarray[DTYPEf_t, ndim=3] x1ta, np.ndarray[DTYPEf_t, ndim=3] x2ta):
cdef DTYPE_t i, j, k, ti1, ti2
cdef DTYPE_t nx = i1.shape[0]
cdef DTYPE_t ny = i1.shape[1]
cdef DTYPE_t nz = i1.shape[2]
cdef np.ndarray[DTYPEf_t, ndim = 3] P = np.empty((nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 3] T = np.empty((nx, ny, nz), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(nz):
ti1 = i1[i, j, k]
ti2 = i2[i, j, k]
P[i, j, k] = CP[0, ti1, ti2] + x1ta[i, j, k] * (CP[1, ti1, ti2] + x1ta[i, j, k] * (CP[2, ti1, ti2] +
x1ta[i, j, k] * CP[3, ti1, ti2])) + x2ta[i, j, k] * (CP[4, ti1, ti2] + x1ta[i, j, k] *
(CP[5, ti1, ti2] + x1ta[i, j, k] * (CP[6, ti1, ti2] + x1ta[i, j, k] * CP[7, ti1, ti2])) +
x2ta[i, j, k] * (CP[8, ti1, ti2] + x1ta[i, j, k] * (CP[9, ti1, ti2] + x1ta[i, j, k] *
(CP[10, ti1, ti2] + x1ta[i, j, k] * CP[11, ti1, ti2])) + x2ta[i, j, k] * (CP[12, ti1, ti2] +
x1ta[i, j, k] * (CP[13, ti1, ti2] + x1ta[i, j, k] * (CP[14, ti1, ti2] + x1ta[i, j, k] *
CP[15, ti1, ti2])))))
T[i, j, k] = CT[0, ti1, ti2] + x1ta[i, j, k] * (CT[1, ti1, ti2] + x1ta[i, j, k] * (CT[2, ti1, ti2] +
x1ta[i, j, k] * CT[3, ti1, ti2])) + x2ta[i, j, k] * (CT[4, ti1, ti2] + x1ta[i, j, k] *
(CT[5, ti1, ti2] + x1ta[i, j, k] * (CT[6, ti1, ti2] + x1ta[i, j, k] * CT[7, ti1, ti2])) +
x2ta[i, j, k] * (CT[8, ti1, ti2] + x1ta[i, j, k] * (CT[9, ti1, ti2] + x1ta[i, j, k] *
(CT[10, ti1, ti2] + x1ta[i, j, k] * CT[11, ti1, ti2])) + x2ta[i, j, k] * (CT[12, ti1, ti2] +
x1ta[i, j, k] * (CT[13, ti1, ti2] + x1ta[i, j, k] * (CT[14, ti1, ti2] + x1ta[i, j, k] *
CT[15, ti1, ti2])))))
return P, T
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef PandT4D(np.ndarray[DTYPEf_t, ndim=3] CP, np.ndarray[DTYPEf_t, ndim=3] CT, np.ndarray[DTYPE_t, ndim=4] i1,
np.ndarray[DTYPE_t, ndim=4] i2, np.ndarray[DTYPEf_t, ndim=4] x1ta, np.ndarray[DTYPEf_t, ndim=4] x2ta):
cdef DTYPE_t i, j, k, l, ti1, ti2
cdef DTYPE_t nt = i1.shape[0]
cdef DTYPE_t nx = i1.shape[1]
cdef DTYPE_t ny = i1.shape[2]
cdef DTYPE_t nz = i1.shape[3]
cdef np.ndarray[DTYPEf_t, ndim = 4] P = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 4] T = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(nz):
ti1 = i1[i, j, k, l]
ti2 = i2[i, j, k, l]
P[i, j, k, l] = CP[0, ti1, ti2] + x1ta[i, j, k, l] * (CP[1, ti1, ti2] + x1ta[i, j, k, l] *
(CP[2, ti1, ti2] + x1ta[i, j, k, l] * CP[3, ti1, ti2])) + x2ta[i, j, k, l] * (CP[4, ti1, ti2] +
x1ta[i, j, k, l] * (CP[5, ti1, ti2] + x1ta[i, j, k, l] * (CP[6, ti1, ti2] + x1ta[i, j, k, l] *
CP[7, ti1, i2[i, j, k ,l]])) + x2ta[i, j, k, l] * (CP[8, ti1, ti2] + x1ta[i, j, k, l] *
(CP[9, ti1, ti2] + x1ta[i, j, k, l] * (CP[10, ti1, ti2] + x1ta[i, j, k, l] * CP[11, ti1, ti2])) +
x2ta[i, j, k ,l] * (CP[12, ti1, ti2] + x1ta[i, j, k, l] * (CP[13, ti1, ti2] + x1ta[i, j, k, l] *
(CP[14, ti1, ti2] + x1ta[i, j, k, l] * CP[15, ti1, ti2])))))
T[i, j, k, l] = CT[0, ti1, ti2] + x1ta[i, j, k, l] * (CT[1, ti1, ti2] + x1ta[i, j, k, l] *
(CT[2, ti1, ti2] + x1ta[i, j, k, l] * CT[3, ti1, ti2])) + x2ta[i, j, k, l] * (CT[4, ti1, ti2] +
x1ta[i, j, k, l] * (CT[5, ti1, ti2] + x1ta[i, j, k, l] * (CT[6, ti1, ti2] + x1ta[i, j, k, l] *
CT[7, ti1, i2[i, j, k ,l]])) + x2ta[i, j, k, l] * (CT[8, ti1, ti2] + x1ta[i, j, k, l] *
(CT[9, ti1, ti2] + x1ta[i, j, k, l] * (CT[10, ti1, ti2] + x1ta[i, j, k, l] * CT[11, ti1, ti2])) +
x2ta[i, j, k ,l] * (CT[12, ti1, ti2] + x1ta[i, j, k, l] * (CT[13, ti1, ti2] + x1ta[i, j, k, l] *
(CT[14, ti1, ti2] + x1ta[i, j, k, l] * CT[15, ti1, ti2])))))
return P, T
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef Pall3D(np.ndarray[DTYPEf_t, ndim=3] rho, np.ndarray[DTYPEf_t, ndim=3] ei, np.ndarray[DTYPEf_t, ndim=3] C,
np.ndarray[DTYPE_t, ndim=3] i1, np.ndarray[DTYPE_t, ndim=3] i2, np.ndarray[DTYPEf_t, ndim=3] x1ta,
np.ndarray[DTYPEf_t, ndim=3] x2ta, DTYPEf_t x2shift):
