Streamplot mgrid - Python - python

I'm working in a project and I have to create a method to generate an image with an background and vector flows. So, I'm using the stream plot from matplotlib.
class ImageData(object):
def __init__(self, width=400, height=400, range_min=-1, range_max=1):
"""
The ImageData constructor
"""
self.width = width
self.height = height
#The values range each pixel can assume
self.range_min = range_min
self.range_max = range_max
#self.data = np.arange(width*height).reshape(height, width)
self.data = []
for i in range(width):
self.data.append([0] * height)
def generate_images_with_streamline(self, file_path, background):
# Getting the vector flow
x_vectors = []
y_vectors = []
for i in range(self.width):
x_vectors.append([0.0] * self.height)
y_vectors.append([0.0] * self.height)
for x in range(1, self.width-1):
for y in range(1, self.height-1):
vector = self.data[x][y]
x_vectors[x][y] = vector[0].item(0)
y_vectors[x][y] = vector[1].item(0)
u_coord = np.array(x_vectors)
v_coord = np.array(y_vectors)
# Static image size
y, x = np.mgrid[-1:1:400j, -1:1:400j]
# Background + vector flow
mg = mpimg.imread(background)
plt.figure()
plt.imshow(mg, extent=[-1, 1, -1, 1])
plt.streamplot(x, y, u_coord, v_coord, color='y', density=2, cmap=plt.cm.autumn)
plt.savefig(file_path+'Streamplot.png')
plt.close()
The problem is 'cause my np.mgrid should vary from -1 to 1 and have the self.width and self.height. But if do:
y, x = np.mgrid[-1:1:self.width, -1:1:self.height]
It doesn't work. And also don't know what this j means, but this seems to be important, 'cause if I this take off the j (even if with an static size), it doesn't work either. So, I'm wondering how I could do this mgrid to be dynamically, following the self size.
Thank you in advance.

Short answer
j is for imaginary part of a complex number, and gives numpy.mgrid the number of values to generate. In your case, here is what you shall write:
y, x = np.mgrid[-1:1:self.width*1j, -1:1:self.height*1j]
Long answer
step value in np.mgrid[start:stop:step] shall be understood as follows:
if step is real, then it is used as stepping from start up to stop, not included.
if step is pure imaginary (e.g. 5j), it is used as the number of steps to return, stop value included.
if step is complex, (e.g. 1+5j), well I must say I don't understand the result...
The j is for an imaginary part.
Examples:
>>> np.mgrid[-1:1:0.5] # values starting at -1, using 0.5 as step, up to 1 (not included)
array([-1. , -0.5, 0. , 0.5])
>>> np.mgrid[-1:1:4j] # values starting at -1 up to +1, 4 values requested
array([-1. , -0.33333333, 0.33333333, 1. ])
>>> np.mgrid[-1:1:1+4j] # ???
array([-1. , -0.3596118 , 0.28077641, 0.92116461])

