def interpolation(x, y, kind):
"""Make the interpolation function"""
assert scipy is not None, (
'You must have scipy installed to use interpolation')
order = None
if len(y) < len(x):
x = x[:len(y)]
x, y = zip(*filter(lambda t: None not in t, zip(x, y)))
if len(x) < 2:
return ident
if isinstance(kind, int):
order = kind
elif kind in KINDS:
order = {
'nearest': 0,
'zero': 0,
'slinear': 1,
'quadratic': 2,
'cubic': 3,
'univariate': 3
}[kind]
if order and len(x) <= order:
kind = len(x) - 1
if kind == 'krogh':
return interpolate.KroghInterpolator(x, y)
elif kind == 'barycentric':
return interpolate.BarycentricInterpolator(x, y)
elif kind == 'univariate':
return interpolate.InterpolatedUnivariateSpline(x, y)
return interpolate.interp1d(x, y, kind=kind, bounds_error=False)
def interpolation(x_axis,
y_axis,
x_value,
model='chip',
method=None,
is_function=False):
methods = [
'linear', 'nearest', 'zero', 'slinear', 'quadratic', 'cubic',
'previous', 'next'
]
# print(type(x_value),type(min(x_axis)))
models = [
'akima', 'chip', 'interp1d', 'cubicspline', 'krogh', 'barycentric'
]
# print('x_axis => ',x_axis)
result = None
f = None
if model is None or model == 'interp1d':
if method in methods:
f = interpolate.interp1d(x_axis, y_axis, kind=method)
else:
f = interpolate.interp1d(x_axis, y_axis, kind='cubic')
elif model in models:
if model == 'akima':
f = interpolate.Akima1DInterpolator(x_axis, y_axis)
elif model == 'chip':
f = interpolate.PchipInterpolator(x_axis, y_axis)
elif model == 'cubicspline':
f = interpolate.CubicSpline(x_axis, y_axis)
elif model == 'krogh':
f = interpolate.KroghInterpolator(x_axis, y_axis)
elif model == 'barycentric':
f = interpolate.BarycentricInterpolator(x_axis, y_axis)
else:
f = interpolate.PchipInterpolator(x_axis, y_axis)
if is_function == True:
return f
else:
if not isinstance(x_value, list):
# if x_value <min(x_axis) or x_value >max(x_axis):
# raise Exception('interpolation error: value requested is outside of range')
# return result
try:
result = float(f(x_value))
except:
return result
else:
result = list(map(lambda x: float(f(x)), x_value))
return result
def max_pos_PDF(PDF_bins, PDF):
'''
Returns max position of PDF
'''
#return PDF_bins[PDF.argmax()]
i_peak = PDF.argmax()
i_min = np.maximum(0, i_peak - 1)
i_max = i_min + 3
if i_max > len(PDF_bins) - 1:
i_max = np.minimum(i_peak + 1, len(PDF_bins) - 1)
i_min = i_max - 3
new_bins = np.arange(PDF_bins[i_min], PDF_bins[i_max], 0.001)
inter = interpolate.KroghInterpolator(PDF_bins[i_min:i_max],
PDF[i_min:i_max])
PDF_inter = inter(new_bins)
return new_bins[PDF_inter.argmax()]
def main():
parser = argparse.ArgumentParser()
parser.add_argument("-d",
"--directory",
help="directory of relax running",
type=str,
default="matflow-running")
args = parser.parse_args()
# making traj: initial and current
os.chdir(args.directory)
dirs_int = []
for i in os.listdir():
if i.isdecimal() == True:
dirs_int.append(int(i))
total_images = max(dirs_int) + 1 # including initial and final
for i in range(total_images):
if i == 0 or i == (total_images - 1):
os.system("sflow convert -i %.2d/POSCAR -o %.2d/POSCAR.xyz" %
