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cstagger.pyx
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cstagger.pyx
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cimport numpy as np
import numpy as np
DTYPE = np.float32
ctypedef np.float32_t DTYPE_t
nz = 0 # initialise nz
###
### C functions
###
cdef inline void xup_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o):
cdef DTYPE_t c = 3./256., b = -25./256., a = 150./256.
cdef int i, j, k, l, m=mx
for k in range(mz):
for j in range(my):
l = j*mx + k*mx*my
o[l + (m-3)] = (
a*(f[l + (m-2)]+f[l + (m-3)]) +
b*(f[l + (m-1)]+f[l + (m-4)]) +
c*(f[l + (0)]+f[l + (m-5)]))
o[l + (m-2)] = (
a*(f[l + (m-1)]+f[l + (m-2)]) +
b*(f[l + (0)]+f[l + (m-3)]) +
c*(f[l + (1)]+f[l + (m-4)]))
o[l + (m-1)] = (
a*(f[l + (0)]+f[l + (m-1)]) +
b*(f[l + (1)]+f[l + (m-2)]) +
c*(f[l + (2)]+f[l + (m-3)]))
o[l + (0)] = (
a*(f[l + (1)]+f[l + (0)]) +
b*(f[l + (2)]+f[l + (m-1)]) +
c*(f[l + (3)]+f[l + (m-2)]))
o[l + (1)] = (
a*(f[l + (2)]+f[l + (1)]) +
b*(f[l + (3)]+f[l + (0)]) +
c*(f[l + (4)]+f[l + (m-1)]))
for j in range(my):
l = j*mx + k*mx*my
for i in range(2,mx-3):
o[l + (i)] = (
a*(f[l + (i+1)] + f[l + i]) +
b*(f[l + (i+2)] + f[l + (i-1)]) +
c*(f[l + (i+3)] + f[l + (i-2)]))
return
#---------------------------------------------------------------------------
cdef inline void yup_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o):
cdef DTYPE_t c = 3./256., b = -25./256., a = 150./256.
cdef int i, j, k, l, m=my
for k in range(mz):
for i in range(mx):
l = i + k*mx*my
o[l + (m-3)*mx] = (
a*(f[l + (m-2)*mx]+f[l + (m-3)*mx]) +
b*(f[l + (m-1)*mx]+f[l + (m-4)*mx]) +
c*(f[l + (0)*mx]+f[l + (m-5)*mx]))
o[l + (m-2)*mx] = (
a*(f[l + (m-1)*mx]+f[l + (m-2)*mx]) +
b*(f[l + (0)*mx]+f[l + (m-3)*mx]) +
c*(f[l + (1)*mx]+f[l + (m-4)*mx]))
o[l + (m-1)*mx] = (
a*(f[l + (0)*mx]+f[l + (m-1)*mx]) +
b*(f[l + (1)*mx]+f[l + (m-2)*mx]) +
c*(f[l + (2)*mx]+f[l + (m-3)*mx]))
o[l + (0)*mx] = (
a*(f[l + (1)*mx]+f[l + (0)*mx]) +
b*(f[l + (2)*mx]+f[l + (m-1)*mx]) +
c*(f[l + (3)*mx]+f[l + (m-2)*mx]))
o[l + (1)*mx] = (
a*(f[l + (2)*mx]+f[l + (1)*mx]) +
b*(f[l + (3)*mx]+f[l + (0)*mx]) +
c*(f[l + (4)*mx]+f[l + (m-1)*mx]))
for j in range(2,my-3):
for i in range(mx):
l = i + k*mx*my
o[l + (j)*mx] = (
a*(f[l + (j+1)*mx] + f[l + j*mx]) +
b*(f[l + (j+2)*mx] + f[l + (j-1)*mx]) +
c*(f[l + (j+3)*mx] + f[l + (j-2)*mx]))
return
#---------------------------------------------------------------------------
cdef inline void zup_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o, DTYPE_t *zzupc):
cdef DTYPE_t d
cdef int i, j, k, l, m=mz
for k in range(mz):
m = k-2
if (k < 3): m = 0
if (k > mz-4): m = mz-6
for j in range(my):
for i in range(mx):
d = 0
for l in range(6):
d += zzupc[k*6 + l]*f[((m+l)*my + j)*mx + i];
o[(k * my + j) * mx + i] = d
return
#---------------------------------------------------------------------------
cdef inline void xdn_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o):
cdef DTYPE_t c = 3./256., b = -25./256., a = 150./256.