Related

TextItem scaling in pyqtgraph

I'm having a problem with the font scaling of TextItems in pyqtgraph, like you can see from the following code when I zoom in/zoom out in the main graph the font of the TextItems stays the same while I'm trying to make It scale in the same exact way (rate) of the QGraphicsRectItem. I've tried to look on all the forums I know but I haven't find an answer so I really hope someone has a solution for this.
import sys
import pyqtgraph as pg
from PyQt6.QtWidgets import QApplication, QGraphicsRectItem
from pyqtgraph.Qt import QtCore
app = QApplication(sys.argv)
view = pg.GraphicsView()
l = pg.GraphicsLayout()
view.setCentralItem(l)
view.show()
view.resize(800, 600)
p0 = l.addPlot(0, 0)
p0.showGrid(x=True, y=True, alpha=1.0)
# have no x-axis tickmark below the upper plot (coordinate 0,0)
# without these lines, there will be separate coordinate systems with a gap inbetween
ay0 = p0.getAxis('left') # get handle to y-axis 0
ay0.setStyle(showValues=False) # this will remove the tick labels and reduces gap b/w plots almost to zero
# there will be a double line separating the plot rows
# ay02 = p0.getAxis('right')
# ay02.setStyle(showValues=False)
p0.hideAxis('right')
ax02 = p0.getAxis('top')
ax02.setStyle(showValues=False)
p1 = l.addPlot(0, 1)
# p1.showGrid(x=True, y=True, alpha=1.0)
p1.setYLink(p0)
l.layout.setSpacing(0.5)
l.setContentsMargins(0., 0., 0., 0.)
p1.setFixedWidth(300)
# p1.setFixedHeight(h-451)
p1.setMouseEnabled(x=False)
# ay1 = p1.getAxis('left')
# ay1.setStyle(showValues=False)
ax12 = p1.getAxis('top')
ax12.setStyle(showValues=False)
# ax1 = p1.getAxis('bottom')
# ax1.setStyle(showValues=False)
p1.showAxis('right')
p1.hideAxis('left')
p1.setXRange(0, 6, padding=0) # Then add others like 1 pip
# p1.getAxis('bottom').setTextPen('black')
board = ['123456',
'abcdef',
'ghilmn']
def draw_board(board2):
for j, row in enumerate(board2):
for i, cell in enumerate(row):
rect_w = 1
rect_h = 1
r = QGraphicsRectItem(i, -j+2, rect_w, rect_h)
r.setPen(pg.mkPen((0, 0, 0, 100)))
r.setBrush(pg.mkBrush((50, 50, 200)))
p1.addItem(r)
t_up = pg.TextItem(cell, (255, 255, 255), anchor=(0, 0))
t_up.setPos(i, -j+1+2)
p1.addItem(t_up)
draw_board(board)
if __name__ == '__main__':
if (sys.flags.interactive != 1) or not hasattr(QtCore, 'PYQT_VERSION'):
QApplication.instance().exec()
Scaling of a text item is quite difficult, as you need to consider a constant aspect ratio of the base scale, and the problems related to the way fonts are positioned and drawn relative to the origin point.
Assuming that the displayed text will always be a single character and that the characters used are standard ascii letters and numbers, the only possibility is to cycle through all possible characters, and create properly aligned paths for each of them.
So, for every character:
construct a QPainterPath;
add the letter to the path;
get the max() of that path width and the others;
get the minimum Y and maximum bottom of the bounding rectangle;
translate the path based on all other values computed above (in a separate loop);
Then, you have to set a reference size for the letter (using the maximum width above and the font metrics' height) and get the aspect ratio for that size.
The last part is implemented in the paint() function of the QGraphicsRectItem subclass, which is required to get the proper geometry of the item (if any transformation is applied to a parent item, the item will not know it), and get the maximum rectangle for the reference size based on the current rectangle size.
class NumberRectItem(QGraphicsRectItem):
textSize = None
textPaths = {}
textPath = None
def __init__(self, x, y, width, height, letter=''):
super().__init__(x, y, width, height)
if letter:
if not self.textPaths:
self._buildTextPaths()
self.textPath = self.textPaths[letter]
def _buildTextPaths(self):
from string import ascii_letters, digits
font = QApplication.font()
fm = QFontMetricsF(font)
maxWidth = 0
minY = 1000
maxY = 0
for l in ascii_letters + digits:
path = QPainterPath()
path.addText(0, 0, font, l)
br = path.boundingRect()
maxWidth = max(maxWidth, br.width())
minY = min(minY, br.y())
maxY = max(maxY, br.bottom())
self.textPaths[l] = path
self.__class__.textSize = QSizeF(maxWidth, fm.height())
self.__class__.textRatio = self.textSize.height() / self.textSize.width()
middle = minY + (maxY - minY) / 2
for path in self.textPaths.values():
path.translate(
-path.boundingRect().center().x(),
-middle)
def paint(self, qp, opt, widget=None):
super().paint(qp, opt, widget)
if not self.textPath:
return
qp.save()
qp.resetTransform()
view = widget.parent()
sceneRect = self.mapToScene(self.rect())
viewRect = view.mapFromScene(sceneRect).boundingRect()
rectSize = QSizeF(viewRect.size())
newSize = self.textSize.scaled(rectSize, Qt.KeepAspectRatio)
if newSize.width() == rectSize.width():
# width is the maximum
ratio = newSize.width() / self.textSize.width()
else:
ratio = newSize.height() / self.textSize.height()
transform = QTransform().scale(ratio, ratio)
path = transform.map(self.textPath)
qp.setRenderHint(qp.Antialiasing)
qp.setPen(Qt.NoPen)
qp.setBrush(Qt.white)
qp.drawPath(path.translated(viewRect.center()))
qp.restore()
def draw_board(board2):
for j, row in enumerate(board2):
for i, cell in enumerate(row):
rect_w = 1
rect_h = 1
r = NumberRectItem(i, -j+2, rect_w, rect_h, letter=cell)
r.setPen(pg.mkPen((150, 0, 0, 255)))
r.setBrush(pg.mkBrush((50, 50, 200, 128)))
p1.addItem(r)
Note: for PyQt6 you need to use the full enum names: Qt.GlobalColor.white, etc.

