added evaulation for 2d fft
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2194FC747048A7FD
182
cal.py
182
cal.py
@ -1,12 +1,12 @@
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import numpy as np
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from scipy.stats import multivariate_normal
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import matplotlib.pyplot as plt
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import scipy
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import scipy.fftpack as sfft
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import matplotlib.patches as patches
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import matplotlib
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def deg_2_rad(winkel):
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return winkel/180.0 * np.pi
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return winkel / 180.0 * np.pi
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# all units in angstrom
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@ -28,7 +28,6 @@ def mono_2_rutile(c_m, a_m):
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class Lattice:
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def _get_rutile(self, X, Y):
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self.atom_x_rut = X * base_c_r + np.mod(Y, 4) * 0.5 * base_c_r
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self.atom_y_rut = Y * 0.5 * base_a_r
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@ -41,8 +40,7 @@ class Lattice:
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print("A_r: ", offset_a_r, "C_r: ", offset_c_r)
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self.atom_x_mono = offset_a_r + X * \
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base_c_r + np.mod(Y, 4) * 0.5 * base_c_r
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self.atom_x_mono = offset_a_r + X * base_c_r + np.mod(Y, 4) * 0.5 * base_c_r
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self.atom_x_mono[np.mod(X, 2) == 0] -= 2 * offset_a_r
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self.atom_y_mono = offset_c_r + 0.5 * Y * base_a_r
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@ -52,15 +50,15 @@ class Lattice:
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x = np.arange(x_len)
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y = np.arange(y_len)
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X, Y = np.meshgrid(x, y)
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X[np.mod(Y, 4) == 3] = X[np.mod(Y, 4) == 3]-1
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X[np.mod(Y, 4) == 2] = X[np.mod(Y, 4) == 2]-1
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X[np.mod(Y, 4) == 3] = X[np.mod(Y, 4) == 3] - 1
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X[np.mod(Y, 4) == 2] = X[np.mod(Y, 4) == 2] - 1
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assert np.mod(x.size, 2) == 0
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assert np.mod(y.size, 2) == 0
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return X, Y
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def __init__(self, x_len: int, y_len: int):
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X, Y = self._generate_vec(x_len*2, y_len*2)
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X, Y = self._generate_vec(x_len * 2, y_len * 2)
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self._get_mono(X, Y)
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self._get_rutile(X, Y)
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@ -102,6 +100,7 @@ def test_lattice():
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RESOLUTION = 0.1
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CMAP = "Greys"
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def image_from_pos(pos_x, pos_y):
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@ -141,40 +140,175 @@ def gaussian(img):
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x = np.linspace(-ratio, ratio, img.shape[0])
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y = np.linspace(-1, 1, img.shape[1])
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X, Y = np.meshgrid(x, y)
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sigma = 0.3
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z = (1/(2*np.pi*sigma*sigma) * np.exp(-(X**2/(2*sigma**2)
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+ Y**2/(2*sigma**2))))
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sigma = 0.5
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z = (
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1
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/ (2 * np.pi * sigma * sigma)
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* np.exp(-(X**2 / (2 * sigma**2) + Y**2 / (2 * sigma**2)))
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)
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return np.multiply(img, z.T)
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def padding(array, xx, yy):
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"""
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:param array: numpy array
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:param xx: desired height
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:param yy: desirex width
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:return: padded array
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"""
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h = array.shape[0]
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w = array.shape[1]
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a = (xx - h) // 2
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aa = xx - a - h
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b = (yy - w) // 2
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bb = yy - b - w
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return np.pad(array, pad_width=((a, aa), (b, bb)), mode="constant")
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def rect_at_point(x, y, color):
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length_2 = 0.08
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rect = patches.Rectangle(
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(x - length_2, y - length_2),
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2 * length_2,
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2 * length_2,
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linewidth=1,
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edgecolor=color,
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facecolor="none",
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)
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return rect
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def reci_rutile():
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x = np.arange(-2, 3)
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y = np.arange(-2, 3)
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X, Y = np.meshgrid(x, y)
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return (X * 0.22 + Y * 0.44).flatten(), (X * 0.349).flatten()
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def reci_mono():
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x, y = reci_rutile()
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return x + 0.1083, y + 0.1719
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def draw_big_val_rect(img, x, y, x_index, y_index):
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length_2 = 0.08
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pos_x_lower = x - length_2
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pos_x_upper = x + length_2
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pos_y_lower = y - length_2
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pos_y_upper = y + length_2
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x_lower = np.searchsorted(x_index, pos_x_lower)