cdef DTYPE_t i, j, k, ti1, ti2
cdef DTYPE_t nx = rho.shape[0]
cdef DTYPE_t ny = rho.shape[1]
cdef DTYPE_t nz = rho.shape[2]
cdef np.ndarray[DTYPEf_t, ndim = 3] P = np.empty((nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 3] dPdrho = np.empty((nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 3] dPde = np.empty((nx, ny, nz), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(nz):
ti1 = i1[i, j, k]
ti2 = i2[i, j, k]
P[i, j, k] = exp(C[0, ti1, ti2] + x1ta[i, j, k] * (C[1, ti1, ti2] + x1ta[i, j, k] * (C[2, ti1, ti2] +
x1ta[i, j, k] * C[3, ti1, ti2])) + x2ta[i, j, k] * (C[4, ti1, ti2] + x1ta[i, j, k] * (C[5, ti1, ti2] +
x1ta[i, j, k] * (C[6, ti1, ti2] + x1ta[i, j, k] * C[7, ti1, ti2])) + x2ta[i, j, k] * (C[8, ti1, ti2] +
x1ta[i, j, k] * (C[9, ti1, ti2] + x1ta[i, j, k] * (C[10, ti1, ti2] + x1ta[i, j, k] * C[11, ti1, ti2])) +
x2ta[i, j, k] * (C[12, ti1, ti2] + x1ta[i, j, k] * (C[13, ti1, ti2] + x1ta[i, j, k] * (C[14, ti1, ti2] +
x1ta[i, j, k] * C[15, ti1, ti2]))))))
dPdrho[i,j,k] = P[i,j,k] / rho[i,j,k] * (C[1,ti1,ti2] + x1ta[i,j,k] * (2 * C[2,ti1,ti2] + x1ta[i,j,k] *
3 * C[3,ti1,ti2]) + x2ta[i,j,k]*(C[5,ti1,ti2] + x1ta[i,j,k] * (2 * C[6,ti1,ti2] + x1ta[i,j,k] * 3 *
C[7,ti1,ti2]) + x2ta[i,j,k] * (C[9,ti1,ti2] + x1ta[i,j,k] * (2 * C[10,ti1,ti2] + x1ta[i,j,k] * 3 *
C[11,ti1,ti2]) + x2ta[i,j,k] * (C[13,ti1,ti2] + x1ta[i,j,k] * (2 * C[14,ti1,ti2] + x1ta[i,j,k] * 3 *
C[15,ti1,ti2])))))
dPde[i,j,k] = P[i,j,k] / (ei[i,j,k] + x2shift) * (C[4,ti1,ti2] + x1ta[i,j,k] * (C[5,ti1,ti2] + x1ta[i,j,k] *
(C[6,ti1,ti2] + x1ta[i,j,k] * C[7,ti1,ti2])) + 2 * x2ta[i,j,k] * (C[8,ti1,ti2] + x1ta[i,j,k] *
(C[9,ti1,ti2] + x1ta[i,j,k] * (C[10,ti1,ti2] + x1ta[i,j,k] * C[11,ti1,ti2])) + 1.5 * x2ta[i,j,k] *
(C[12,ti1,ti2] + x1ta[i,j,k] * (C[13,ti1,ti2] + x1ta[i,j,k] * (C[14,ti1,ti2] + x1ta[i,j,k] *
C[15,ti1,ti2])))))
return P, dPdrho, dPde
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef Pall4D(np.ndarray[DTYPEf_t, ndim=4] rho, np.ndarray[DTYPEf_t, ndim=4] ei, np.ndarray[DTYPEf_t, ndim=3] C,
np.ndarray[DTYPE_t, ndim=4] i1, np.ndarray[DTYPE_t, ndim=4] i2, np.ndarray[DTYPEf_t, ndim=4] x1ta,
np.ndarray[DTYPEf_t, ndim=4] x2ta, DTYPEf_t x2shift):
cdef DTYPE_t i, j, k, l, ti1, ti2
cdef DTYPE_t nt = rho.shape[0]
cdef DTYPE_t nx = rho.shape[1]
cdef DTYPE_t ny = rho.shape[2]
cdef DTYPE_t nz = rho.shape[3]
cdef np.ndarray[DTYPEf_t, ndim = 4] P = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 4] dPdrho = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim = 4] dPde = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(nz):
ti1 = i1[i,j,k,l]
ti2 = i2[i,j,k,l]
P[i,j,k,l] = exp(C[0,ti1, ti2] + x1ta[i,j,k,l] * (C[1,ti1,ti2] + x1ta[i,j,k,l] * (C[2,ti1,ti2] +
x1ta[i,j,k,l] * C[3,ti1,ti2])) + x2ta[i,j,k,l] * (C[4,ti1,ti2] + x1ta[i,j,k,l] * (C[5,ti1,ti2] +
x1ta[i,j,k,l] * (C[6,ti1,ti2] + x1ta[i,j,k,l] * C[7,ti1,ti2])) + x2ta[i,j,k,l] * (C[8,ti1,ti2] +
x1ta[i,j,k,l] * (C[9,ti1,ti2] + x1ta[i,j,k,l] * (C[10,ti1,ti2] + x1ta[i,j,k,l] * C[11,ti1, ti2])) +
x2ta[i,j,k,l] * (C[12, ti1, ti2] + x1ta[i,j,k,l] * (C[13, ti1, ti2] + x1ta[i,j,k,l] * (C[14, ti1, ti2] +
x1ta[i,j,k,l] * C[15, ti1, ti2]))))))
dPdrho[i,j,k,l] = P[i,j,k,l] / rho[i,j,k,l] * (C[1,ti1,ti2] + x1ta[i,j,k,l] * (2 * C[2,ti1,ti2] +
x1ta[i,j,k,l] * 3 * C[3,ti1,ti2]) + x2ta[i,j,k,l]*(C[5,ti1,ti2] + x1ta[i,j,k,l] *
(2 * C[6,ti1,ti2]+ x1ta[i,j,k,l] * 3 * C[7,ti1,ti2]) + x2ta[i,j,k,l] * (C[9,ti1,ti2] +
x1ta[i,j,k,l] * (2 * C[10,ti1,ti2] + x1ta[i,j,k,l] * 3 * C[11,ti1,ti2]) + x2ta[i,j,k,l] *
(C[13,ti1,ti2] + x1ta[i,j,k,l] * (2 * C[14,ti1,ti2] + x1ta[i,j,k,l] * 3 * C[15,ti1,ti2])))))
dPde[i,j,k,l] = P[i,j,k,l] / (ei[i,j,k,l] + x2shift) * (C[4,ti1,ti2] + x1ta[i,j,k,l] * (C[5,ti1,ti2] +
x1ta[i,j,k,l] * (C[6,ti1,ti2] + x1ta[i,j,k,l] * C[7,ti1,ti2])) + 2 * x2ta[i,j,k,l] * (C[8,ti1,ti2] +