(i, i))
else:
os.system("sflow convert -i %.2d/POSCAR -o %.2d/POSCAR.xyz" %
(i, i))
os.system("sflow convert -i %.2d/CONTCAR -o %.2d/CONTCAR.xyz" %
(i, i))
os.system("mkdir -p post-processing")
for i in range(total_images):
# initial traj
if i == 0:
os.system(
"cat %.2d/POSCAR.xyz > post-processing/traj-initial.xyz" % (i))
else:
os.system(
"cat %.2d/POSCAR.xyz >> post-processing/traj-initial.xyz" %
(i))
# current traj
if i == 0:
os.system(
"cat %.2d/POSCAR.xyz > post-processing/traj-current.xyz" % (i))
elif i == (total_images - 1):
os.system(
"cat %.2d/POSCAR.xyz >> post-processing/traj-current.xyz" %
(i))
else:
os.system(
"cat %.2d/CONTCAR.xyz >> post-processing/traj-current.xyz" %
(i))
# end making the traj
# build the energy barrier plot
import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate as spinterpolate
os.system("nebresults.pl")
neb_dat = np.loadtxt("neb.dat")
# style: linear spline
fun_dat = spinterpolate.interp1d(neb_dat[:, 1],
neb_dat[:, 2],
kind="linear")
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-linear-spline.png")
plt.close()
# style: slinear
fun_dat = spinterpolate.interp1d(neb_dat[:, 1],
neb_dat[:, 2],
kind="slinear")
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-slinear-spline.png")
plt.close()
# style: cubic spline
fun_dat = spinterpolate.interp1d(neb_dat[:, 1],
neb_dat[:, 2],
kind="quadratic")
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-quadratic-spline.png")
plt.close()
# style: cubic spline
fun_dat = spinterpolate.interp1d(neb_dat[:, 1],
neb_dat[:, 2],
kind="cubic")
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-cubic-spline.png")
plt.close()
# style: 5 order spline
fun_dat = spinterpolate.interp1d(neb_dat[:, 1], neb_dat[:, 2], kind=5)
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-5-order-spline.png")
plt.close()
# style: KroghInterpolator
fun_dat = spinterpolate.KroghInterpolator(neb_dat[:, 1], neb_dat[:, 2])
denser_x = np.linspace(neb_dat[:, 1].min(), neb_dat[:, 1].max(),
30 * len(neb_dat))
plt.plot(denser_x, fun_dat(denser_x))
plt.scatter(neb_dat[:, 1], neb_dat[:, 2], marker="o")
plt.xlabel("Reaction Coordinate (Angstrom)")
plt.ylabel("Energy (eV)")
plt.savefig("post-processing/mep-style-kroghinterpolator.png")
plt.close()
f7 = interpolate.Akima1DInterpolator(t, y) y7 = f7(tt) # 区分的 3 次エルミート補間 # y8 = interpolate.pchip_interpolate(t, y, tt)でも結果は同じ f8 = interpolate.PchipInterpolator(t, y) y8 = f8(tt) # 重心補間 # y9 = interpolate.barycentric_interpolate(t, y, tt)でも結果は同じ f9 = interpolate.BarycentricInterpolator(t, y) y9 = f9(tt) # Krogh により提案された補間法 # y10 = interpolate.Krogh_interpolate(t, y, tt)でも結果は同じ f10 = interpolate.KroghInterpolator(t, y) y10 = f10(tt) plt.figure(figsize=(12, 9)) plt.plot(t, y, "o") plt.plot(tt, y1, "r", label="linear") plt.plot(tt, y2, "b", label="quadratic") plt.plot(tt, y3, "g", label="cubic") plt.plot(tt, y4, "y", label="slinear") plt.plot(tt, y5, "m", label="zero") plt.plot(tt, y6, "c", label="nearest") plt.plot(tt, y7, "--r", label="Akima") plt.plot(tt, y8, "--b", label="Pchip") plt.plot(tt, y9, "--g", label="Barycentric") plt.plot(tt, y10, "--y", label="Krogh") plt.legend()