Move points to nearest unoccupied grid position

I have a random distribution of points in 2D space like so:
from sklearn import datasets
import pandas as pd
import numpy as np
arr, labels = datasets.make_moons()
arr, labels = datasets.make_blobs(n_samples=1000, centers=3)
pd.DataFrame(arr, columns=['x', 'y']).plot.scatter('x', 'y', s=1)
I'm trying to assign each of these points to the nearest unoccupied slot on an imaginary hex grid to ensure the points don't overlap. The code I'm using to accomplish this goal produces the plot below. The general idea is to create the hex bins, then iterate over each point and find the minimal radius that allows the algorithm to assign that point to an unoccupied hex bin:
from scipy.spatial.distance import euclidean
def get_bounds(arr):
'''Given a 2D array return the y_min, y_max, x_min, x_max'''
return [
np.min(arr[:,1]),
np.max(arr[:,1]),
np.min(arr[:,0]),
np.max(arr[:,0]),
]
def create_mesh(arr, h=100, w=100):
'''arr is a 2d array; h=number of vertical divisions; w=number of horizontal divisions'''
print(' * creating mesh with size', h, w)
bounds = get_bounds(arr)
# create array of valid positions
y_vals = np.arange(bounds[0], bounds[1], (bounds[1]-bounds[0])/h)
x_vals = np.arange(bounds[2], bounds[3], (bounds[3]-bounds[2])/w)
# create the dense mesh
data = np.tile(
[[0, 1], [1, 0]],
np.array([
int(np.ceil(len(y_vals) / 2)),
int(np.ceil(len(x_vals) / 2)),
]))
# ensure each axis has an even number of slots
if len(y_vals) % 2 != 0 or len(x_vals) % 2 != 0:
data = data[0:len(y_vals), 0:len(x_vals)]
return pd.DataFrame(data, index=y_vals, columns=x_vals)
def align_points_to_grid(arr, h=100, w=100, verbose=False):
'''arr is a 2d array; h=number of vertical divisions; w=number of horizontal divisions'''
h = w = len(arr)/10
grid = create_mesh(arr, h=h, w=w)
# fill the mesh
print(' * filling mesh')
df = pd.DataFrame(arr, columns=['x', 'y'])
bounds = get_bounds(arr)
# store the number of points slotted
c = 0
for site, point in df[['x', 'y']].iterrows():
# skip points not in original points domain
if point.y < bounds[0] or point.y > bounds[1] or \
point.x < bounds[2] or point.x > bounds[3]:
raise Exception('Input point is out of bounds', point.x, point.y, bounds)
# assign this point to the nearest open slot
r_y = (bounds[1]-bounds[0])/h
r_x = (bounds[3]-bounds[2])/w
slotted = False
while not slotted:
bottom = grid.index.searchsorted(point.y - r_y)
top = grid.index.searchsorted(point.y + r_y, side='right')
left = grid.columns.searchsorted(point.x - r_x)
right = grid.columns.searchsorted(point.x + r_x, side='right')
close_grid_points = grid.iloc[bottom:top, left:right]
# store the position in this point's radius that minimizes distortion
best_dist = np.inf
grid_loc = [np.nan, np.nan]
for x, col in close_grid_points.iterrows():
for y, val in col.items():
if val != 1: continue
dist = euclidean(point, (x,y))
if dist < best_dist:
best_dist = dist
grid_loc = [x,y]
# no open slots were found so increase the search radius
if np.isnan(grid_loc[0]):
r_y *= 2
r_x *= 2
# success! report the slotted position to the user
else:
# assign a value other than 1 to mark this slot as filled
grid.loc[grid_loc[0], grid_loc[1]] = 2
df.loc[site, ['x', 'y']] = grid_loc
slotted = True
c += 1
if verbose:
print(' * completed', c, 'of', len(arr), 'assignments')
return df
# plot sample data
df = align_points_to_grid(arr, verbose=False)
df.plot.scatter('x', 'y', s=1)
I'm satisfied with the result of this algorithm, but not with the performance.
Is there a faster solution to this kind of hexbin assignment problem in Python? I feel others with more exposure to the Linear Assignment Problem or the Hungarian Algorithm might have valuable insight into this problem. Any suggestions would be hugely helpful!
It turned out assigning each point to the first available grid spot within its current radius was sufficiently performant.
For others who end up here, my lab wrapped this functionality into a little Python package for convenience. You can pip install pointgrid and then:
from pointgrid import align_points_to_grid
from sklearn import datasets
# create fake data
arr, labels = datasets.make_blobs(n_samples=1000, centers=5)
# get updated point positions
updated = align_points_to_grid(arr)
updated will be a numpy array with the same shape as the input array arr.