x1ta[i,j,k,l] * (C[9,ti1,ti2] + x1ta[i,j,k,l] * (C[10,ti1,ti2] + x1ta[i,j,k,l] * C[11,ti1,ti2])) +
1.5 * x2ta[i,j,k,l] * (C[12,ti1,ti2] + x1ta[i,j,k,l] * (C[13,ti1,ti2] + x1ta[i,j,k,l] *
(C[14,ti1,ti2] + x1ta[i,j,k,l] * C[15,ti1,ti2])))))
return P, dPdrho, dPde
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef Tall3D(np.ndarray[DTYPEf_t, ndim=3] ei, np.ndarray[DTYPEf_t, ndim=3] C, np.ndarray[DTYPE_t, ndim=3] i1,
np.ndarray[DTYPE_t, ndim=3] i2, np.ndarray[DTYPEf_t, ndim=3] x1ta, np.ndarray[DTYPEf_t, ndim=3] x2ta,
DTYPEf_t x2shift):
cdef DTYPE_t i, j, k, ti1, ti2
cdef DTYPE_t nx = ei.shape[0]
cdef DTYPE_t ny = ei.shape[1]
cdef DTYPE_t nz = ei.shape[2]
cdef np.ndarray[DTYPEf_t, ndim=3] T = np.empty((nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=3] dTde = np.empty((nx, ny, nz), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(nz):
ti1 = i1[i, j, k]
ti2 = i2[i, j, k]
T[i, j, k] = exp(C[0, ti1, ti2] + x1ta[i, j, k] * (C[1, ti1, ti2] + x1ta[i, j, k] * (C[2, ti1, ti2] +
x1ta[i, j, k] * C[3, ti1, ti2])) + x2ta[i, j, k] * (C[4, ti1, ti2] + x1ta[i, j, k] * (C[5, ti1, ti2] +
x1ta[i, j, k] * (C[6, ti1, ti2] + x1ta[i, j, k] * C[7, ti1, ti2])) + x2ta[i, j, k] * (C[8, ti1, ti2] +
x1ta[i, j, k] * (C[9, ti1, ti2] + x1ta[i, j, k] * (C[10, ti1, ti2] + x1ta[i, j, k] * C[11, ti1, ti2])) +
x2ta[i, j, k] * (C[12, ti1, ti2] + x1ta[i, j, k] * (C[13, ti1, ti2] + x1ta[i, j, k] * (C[14, ti1, ti2] +
x1ta[i, j, k] * C[15, ti1, ti2]))))))
dTde[i,j,k] = T[i,j,k] / (ei[i,j,k] + x2shift) * (C[4,ti1,ti2] + x1ta[i,j,k] * (C[5,ti1,ti2] + x1ta[i,j,k] *
(C[6,ti1,ti2] + x1ta[i,j,k] * C[7,ti1,ti2])) + 2 * x2ta[i,j,k] * (C[8,ti1,ti2] + x1ta[i,j,k] *
(C[9,ti1,ti2] + x1ta[i,j,k] * (C[10,ti1,ti2] + x1ta[i,j,k] * C[11,ti1,ti2])) + 1.5 * x2ta[i,j,k] *
(C[12,ti1,ti2] + x1ta[i,j,k] * (C[13,ti1,ti2] + x1ta[i,j,k] * (C[14,ti1,ti2] + x1ta[i,j,k] *
C[15,ti1,ti2])))))
return T, dTde
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef Tall4D(np.ndarray[DTYPEf_t, ndim=4] ei, np.ndarray[DTYPEf_t, ndim=3] C, np.ndarray[DTYPE_t, ndim=4] i1,
np.ndarray[DTYPE_t, ndim=4] i2, np.ndarray[DTYPEf_t, ndim=4] x1ta, np.ndarray[DTYPEf_t, ndim=4] x2ta,
DTYPEf_t x2shift):
cdef DTYPE_t i, j, k, l, ti1, ti2
cdef DTYPE_t nt = ei.shape[0]
cdef DTYPE_t nx = ei.shape[1]
cdef DTYPE_t ny = ei.shape[2]
cdef DTYPE_t nz = ei.shape[3]
cdef np.ndarray[DTYPEf_t, ndim=4] T = np.empty((nx, ny, nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=4] dTde = np.empty((nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(nz):
ti1 = i1[i,j,k,l]
ti2 = i2[i,j,k,l]
T[i,j,k,l] = exp(C[0,ti1, ti2] + x1ta[i,j,k,l] * (C[1,ti1,ti2] + x1ta[i,j,k,l] * (C[2,ti1,ti2] +
x1ta[i,j,k,l] * C[3,ti1,ti2])) + x2ta[i,j,k,l] * (C[4,ti1,ti2] + x1ta[i,j,k,l] * (C[5,ti1,ti2] +
x1ta[i,j,k,l] * (C[6,ti1,ti2] + x1ta[i,j,k,l] * C[7,ti1,ti2])) + x2ta[i,j,k,l] * (C[8,ti1,ti2] +
x1ta[i,j,k,l] * (C[9,ti1,ti2] + x1ta[i,j,k,l] * (C[10,ti1,ti2] + x1ta[i,j,k,l] * C[11,ti1, ti2])) +
x2ta[i,j,k,l] * (C[12, ti1, ti2] + x1ta[i,j,k,l] * (C[13, ti1, ti2] + x1ta[i,j,k,l] *
(C[14, ti1, ti2] + x1ta[i,j,k,l] * C[15, ti1, ti2]))))))
dTde[i,j,k,l] = T[i,j,k,l] / (ei[i,j,k,l] + x2shift) * (C[4,ti1,ti2] + x1ta[i,j,k,l] * (C[5,ti1,ti2] +
x1ta[i,j,k,l] * (C[6,ti1,ti2] + x1ta[i,j,k,l] * C[7,ti1,ti2])) + 2 * x2ta[i,j,k,l] * (C[8,ti1,ti2] +
x1ta[i,j,k,l] * (C[9,ti1,ti2] + x1ta[i,j,k,l] * (C[10,ti1,ti2] + x1ta[i,j,k,l] * C[11,ti1,ti2])) +
1.5 * x2ta[i,j,k,l] * (C[12,ti1,ti2] + x1ta[i,j,k,l] * (C[13,ti1,ti2] + x1ta[i,j,k,l] *
(C[14,ti1,ti2] + x1ta[i,j,k,l] * C[15,ti1,ti2])))))
return T, dTde
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef logPT2kappa3D(np.ndarray[DTYPEf_t, ndim=3] log10P, np.ndarray[DTYPEf_t, ndim=3] log10T,
np.ndarray[DTYPEf_t, ndim=1] tabP, np.ndarray[DTYPEf_t, ndim=1] tabT,