from scipy import interpolate import numpy as np import matplotlib.pyplot as plt # Parametric Variable t = np.linspace(0, 2 * np.pi, 5) t_dense = np.linspace(0, 2. * np.pi, 100) # We are creating a circle x = np.cos(t) y = np.sin(t) # Make a spline with no boundary conditions: spl_no_bc = interpolate.KroghInterpolator(t, np.c_[x, y]) # Plot the spline and the original points for reference x_new, y_new = spl_no_bc(t_dense).T plt.figure(0) plt.plot(x, y, 'o') plt.plot(x_new, y_new, '-') plt.show(block=False) # Now I'm going to f**k with the lists to set the endpoint first and second derivatives # (this can actually be done at anypoint) # The way to set derivatives is as follows: # To create a new knot in the spline, t must increase, never decrease # The first time a point is in the t list it creates a knot # The second time a point is in the t list it sets the 1st derivative at that knot # The third time a point is in the t list it sets the 2nd derivative at that knot
sys.stderr.write('N = 5: 3d Hermite-interpolation\n')
f = interpolate.PchipInterpolator(t0, x0)
x1 = f(t1)
elif n == 6:
# Akima interpolate
sys.stderr.write('N = 6: Akima-interpolation\n')
f = interpolate.Akima1DInterpolator(t0, x0)
x1 = f(t1)
elif n == 7:
# Barycentric interpolate
sys.stderr.write('N = 7: Barycentric-interpolation\n')
f = interpolate.BarycentricInterpolator(t0, x0)
x1 = f(t1)
elif n == 8:
# Krogh interpolate
sys.stderr.write('N = 8: Krogh-interpolation\n')
f = interpolate.KroghInterpolator(t0, x0)
x1 = f(t1)
elif n == 9:
# lagrange interpolate
sys.stderr.write('N = 9: Lagrange-interpolation\n')
f = interpolate.lagrange(t0, x0)
x1 = f(t1)
else:
sys.stderr.write('! Argument N is not defined\n')
sys.exit()
# Output
out = np.vstack((t1, x1))
np.savetxt(sys.stdout, out.T)
Z3 = poly3(X) plt.figure() plt.plot(x, y, 'ro') plt.plot(X, Z1, 'y', label='Lagrange Interpolate') plt.plot(X, Z2, 'b', label='Cubic Spline') plt.plot(X, Z3, 'r', label='Linear Spline') plt.grid() plt.legend() plt.show() #DD Gener. #EJERCICIO 3 x = np.array([0, 0, 125, 125, 240, 240]) y = np.array([0, 0, 6500, 65, 13000, 70]) pkro1 = si.KroghInterpolator(x[0::2], y[0::2]) pkro2 = si.KroghInterpolator(x[0::2], y[1::2]) X = np.linspace(0, 240, 1001) fig = plt.figure(1) plt.plot(x[0::2], y[0::2], 'ro', label='datos') plt.plot(X, pkro1(X)) plt.grid() plt.show() fig = plt.figure(2) plt.plot(x[1::2], y[1::2], 'ro', label='datos') plt.plot(X, pkro2(X)) plt.grid() plt.show()
y[i] = org_func(x[i])
print('x = ', x)
print('y = ', y)
# Vandermonde行列生成
v_mat = np.zeros((n, n))
for i in range(0, n):
for j in range(0, n):
v_mat[i, j] = x[i]**j
print('V = ')
print(v_mat)
# new_y := V^(^1) * y
v_coef = slinalg.inv(v_mat) @ y
print('v_coef = ', np.flip(v_coef))
# Lagrange補間
l_poly = sipl.lagrange(x, y)
print('l_coef = ', l_poly.coef)
# Kroph補間
k_poly = sipl.KroghInterpolator(x, y)
print('k(x) = ', k_poly(x))
print('k\'(x) = ', k_poly.derivative(x, der=1))
print('k\'\'(x) = ', k_poly.derivative(x, der=2))
# 条件数
print('||mat_a||_2 * ||mat_a^(-1)|| = ',
slinalg.norm(v_mat) * slinalg.norm(slinalg.inv(v_mat)))