How can i append multiple values to numPy array?

I am making a snake game in pygame, and i need to make an array of pygame rects. When i was testing the code to see if the basic idea works, it didn't. When it was supposed to print
[[0,0],
[10,0],
[20,0],
and so on until it got to the biggest x value, and then it would add ten to the y value, it just prints the x values when the y value is always 0. I am new to pygame and python, so any help would be appreciated.
My code:
class Grid:
def __init__(self, gridSize):
self.gridSize = gridSize
self.numX = int(screenX / gridSize)
self.numY = int(screenX / gridSize)
self.xList = []
for y in range(0, self.numY * 10, 10):
for x in range(0, self.numX * 10, 10):
self.xList.append((x,y))
if y == 0:
self.array = np.array(self.xList)
else:
np.append(self.array, self.xList)
self.xList = []
print(self.array)
Most (if not all) numpy commands don't modify their arrays in-place. They return a new array, but the old array stays as it is.
Thus, under your else, you'll need
else:
self.array = np.append(self.array, self.xList)
This will update self.array so that it holds the new, appended array.
It also explains why you're only seeing print-outs for y = 0 and not other values. (You could possibly arrive at this same conclusion by debugging and stepping through your code. Maybe next time? :-) )
For starters, you aren't iterating over the Y range:
self.numY = int(screenX / gridSize) needs to be self.numY = int(screenY/ gridSize)