np.ndarray[DTYPEf_t, ndim=3] tabKap, np.ndarray[DTYPEf_t, ndim=1] tabTBN,
np.ndarray[DTYPEf_t, ndim=1] tabDTB, np.ndarray[DTYPE_t, ndim=1] idxTBN,
np.ndarray[DTYPEf_t, ndim=1] tabPBN, np.ndarray[DTYPEf_t, ndim=1] tabDPB,
np.ndarray[DTYPE_t, ndim=1] idxPBN, DTYPE_t iband):
cdef size_t i, j, k, iTx, iTx0, iTx1, iTx2, iPx, iPx0, iPx1, iPx2, nTx, nPx
cdef DTYPE_t t1, t2, t3, t4, p1, p2, p3, p4
cdef DTYPE_t nx = log10T.shape[0]
cdef DTYPE_t ny = log10T.shape[1]
cdef DTYPE_t nz = log10T.shape[2]
cdef DTYPE_t NT = tabT.size - 1
cdef DTYPE_t NP = tabP.size - 1
cdef DTYPEf_t Tx, Px, gT1, gT2, gT3, gT4, gP1, gP2, gP3, gP4, fP1, fP2, fP3, fP4, dT, dT1, dtabT1, dtabT01
cdef np.ndarray[DTYPEf_t, ndim=3] xkaros = np.empty((nx, ny, nz), dtype=DTYPEf)
for i in range(nx):
for j in range(ny):
for k in range(nz):
Tx = float_min(tabT[NT - 1], float_max(tabT[1], log10T[i, j, k]))
Px = float_min(tabP[NP - 1], float_max(tabP[1], log10P[i, j, k]))
if Tx < tabTBN[1]:
nTx = <int>((Tx - tabTBN[0]) / tabDTB[0]) + idxTBN[0]
elif Tx < tabTBN[2]:
nTx = <int>((Tx - tabTBN[1]) / tabDTB[1]) + idxTBN[1]
elif Tx < tabTBN[3]:
nTx = <int>((Tx - tabTBN[2]) / tabDTB[2]) + idxTBN[2]
else:
nTx = NT
iTx = int_min(int_max(1, nTx), NT)
iTx0 = iTx - 1
iTx1 = iTx + 1
iTx2 = iTx + 2
if Px < tabPBN[1]:
nPx = <int>((Px - tabPBN[0]) / tabDPB[0]) + idxPBN[0]
elif Px < tabPBN[2]:
nPx = <int>((Px - tabPBN[1]) / tabDPB[1]) + idxPBN[1]
elif Px < tabPBN[3]:
nPx = <int>((Px - tabPBN[2]) / tabDPB[2]) + idxPBN[2]
else:
nPx = NP
iPx = int_min(int_max(1, nPx), NP)
iPx0 = iPx - 1
iPx1 = iPx + 1
iPx2 = iPx + 2
dT = Tx - tabT[iTx]
dT1 = Tx - tabT[iTx1]
dtabT1 = tabT[iTx] - tabT[iTx1]
dtabT01 = tabT[iTx0] - tabT[iTx1]
gT1 = dT * dT1 * dT1 / ( (tabT[iTx0] - tabT[iTx] ) * dtabT01 * dtabT1)
gT2 = dT1 * ((tabT[iTx2] - tabT[iTx0]) * dT * dT - dtabT1 * (tabT[iTx] - tabT[iTx2]) * (Tx - tabT[iTx0])) /\
( (tabT[iTx0] - tabT[iTx] ) * dtabT1 * dtabT1 * (tabT[iTx] - tabT[iTx2]))
gT3 = dT * ( (tabT[iTx0] - tabT[iTx2]) * dT1 * dT1 - dtabT01 * dtabT1 * (Tx - tabT[iTx2])) /\
( dtabT01 * dtabT1 * dtabT1 * (tabT[iTx1] - tabT[iTx2]))
gT4 = -dT * dT * dT1 / ( dtabT1 * (tabT[iTx] - tabT[iTx2]) * (tabT[iTx1]- tabT[iTx2]))
dT = Px - tabP[iPx]
dT1 = Px - tabP[iPx1]
dtabT1 = tabP[iPx] - tabP[iPx1]
dtabT01 = tabP[iPx0] - tabP[iPx1]
gP1 = dT * dT1 * dT1 / ((tabP[iPx0] - tabP[iPx]) * dtabT01 * dtabT1)
gP2 = dT1 * ((tabP[iPx2] - tabP[iPx0]) * dT * dT - dtabT1 * (tabP[iPx] - tabP[iPx2]) * (Px - tabP[iPx0])) / (
(tabP[iPx0] - tabP[iPx]) * dtabT1 * dtabT1 *
(tabP[iPx] - tabP[iPx2]))
gP3 = dT * ((tabP[iPx0] - tabP[iPx2]) * dT1 * dT1 - dtabT01 * dtabT1 * (Px - tabP[iPx2])) / (
dtabT01 * dtabT1 * dtabT1 * (tabP[iPx1] - tabP[iPx2]))
gP4 = -dT * dT * dT1 / (dtabT1 * (tabP[iPx] - tabP[iPx2]) * (tabP[iPx1] - tabP[iPx2]))
fP1 = tabKap[iTx0, iPx0, iband] * gT1 + tabKap[iTx, iPx0, iband] * gT2 + \
tabKap[iTx1, iPx0, iband] * gT3 + tabKap[iTx2, iPx0, iband] * gT4
fP2 = tabKap[iTx0, iPx, iband] * gT1 + tabKap[iTx, iPx, iband] * gT2 + \
tabKap[iTx1, iPx, iband] * gT3 + tabKap[iTx2, iPx, iband] * gT4
fP3 = tabKap[iTx0, iPx1, iband] * gT1 + tabKap[iTx, iPx1, iband] * gT2 + \
tabKap[iTx1, iPx1, iband] * gT3 + tabKap[iTx2, iPx1, iband] * gT4
fP4 = tabKap[iTx0, iPx2, iband] * gT1 + tabKap[iTx, iPx2, iband] * gT2 + \
tabKap[iTx1, iPx2, iband] * gT3 + tabKap[iTx2, iPx2, iband] * gT4
xkaros[i, j, k] = fP1 * gP1 + fP2 * gP2 + fP3 * gP3 + fP4 * gP4
return xkaros
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef logPT2kappa4D(np.ndarray[DTYPEf_t, ndim=4] log10P, np.ndarray[DTYPEf_t, ndim=4] log10T,
np.ndarray[DTYPEf_t, ndim=1] tabP, np.ndarray[DTYPEf_t, ndim=1] tabT,
np.ndarray[DTYPEf_t, ndim=3] tabKap, np.ndarray[DTYPEf_t, ndim=1] tabTBN,
np.ndarray[DTYPEf_t, ndim=1] tabDTB, np.ndarray[DTYPE_t, ndim=1] idxTBN,