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x_upper = np.searchsorted(x_index, pos_x_upper)
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y_lower = np.searchsorted(y_index, pos_y_lower)
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y_upper = np.searchsorted(y_index, pos_y_upper)
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img[y_lower:y_upper, x_lower:x_upper] = 1e4
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return img
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def extract_rect(img, x, y, x_index, y_index):
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length_2 = 0.08
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pos_x_lower = x - length_2
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pos_x_upper = x + length_2
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pos_y_lower = y - length_2
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pos_y_upper = y + length_2
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x_lower = np.searchsorted(x_index, pos_x_lower)
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x_upper = np.searchsorted(x_index, pos_x_upper)
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y_lower = np.searchsorted(y_index, pos_y_lower)
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y_upper = np.searchsorted(y_index, pos_y_upper)
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return img[y_lower:y_upper, x_lower:x_upper]
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def main():
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FFT_KWARGS = {"norm": matplotlib.colors.LogNorm(vmin=1), "cmap": "Greys"}
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IMSHOW_WARGS = {"cmap": "Greys"}
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SIZE = 601
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lat = Lattice(10, 10)
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maske = np.ones((10, 10), dtype=bool)
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x, y = lat.get_from_mask(maske)
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img = image_from_pos(x, y)
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fig, [axs,axs2] = plt.subplots(2, 3)
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axs[0].imshow(img)
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img = padding(img, SIZE, SIZE)
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fig, [axs, axs2] = plt.subplots(2, 3)
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axs[0].imshow(img, **IMSHOW_WARGS)
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img = gaussian(img)
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axs[1].imshow(img)
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plt.pause(.1)
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axs[1].imshow(img, **IMSHOW_WARGS)
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plt.pause(0.1)
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freqx, freqy, intens = fft(img)
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axs[2].imshow(intens, extent = (np.min(freqx), np.max(
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freqx), np.min(freqy), np.max(freqy)))
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axs[2].imshow(
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intens,
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extent=(np.min(freqx), np.max(freqx), np.min(freqy), np.max(freqy)),
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**FFT_KWARGS,
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)
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intens_rut = intens
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maske = np.zeros((10, 10), dtype=bool)
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x, y = lat.get_from_mask(maske)
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img = image_from_pos(x, y)
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img = padding(img, SIZE, SIZE)
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axs2[0].imshow(img)
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axs2[0].imshow(img, **IMSHOW_WARGS)
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img = gaussian(img)
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axs2[1].imshow(img)
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plt.pause(.1)
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axs2[1].imshow(img, **IMSHOW_WARGS)
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plt.pause(0.1)
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freqx, freqy, intens = fft(img)
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axs2[2].imshow(intens, extent = (np.min(freqx), np.max(
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freqx), np.min(freqy), np.max(freqy)))
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axs2[2].imshow(
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intens,
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extent=(np.min(freqx), np.max(freqx), np.min(freqy), np.max(freqy)),
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**FFT_KWARGS,
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)
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# Create a Rectangle patch
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# Add the patch to the Axes
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point_x, point_y = reci_rutile()
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for px, py in zip(point_x, point_y):
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rect = rect_at_point(px, py, "r")
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axs[2].add_patch(rect)
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axs[2].text(
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px, py, f"{np.sum(extract_rect(intens_rut, px, py, freqx, freqy)):0.2}"
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)
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rect = rect_at_point(px, py, "r")
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axs2[2].add_patch(rect)
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axs2[2].text(
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px, py, f"{np.sum(extract_rect(intens, px, py, freqx, freqy)):0.2}"
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)
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point_x, point_y = reci_mono()
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for px, py in zip(point_x, point_y):
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# rect = rect_at_point(px, py,"b")
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# axs[2].add_patch(rect)
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rect = rect_at_point(px, py, "b")
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axs2[2].add_patch(rect)
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axs2[2].text(
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px, py, f"{np.sum(extract_rect(intens, px, py, freqx, freqy)):0.2}"
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)
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axs[2].set_xlim(-1.0, 1.0)
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axs[2].set_ylim(-1.0, 1.0)
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axs2[2].set_xlim(-1.0, 1.0)
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axs2[2].set_ylim(-1.0, 1.0)
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plt.figure()
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diff = intens_rut - intens
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plt.imshow(
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diff, extent=(np.min(freqx), np.max(freqx), np.min(freqy), np.max(freqy))
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)
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plt.xlim(-1.0, 1.0)
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plt.ylim(-1.0, 1.0)
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plt.show()
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