cdef int i, j, k, l, m=mx
for k in range(mz):
for j in range(my):
l = j*mx + k*mx*my
o[l + (m-2)] = (
a*(f[l + (m-2)]+f[l + (m-3)]) +
b*(f[l + (m-1)]+f[l + (m-4)]) +
c*(f[l + (0)]+f[l + (m-5)]))
o[l + (m-1)] = (
a*(f[l + (m-1)]+f[l + (m-2)]) +
b*(f[l + (0)]+f[l + (m-3)]) +
c*(f[l + (1)]+f[l + (m-4)]))
o[l + (0)] = (
a*(f[l + (0)]+f[l + (m-1)]) +
b*(f[l + (1)]+f[l + (m-2)]) +
c*(f[l + (2)]+f[l + (m-3)]))
o[l + (1)] = (
a*(f[l + (1)]+f[l + (0)]) +
b*(f[l + (2)]+f[l + (m-1)]) +
c*(f[l + (3)]+f[l + (m-2)]))
o[l + (2)] = (
a*(f[l + (2)]+f[l + (1)]) +
b*(f[l + (3)]+f[l + (0)]) +
c*(f[l + (4)]+f[l + (m-1)]))
for j in range(my):
l = j*mx + k*mx*my
for i in range(2,mx-3):
o[l + (i+1)] = (
a*(f[l + (i+1)] + f[l + i]) +
b*(f[l + (i+2)] + f[l + (i-1)]) +
c*(f[l + (i+3)] + f[l + (i-2)]))
return
#------------------------------------------------------------------------------
cdef inline void ydn_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o):
cdef DTYPE_t c = 3./256., b = -25./256., a = 150./256.
cdef int i, j, k, l, m=my
for k in range(mz):
for i in range(mx):
l = i + k*mx*my
o[l + (m-2)*mx] = (
a*(f[l + (m-2)*mx]+f[l + (m-3)*mx]) +
b*(f[l + (m-1)*mx]+f[l + (m-4)*mx]) +
c*(f[l + (0)*mx]+f[l + (m-5)*mx]))
o[l + (m-1)*mx] = (
a*(f[l + (m-1)*mx]+f[l + (m-2)*mx]) +
b*(f[l + (0)*mx]+f[l + (m-3)*mx]) +
c*(f[l + (1)*mx]+f[l + (m-4)*mx]))
o[l + (0)*mx] = (
a*(f[l + (0)*mx]+f[l + (m-1)*mx]) +
b*(f[l + (1)*mx]+f[l + (m-2)*mx]) +
c*(f[l + (2)*mx]+f[l + (m-3)*mx]))
o[l + (1)*mx] = (
a*(f[l + (1)*mx]+f[l + (0)*mx]) +
b*(f[l + (2)*mx]+f[l + (m-1)*mx]) +
c*(f[l + (3)*mx]+f[l + (m-2)*mx]))
o[l + (2)*mx] = (
a*(f[l + (2)*mx]+f[l + (1)*mx]) +
b*(f[l + (3)*mx]+f[l + (0)*mx]) +
c*(f[l + (4)*mx]+f[l + (m-1)*mx]))
for j in range(2,my-3):
for i in range(mx):
l = i + k*mx*my
o[l + (j+1)*mx] = (
a*(f[l + (j+1)*mx] + f[l + j*mx]) +
b*(f[l + (j+2)*mx] + f[l + (j-1)*mx]) +
c*(f[l + (j+3)*mx] + f[l + (j-2)*mx]))
return
#------------------------------------------------------------------------------
cdef inline void zdn_c(int mx, int my, int mz, DTYPE_t *f, DTYPE_t *o, DTYPE_t *zzdnc):
cdef DTYPE_t d
cdef int i, j, k, l, m=mz
for k in range(mz):
m = k-3
if (k < 3): m = 0
if (k > mz-4): m = mz-6
for j in range(my):
for i in range(mx):
d = 0
for l in range(6):
d += zzdnc[k*6+l]*f[((m+l)*my + j)*mx + i];
o[(k * my + j) * mx + i] = d
return
#------------------------------------------------------------------------------
###
### Python wrappers
###
#------------------------------------------------------------------------------
### init functions
#------------------------------------------------------------------------------
def calc_stagger_inv(x, int n, int y, int o, r):
''' Auxiliary function for init_stagger. '''
cdef DTYPE_t c[6], b[6], t
cdef int i, j
for i in range(n+1): c[i] = 0.
c[n] = -x[0]
for i in range(1,n+1):
for j in range(n-i, n): c[j] -= x[i]*c[j+1]
c[n] -= x[i]
for i in range(6): r[i] = 0.
for i in range(n+1):
t = 1.
b[n] = 1.
for j in range(n, 0, -1):
b[j-1] = c[j] + x[i]*b[j]
t = x[i]*t + b[j-1]
r[i+o] = b[y]/t
return
#------------------------------------------------------------------------------
def init_stagger(int mz, np.ndarray[DTYPE_t, ndim=1] z, np.ndarray[DTYPE_t, ndim=1] zdn):
''' init_stagger(int mz, np.ndarray[DTYPE_t] z, np.ndarray[DTYPE_t] zdn)
Initialises zupc and zdnc structures (for using with zdn and zup).