np.ndarray[DTYPEf_t, ndim=1] tabPBN, np.ndarray[DTYPEf_t, ndim=1] tabDPB,
np.ndarray[DTYPE_t, ndim=1] idxPBN, DTYPE_t iband):
cdef DTYPE_t i, j, k, l, iTx, iTx0, iTx1, iTx2, iPx, iPx0, iPx1, iPx2, nTx, nPx
cdef DTYPE_t nt = log10T.shape[0]
cdef DTYPE_t nx = log10T.shape[1]
cdef DTYPE_t ny = log10T.shape[2]
cdef DTYPE_t nz = log10T.shape[2]
cdef DTYPE_t NT = tabT.size - 1
cdef DTYPE_t NP = tabP.size - 1
cdef DTYPEf_t Tx, Px, gT1, gT2, gT3, gT4, gP1, gP2, gP3, gP4, fP1, fP2, fP3, fP4, dT, dT1, dtabT1, dtabT01
cdef np.ndarray[DTYPEf_t, ndim=4] xkaros = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
for j in range(nx):
for k in range(ny):
for l in range(nz):
Tx = float_min(tabT[NT-1], float_max(tabT[1], log10T[i, j, k, l]))
Px = float_min(tabP[NP-1], float_max(tabP[1], log10P[i, j, k, l]))
if Tx < tabTBN[1]:
nTx = <int>((Tx - tabTBN[0]) / tabDTB[0]) + idxTBN[0]
elif Tx < tabTBN[2]:
nTx = <int>((Tx - tabTBN[1]) / tabDTB[1]) + idxTBN[1]
elif Tx < tabTBN[3]:
nTx = <int>((Tx - tabTBN[2]) / tabDTB[2]) + idxTBN[2]
else:
nTx = NT
iTx = int_min(int_max(1, nTx), NT)
iTx0 = iTx - 1
iTx1 = iTx + 1
iTx2 = iTx + 2
if Px < tabPBN[1]:
nPx = <int>((Px - tabPBN[0]) / tabDPB[0]) + idxPBN[0]
elif Px < tabPBN[2]:
nPx = <int>((Px - tabPBN[1]) / tabDPB[1]) + idxPBN[1]
elif Px < tabPBN[3]:
nPx = <int>((Px - tabPBN[2]) / tabDPB[2]) + idxPBN[2]
else:
nPx = NP
iPx = int_min(int_max(1, nPx), NP)
iPx0 = iPx - 1
iPx1 = iPx + 1
iPx2 = iPx + 2
dT = Tx - tabT[iTx]
dT1 = Tx - tabT[iTx1]
dtabT1 = tabT[iTx] - tabT[iTx1]
dtabT01 = tabT[iTx0] - tabT[iTx1]
gT1 = dT * dT1 * dT1 / ( (tabT[iTx0] - tabT[iTx] ) * dtabT01 * dtabT1)
gT2 = dT1 * ((tabT[iTx2] - tabT[iTx0]) * dT * dT - dtabT1 * (tabT[iTx] - tabT[iTx2]) * (Tx - tabT[iTx0])) /\
( (tabT[iTx0] - tabT[iTx] ) * dtabT1 * dtabT1 * (tabT[iTx] - tabT[iTx2]))
gT3 = dT * ( (tabT[iTx0] - tabT[iTx2]) * dT1 * dT1 - dtabT01 * dtabT1 * (Tx - tabT[iTx2])) /\
( dtabT01 * dtabT1 * dtabT1 * (tabT[iTx1] - tabT[iTx2]))
gT4 = -dT * dT * dT1 / ( dtabT1 * (tabT[iTx] - tabT[iTx2]) * (tabT[iTx1]- tabT[iTx2]))
dT = Px - tabP[iPx]
dT1 = Px - tabP[iPx1]
dtabT1 = tabP[iPx] - tabP[iPx1]
dtabT01 = tabP[iPx0] - tabP[iPx1]
gP1 = dT * dT1 * dT1 / ((tabP[iPx0] - tabP[iPx]) * dtabT01 * dtabT1)
gP2 = dT1 * ((tabP[iPx2] - tabP[iPx0]) * dT * dT - dtabT1 * (tabP[iPx] - tabP[iPx2]) * (Px - tabP[iPx0])) / (
(tabP[iPx0] - tabP[iPx]) * dtabT1 * dtabT1 * (tabP[iPx] - tabP[iPx2]))
gP3 = dT * ((tabP[iPx0] - tabP[iPx2]) * dT1 * dT1 - dtabT01 * dtabT1 * (Px - tabP[iPx2])) / (
dtabT01 * dtabT1 * dtabT1 * (tabP[iPx1] - tabP[iPx2]))
gP4 = -dT * dT * dT1 / (dtabT1 * (tabP[iPx] - tabP[iPx2]) * (tabP[iPx1] - tabP[iPx2]))
fP1 = tabKap[iTx0, iPx0, iband] * gT1 + tabKap[iTx, iPx0, iband] * gT2 + \
tabKap[iTx1, iPx0, iband] * gT3 + tabKap[iTx2, iPx0, iband] * gT4
fP2 = tabKap[iTx0, iPx, iband] * gT1 + tabKap[iTx, iPx, iband] * gT2 + \
tabKap[iTx1, iPx, iband] * gT3 + tabKap[iTx2, iPx, iband] * gT4
fP3 = tabKap[iTx0, iPx1, iband] * gT1 + tabKap[iTx, iPx1, iband] * gT2 + \
tabKap[iTx1, iPx1, iband] * gT3 + tabKap[iTx2, iPx1, iband] * gT4
fP4 = tabKap[iTx0, iPx2, iband] * gT1 + tabKap[iTx, iPx2, iband] * gT2 + \
tabKap[iTx1, iPx2, iband] * gT3 + tabKap[iTx2, iPx2, iband] * gT4
xkaros[i, j, k, l] = fP1 * gP1 + fP2 * gP2 + fP3 * gP3 + fP4 * gP4
return xkaros
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef tau3D(np.ndarray[DTYPEf_t, ndim=3] kaprho, np.ndarray[DTYPEf_t, ndim=1] dz, DTYPEf_t radHtautop):
cdef DTYPE_t i, j, k, kt
cdef DTYPE_t nx = kaprho.shape[0]
cdef DTYPE_t ny = kaprho.shape[1]
cdef DTYPE_t nz = kaprho.shape[2]
cdef DTYPE_t k1 = nz - 1
cdef DTYPE_t k2 = nz - 2
cdef DTYPE_t k3 = nz - 3
cdef DTYPEf_t s3, s4, s5
cdef np.ndarray[DTYPEf_t, ndim=1] dkds = np.empty((nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=1] dxds = np.empty((nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=3] tau = np.empty((nx, ny, nz), dtype=DTYPEf)
for i in range(nx):
for j in range(ny):
tau[i, j, k1] = kaprho[i, j, k1] * radHtautop
for k in range(k1):
dkds[k] = -(kaprho[i, j, k+1] - kaprho[i, j, k]) / dz[k]
s3 = (dkds[k2] * dz[k3] + dkds[k3] * dz[k2]) / (2 * (dz[k2] + dz[k3]))
s4 = float_min(float_min(s3, dkds[k2]), dkds[k3])
s5 = float_max(float_max(s3, dkds[k2]), dkds[k3])
dxds[k1] = 1.5 * dkds[k2] - (float_max(s4, 0.0) + float_min(s5, 0.0))
for k in range(k2, 0, -1):
kt = k - 1
s3 = (dkds[k] * dz[kt] + dkds[kt] * dz[k]) / (2.0 * (dz[k] + dz[kt]))
s4 = float_min(float_min(s3, dkds[k]), dkds[kt])
s5 = float_max(float_max(s3, dkds[k]), dkds[kt])
dxds[k] = 2.0 * (float_max(s4, 0.0) + float_min(s5, 0.0))
dxds[0] = 1.5 * dkds[0] - 0.5 * dxds[1]
for k in range(k2, -1, -1):
kt = k + 1
tau[i, j, k] = tau[i, j, kt] + dz[k] * (0.5 * (kaprho[i, j, kt] + kaprho[i, j, k]) +
dz[k] * (dxds[kt] - dxds[k]) / 12.0)
return tau
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef tau4D(np.ndarray[DTYPEf_t, ndim=4] kaprho, np.ndarray[DTYPEf_t, ndim=1] dz, DTYPEf_t radHtautop):
cdef DTYPE_t i, j, k, l, lt
cdef DTYPE_t nt = kaprho.shape[0]
cdef DTYPE_t nx = kaprho.shape[1]
cdef DTYPE_t ny = kaprho.shape[2]
cdef DTYPE_t nz = kaprho.shape[3]
cdef DTYPE_t l1 = nz - 1
cdef DTYPE_t l2 = nz - 2
cdef DTYPE_t l3 = nz - 3
cdef DTYPEf_t s3, s4, s5
cdef np.ndarray[DTYPEf_t, ndim=1] dkds = np.empty((nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=1] dxds = np.empty((nz), dtype=DTYPEf)
cdef np.ndarray[DTYPEf_t, ndim=4] tau = np.empty((nt, nx, ny, nz), dtype=DTYPEf)
for i in range(nt):
for j in range(nx):
for k in range(ny):
tau[i, j, k, l1] = kaprho[i, j, k, l1] * radHtautop
for l in range(l1):
dkds[l] = -(kaprho[i, j, k, l+1] - kaprho[i, j, k, l]) / dz[l]
s3 = (dkds[l2] * dz[l3] + dkds[l3] * dz[l2]) / (2 * (dz[l2] + dz[l3]))
s4 = float_min(float_min(s3, dkds[l2]), dkds[l3])
s5 = float_max(float_max(s3, dkds[l2]), dkds[l3])
dxds[l1] = 1.5 * dkds[l2] - (float_max(s4, 0.0 ) + float_min(s5, 0.0))
for l in range(l2, 0, -1):
lt = l - 1
s3 = (dkds[l] * dz[lt] + dkds[lt] * dz[l]) / (2.0 * (dz[l] + dz[lt]))
s4 = float_min(float_min(s3, dkds[l]), dkds[lt])
s5 = float_max(float_max(s3, dkds[l]), dkds[lt])
dxds[l] = 2.0 * (float_max(s4, 0.0) + float_min(s5, 0.0))
dxds[0] = 1.5 * dkds[0] - 0.5 * dxds[1]
for l in range(l2, -1, -1):
lt = l + 1
tau[i, j, k, l] = tau[i, j, k, lt] + dz[l] * (0.5 * (kaprho[i, j, k, lt] + kaprho[i, j, k, l]) +
dz[l] * (dxds[lt] - dxds[l]) / 12.0)
return tau
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef height3D(np.ndarray[DTYPEf_t, ndim=3] tau, np.ndarray[DTYPEf_t, ndim=1] z, DTYPEf_t val):
"""
Description:
Computes the height-surface of tau=val. It assumes linear interpolation of tau along the last axis.
input:
tau: 3D ndarray (float64), Containing optical depth. Last dimension is height-dimension
z: 1D ndarray (float64), Vertical axis along last dimension of tau.
val: float64, Value of tau, at which geometrical height is to be computed.
out: 2D ndarray (float32), height of tau=val-level
"""
tau -= val
cdef DTYPE_t i, j, k
cdef DTYPE_t nx = tau.shape[0]
cdef DTYPE_t ny = tau.shape[1]
cdef DTYPE_t nz = tau.shape[2]
cdef np.ndarray[DTYPEf_t, ndim=2] out = np.empty((nx, ny), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(nz):
if tau[i, j, k] < 0:
out[i, j] = (z[k - 1] - z[k]) / (tau[i, j, k] - tau[i, j, k-1]) * tau[i, j, k] + z[k]
break
return out
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef height4D(np.ndarray[DTYPEf_t, ndim=4] tau, np.ndarray[DTYPEf_t, ndim=1] z, DTYPEf_t val):
"""
Description:
Computes the height-surface of tau=val. It assumes linear interpolation of tau along the last axis.