From init_stagger.c and init_stagger.pro
IN: mz, z, zdn (latter two are 'z' and 'zdn' from mesh)
'''
cdef int i, j, k
global zupc, zdnc, nz
zupc = np.zeros((mz,6),dtype=DTYPE)
zdnc = np.zeros((mz,6),dtype=DTYPE)
nz = mz
cdef np.ndarray[DTYPE_t, ndim=1] zh = np.sort(np.concatenate([z,zdn]))
cdef np.ndarray[DTYPE_t, ndim=1] a = np.zeros(6, dtype=DTYPE)
iordl = np.array([1,3,4,5])
iordu = np.array([1,3,4,5])
dordl = np.array([2,3,4,5])
dordu = np.array([2,3,4,5])
for k in range(1,4):
for j in range(6): a[j] = zh[2*j] - zh[k*2-1]
calc_stagger_inv(a, iordl[k], 0, 0, zupc[k-1])
for j in range(6): a[j] = zh[2*j+1] - zh[k*2-2]
calc_stagger_inv(a, iordl[k-1], 0, 0, zdnc[k-1])
for k in range(4, mz-2):
for j in range(6): a[j] = zh[2*(k-2+j)-2] - zh[k*2-1]
calc_stagger_inv(a, 5, 0, 0, zupc[k-1])
for j in range(6): a[j] = zh[2*(k-3+j)-1] - zh[k*2-2];
calc_stagger_inv(a, 5, 0, 0, zdnc[k-1])
for k in range(mz-2, mz+1):
for j in range(iordu[mz-k]+1): a[j] = zh[2*(mz+j-iordu[mz-k])-2] - zh[k*2-1]
for j in range(iordu[mz-k]+1, 6): a[j] = 0
calc_stagger_inv(a, iordu[mz-k], 0, 5-iordu[mz-k], zupc[k-1])
for j in range(iordu[mz-k+1]+1): a[j] = zh[2*(mz+j-iordu[mz-k+1])-1] - zh[k*2-2]
for j in range(iordu[mz-k+1]+1, 6): a[j] = 0
calc_stagger_inv(a, iordu[mz-k+1], 0, 5-iordu[mz-k+1], zdnc[k-1])
return
#------------------------------------------------------------------------------
### up and down functions
#------------------------------------------------------------------------------
def xup(np.ndarray[DTYPE_t, ndim=3] inarr):
''' xup(np.ndarray[DTYPE_t, ndim=3] inarr)
stagger xup function.
IN: inarr (mx,my,mz)
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
xup_c(mx, my, mz, <DTYPE_t *> inarr.data, <DTYPE_t *> outarr.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------
def yup(np.ndarray[DTYPE_t, ndim=3] inarr):
''' yup(np.ndarray[DTYPE_t, ndim=3] inarr)
cstagger yup function.
IN: inarr (mx,my,mz) float array
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
yup_c(mx, my, mz, <DTYPE_t *> inarr.data, <DTYPE_t *> outarr.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------
def zup(np.ndarray[DTYPE_t, ndim=3] inarr):
''' zup(np.ndarray[DTYPE_t, ndim=3] inarr)
cstagger zup function.
IN: inarr (mx,my,mz) float array
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if (mz != nz): raise ValueError('zup: nz mismatch, must run init_stagger first!')
cdef np.ndarray[DTYPE_t, ndim=2] zz = zupc
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
zup_c(mx,my,mz,<DTYPE_t *> inarr.data,<DTYPE_t *> outarr.data,<DTYPE_t *> zz.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------
def xdn(np.ndarray[DTYPE_t, ndim=3] inarr):
''' xdn(np.ndarray[DTYPE_t, ndim=3] inarr)
stagger xdn function.
IN: inarr (mx,my,mz)
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
xdn_c(mx, my, mz, <DTYPE_t *> inarr.data, <DTYPE_t *> outarr.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------
def ydn(np.ndarray[DTYPE_t, ndim=3] inarr):
''' ydn(np.ndarray[DTYPE_t, ndim=3] inarr)
cstagger ydn function.
IN: inarr (mx,my,mz) float array
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
ydn_c(mx, my, mz, <DTYPE_t *> inarr.data, <DTYPE_t *> outarr.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------
def zdn(np.ndarray[DTYPE_t, ndim=3] inarr):
''' zdn(np.ndarray[DTYPE_t, ndim=3] inarr)
cstagger zdn function.
IN: inarr (mx,my,mz) float array
OUT: array of same shape and type.'''
cdef int mx = inarr.shape[0], my = inarr.shape[1], mz = inarr.shape[2]
cdef np.ndarray[DTYPE_t, ndim=3] outarr = np.zeros((mx, my, mz), dtype=DTYPE)
if (mz != nz): raise ValueError('zdn: nz mismatch, must run init_stagger first!')
cdef np.ndarray[DTYPE_t, ndim=2] zz = zdnc
if not inarr.flags["C_CONTIGUOUS"]:
inarr = inarr.copy('C')
zdn_c(mx,my,mz,<DTYPE_t *> inarr.data,<DTYPE_t *> outarr.data,<DTYPE_t *> zz.data)
return np.transpose(np.reshape(outarr, (mz, my, mx)))
#------------------------------------------------------------------------------