input:
tau: 4D ndarray (float64), Containing optical depth. Last dimension is height-dimension
z: 1D ndarray (float64), Vertical axis along last dimension of tau.
val: float64, Value of tau, at which geometrical height is to be computed.
out: 3D ndarray (float32), height of tau=val-level
"""
tau -= val
cdef DTYPE_t i, j, k, l
cdef DTYPE_t nt = tau.shape[0]
cdef DTYPE_t nx = tau.shape[1]
cdef DTYPE_t ny = tau.shape[2]
cdef DTYPE_t nz = tau.shape[3]
cdef np.ndarray[DTYPEf_t, ndim=3] out = np.empty((nt, nx, ny), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(1, nz):
if tau[i, j, k , l] < 0:
out[i, j, k] = (z[l - 1] - z[l]) / (tau[i, j, k, l] - tau[i, j, k, l-1]) * tau[i, j, k, l] + z[l]
break
return out
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef height3Dvec(np.ndarray[DTYPEf_t, ndim=3] tau, np.ndarray[DTYPEf_t, ndim=1] z,
np.ndarray[DTYPEf_t, ndim=1] val):
"""
Description:
Computes the geometrical height of tau=val. It assumes linear interpolation of tau along the last axis.
input:
tau: 3D ndarray (float64), Containing optical depth. Last dimension is height-dimension
z: 1D ndarray (float64), Vertical axis along last dimension of tau.
val: 1D ndarray (float64), Values of tau, at which geometrical height is to be computed.
out: 3D ndarray (float32), heights of tau=val-level
"""
cdef DTYPE_t i, j, k, l
cdef DTYPE_t nx = tau.shape[0]
cdef DTYPE_t ny = tau.shape[1]
cdef DTYPE_t nz = tau.shape[2]
cdef DTYPE_t nv = val.shape[0]
cdef np.ndarray[DTYPEf_t, ndim=3] out = np.empty((nx, ny, nv), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for l in range(nv):
for k in range(1, nz):
if tau[i, j, k] - val[l] < 0:
out[i, j, l] = (z[k - 1] - z[k]) / (tau[i, j, k] - tau[i, j, k-1]) * tau[i, j, k] + z[k]
break
return out
@cython.cdivision(True)
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef height4Dvec(np.ndarray[DTYPEf_t, ndim=4] tau, np.ndarray[DTYPEf_t, ndim=1] z,
np.ndarray[DTYPEf_t, ndim=1] val):
"""
Description:
Computes the height-surface of tau=val. It assumes linear interpolation of tau along the last axis.
input:
tau: 4D ndarray (float64), Containing optical depth. Last dimension is height-dimension
z: 1D ndarray (float64), Vertical axis along last dimension of tau.
val: 1D ndarray (float64), Values of tau, at which geometrical height is to be computed.
out: 4D ndarray (float32), heights of tau=val-level
"""
cdef DTYPE_t i, j, k, l, m
cdef DTYPE_t nt = tau.shape[0]
cdef DTYPE_t nx = tau.shape[1]
cdef DTYPE_t ny = tau.shape[2]
cdef DTYPE_t nz = tau.shape[3]
cdef DTYPE_t nv = val.shape[0]
cdef np.ndarray[DTYPEf_t, ndim=4] out = np.empty((nt, nx, ny, nv), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for m in range(nv):
for l in range(1, nz):
if tau[i, j, k , l] - val[m] < 0:
out[i, j, k, m] = (z[l - 1] - z[l]) / (tau[i, j, k, l] - tau[i, j, k, l-1]) * tau[i, j, k, l] + z[l]
break
return out
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef interp3d(np.ndarray[DTYPEf_t, ndim=1] x, np.ndarray[DTYPEf_t, ndim=3] y, np.ndarray[DTYPEf_t, ndim=2] new_x):
"""
interp3d(x, y, new_x)
Performs linear interpolation over the last dimension of a 3D array, according to new values from a 2D array new_x.
Thus, interpolate y[i, j, :] for new_x[i, j]. Modified for tau-interpolation (tau as axis)!
Parameters
----------
x : 1-D ndarray (double type)
Array containing the x (abcissa) values. Must be monotonically decreasing.
y : 3-D ndarray (double type)
Array containing the y values to interpolate.
x_new: 2-D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3-D ndarray
Interpolated values.
"""
cdef DTYPE_t nx = y.shape[0]
cdef DTYPE_t ny = y.shape[1]
cdef DTYPE_t nz = y.shape[2]
cdef DTYPE_t i, j, k
cdef np.ndarray[DTYPEf_t, ndim=2] new_y = np.zeros((nx, ny), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for k in range(1, nz):
if x[k] < new_x[i, j]:
new_y[i, j] = (y[i, j, k] - y[i, j, k - 1]) * (new_x[i, j] - x[k-1]) /\
(x[k] - x[k - 1]) + y[i, j, k - 1]
break
return new_y
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef interp4d(np.ndarray[DTYPEf_t, ndim=1] x, np.ndarray[DTYPEf_t, ndim=4] y, np.ndarray[DTYPEf_t, ndim=3] new_x):
"""
interp4d(x, y, new_x)
Performs linear interpolation over the last dimension of a 4D array, according to new values from a 3D array new_x.
Thus, interpolate y[i, j, :] for new_x[i, j]. Modified for tau-interpolation (tau as axis)!
Parameters
----------
x : 1D ndarray (double type)
Array containg the x (abcissa) values. Must be monotonically decreasing.
y : 4D ndarray (double type)
Array containing the y values to interpolate.
x_new: 3D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3D ndarray
Interpolated values.
"""
cdef DTYPE_t nt = y.shape[0]
cdef DTYPE_t nx = y.shape[1]
cdef DTYPE_t ny = y.shape[2]
cdef DTYPE_t nz = y.shape[3]
cdef DTYPE_t i, j, k, l
cdef np.ndarray[DTYPEf_t, ndim=3] new_y = np.zeros((nt, nx, ny), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for l in range(1, nz):
if x[l] < new_x[i, j, k]:
new_y[i, j, k] = (y[i, j, k, l] - y[i, j, k, l - 1]) * (new_x[i, j, k] - x[l-1]) /\
(x[l] - x[l - 1]) + y[i, j, k, l - 1]
break
return new_y
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef interp3dcube(np.ndarray[DTYPEf_t, ndim=1] x, np.ndarray[DTYPEf_t, ndim=3] y,
np.ndarray[DTYPEf_t, ndim=3] new_x):
"""
interp3d(x, y, new_x)
Performs linear interpolation over the last dimension of a 3D array, according to new values from a 2D array new_x.
Thus, interpolate y[i, j, :] for new_x[i, j]. Modified for tau-interpolation (tau as axis)!
Parameters
----------
x : 1-D ndarray (double type)
Array containg the x (abcissa) values. Must be monotonically decreasing.
y : 3-D ndarray (double type)
Array containing the y values to interpolate.
x_new: 2-D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3-D ndarray
Interpolated values.
"""
cdef DTYPE_t nx = y.shape[0]
cdef DTYPE_t ny = y.shape[1]
cdef DTYPE_t nz = y.shape[2]
cdef DTYPE_t nxn = new_x.shape[2]
cdef DTYPE_t i, j, k, l
cdef np.ndarray[DTYPEf_t, ndim=3] new_y = np.zeros((nx, ny, nxn), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for l in range(nxn):
for k in range(1, nz):
if x[k] < new_x[i, j, l]:
new_y[i, j, l] = (y[i, j, k] - y[i, j, k - 1]) * (new_x[i, j, l] - x[k-1]) /\
(x[k] - x[k - 1]) + y[i, j, k - 1]
break
return new_y
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef interp4dcube(np.ndarray[DTYPEf_t, ndim=1] x, np.ndarray[DTYPEf_t, ndim=4] y,
np.ndarray[DTYPEf_t, ndim=4] new_x):
"""
interp4d(x, y, new_x)
Performs linear interpolation over the last dimension of a 4D array, according to new values from a 3D array new_x.
Thus, interpolate y[i, j, :] for new_x[i, j]. Modified for tau-interpolation (tau as axis)!
Parameters
----------
x : 1D ndarray (double type)
Array containg the x (abcissa) values. Must be monotonically decreasing.
y : 4D ndarray (double type)
Array containing the y values to interpolate.
x_new: 3D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3D ndarray
Interpolated values.
"""
cdef DTYPE_t nt = y.shape[0]
cdef DTYPE_t nx = y.shape[1]
cdef DTYPE_t ny = y.shape[2]
cdef DTYPE_t nz = y.shape[3]
cdef DTYPE_t nxn = new_x.shape[3]
cdef DTYPE_t i, j, k, l, m
cdef np.ndarray[DTYPEf_t, ndim=4] new_y = np.zeros((nt, nx, ny, nxn), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for m in range(nxn):
for l in range(1, nz):
if x[l] < new_x[i, j, k, m]:
new_y[i, j, k, m] = (y[i, j, k, l] - y[i, j, k, l - 1]) * (new_x[i, j, k, m] - x[l-1]) /\
(x[l] - x[l - 1]) + y[i, j, k, l - 1]
break
return new_y
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef cubeinterp3dcube(np.ndarray[DTYPEf_t, ndim=3] x, np.ndarray[DTYPEf_t, ndim=3] y,
np.ndarray[DTYPEf_t, ndim=3] new_x):
"""
interp3d(x, y, new_x)
Performs linear interpolation over the last dimension of a 3D array,
according to new values from a 2D array new_x. Thus, interpolate
y[i, j, :] for new_x[i, j].
Parameters
----------
x : 1-D ndarray (double type)
Array containg the x (abcissa) values. Must be monotonically
increasing.
y : 3-D ndarray (double type)
Array containing the y values to interpolate.
x_new: 2-D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3-D ndarray
Interpolated values.
"""
cdef DTYPE_t nx = y.shape[0]
cdef DTYPE_t ny = y.shape[1]
cdef DTYPE_t nz = y.shape[2]
cdef DTYPE_t nxn = new_x.shape[2]
cdef DTYPE_t i, j, k, l
cdef np.ndarray[DTYPEf_t, ndim=3] new_y = np.zeros((nx, ny, nxn), dtype=DTYPEf)
# for i in range(nx):
for i in prange(nx, nogil=True):
for j in range(ny):
for l in range(nxn):
for k in range(1, nz):
if x[i, j, k] < new_x[i, j, l]:
new_y[i, j, l] = (y[i, j, k] - y[i, j, k - 1]) * (new_x[i, j, l] - x[i, j, k-1]) /\
(x[i, j, k] - x[i, j, k - 1]) + y[i, j, k - 1]
break
return new_y
@cython.cdivision(True)
@cython.boundscheck(False) # turn off bounds-checking for entire function
@cython.wraparound(False) # turn off bounds-checking for entire function
cpdef cubeinterp4dcube(np.ndarray[DTYPEf_t, ndim=4] x, np.ndarray[DTYPEf_t, ndim=4] y,
np.ndarray[DTYPEf_t, ndim=4] new_x):
"""
interp4d(x, y, new_x)
Performs linear interpolation over the last dimension of a 4D array,
according to new values from a 3D array new_x. Thus, interpolate
y[i, j, :] for new_x[i, j].
Parameters
----------
x : 1D ndarray (double type)
Array containg the x (abcissa) values. Must be monotonically
increasing.
y : 4D ndarray (double type)
Array containing the y values to interpolate.
x_new: 3D ndarray (double type)
Array with new abcissas to interpolate.
Returns
-------
new_y : 3D ndarray
Interpolated values.
"""
cdef DTYPE_t nt = y.shape[0]
cdef DTYPE_t nx = y.shape[1]
cdef DTYPE_t ny = y.shape[2]
cdef DTYPE_t nz = y.shape[3]
cdef DTYPE_t nxn = new_x.shape[3]
cdef DTYPE_t i, j, k, l, m
cdef np.ndarray[DTYPEf_t, ndim=4] new_y = np.zeros((nt, nx, ny, nxn), dtype=DTYPEf)
for i in range(nt):
# for j in range(nx):
for j in prange(nx, nogil=True):
for k in range(ny):
for m in range(nxn):
for l in range(1, nz):
if x[i, j, k, l] < new_x[i, j, k, m]:
new_y[i, j, k, m] = (y[i, j, k, l] - y[i, j, k, l - 1]) * (new_x[i, j, k, m] - x[i, j, k, l-1]) /\
(x[i, j, k, l] - x[i, j,k, l - 1]) + y[i, j, k, l - 1]
break
return new_y