Improving a numpy implementation of a simple spring network

I wanted a very simple spring system written in numpy. The system would be defined as a simple network of knots, linked by links. I'm not interested in evaluating the system over time, but instead I want to go from an initial state, change a variable (usually move a knot to a new position) and solve the system until it reaches a stable state (last applied force is below a given threshold). The knots have no mass, there's no gravity, the forces are all derived from each link's current lengths/init lengths. And the only "special" variable is that each knot can bet set as "anchored" (doesn't move).
So I wrote this simple solver below, and included a simple example. Jump to the very end for my question.
import numpy as np
from numpy.core.umath_tests import inner1d
np.set_printoptions(precision=4)
np.set_printoptions(suppress=True)
np.set_printoptions(linewidth =150)
np.set_printoptions(threshold=10)
def solver(kPos, kAnchor, link0, link1, w0, cycles=1000, precision=0.001, dampening=0.1, debug=False):
"""
kPos : vector array - knot position
kAnchor : float array - knot's anchor state, 0 = moves freely, 1 = anchored (not moving)
link0 : int array - array of links connecting each knot. each index corresponds to a knot
link1 : int array - array of links connecting each knot. each index corresponds to a knot
w0 : float array - initial link length
cycles : int - eval stops when n cycles reached
precision : float - eval stops when highest applied force is below this value
dampening : float - keeps system stable during each iteration
"""
kPos = np.asarray(kPos)
pos = np.array(kPos) # copy of kPos
kAnchor = 1-np.clip(np.asarray(kAnchor).astype(float),0,1)[:,None]
link0 = np.asarray(link0).astype(int)
link1 = np.asarray(link1).astype(int)
w0 = np.asarray(w0).astype(float)
F = np.zeros(pos.shape)
i = 0
for i in xrange(cycles):
# Init force applied per knot
F = np.zeros(pos.shape)
# Calculate forces
AB = pos[link1] - pos[link0] # get link vectors between knots
w1 = np.sqrt(inner1d(AB,AB)) # get link lengths
AB/=w1[:,None] # normalize link vectors
f = (w1 - w0) # calculate force vectors
f = f[:,None] * AB
# Apply force vectors on each knot
np.add.at(F, link0, f)
np.subtract.at(F, link1, f)
# Update point positions
pos += F * dampening * kAnchor
# If the maximum force applied is below our precision criteria, exit
if np.amax(F) < precision:
break
# Debug info
if debug:
print 'Iterations: %s'%i
print 'Max Force: %s'%np.amax(F)
return pos
Here's some test data to show how it works. In this case i'm using a grid, but in reality this can be any type of network, like a string with many knots, or a mess of polygons...:
import cProfile
# Create a 5x5 3D knot grid
z = np.linspace(-0.5, 0.5, 5)
x = np.linspace(-0.5, 0.5, 5)[::-1]
x,z = np.meshgrid(x,z)
kPos = np.array([np.array(thing) for thing in zip(x.flatten(), z.flatten())])
kPos = np.insert(kPos, 1, 0, axis=1)
'''
array([[-0.5 , 0. , 0.5 ],
[-0.25, 0. , 0.5 ],
[ 0. , 0. , 0.5 ],
...,
[ 0. , 0. , -0.5 ],
[ 0.25, 0. , -0.5 ],
[ 0.5 , 0. , -0.5 ]])
'''
# Define the links connecting each knots
link0 = [0,1,2,3,5,6,7,8,10,11,12,13,15,16,17,18,20,21,22,23,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
link1 = [1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
AB = kPos[link0]-kPos[link1]
w0 = np.sqrt(inner1d(AB,AB)) # this is a square grid, each link's initial length will be 0.25
# Set the anchor states
kAnchor = np.zeros(len(kPos)) # All knots will be free floating
kAnchor[12] = 1 # Middle knot will be anchored
This is what the grid looks like:
If we run my code using this data, nothing will happen since the links aren't pushing or stretching:
print np.allclose(kPos,solver(kPos, kAnchor, link0, link1, w0, debug=True))
# Returns True
# Iterations: 0
# Max Force: 0.0
Now lets move that middle anchored knot up a bit and solve the system:
# Move the center knot up a little
kPos[12] = np.array([0,0.3,0])
# eval the system
new = solver(kPos, kAnchor, link0, link1, w0, debug=True) # positions will have moved
#Iterations: 102
#Max Force: 0.000976603249133
# Rerun with cProfile to see how fast it runs
cProfile.run('solver(kPos, kAnchor, link0, link1, w0)')
# 520 function calls in 0.008 seconds
And here's what the grid looks like after being pulled by that single anchored knot:
Question:
My actual use cases are a little more complex than this example and solve a little too slow for my taste: (100-200 knots with a network anywhere between 200-300 links, solves in a few seconds).
How can i make my solver function run faster? I'd consider Cython but i have zero experience with C. Any help would be greatly appreciated.
Your method, at a cursory glance, appears to be an explicit under-relaxation type of method. Calculate the residual force at each knot, apply a factor of that force as a displacement, repeat until convergence. It's the repeating until convergence that takes the time. The more points you have, the longer each iteration takes, but you also need more iterations for the constraints at one end of the mesh to propagate to the other.
Have you considered an implicit method? Write the equation for the residual force at each non-constrained node, assemble them into a large matrix, and solve in one step. Information now propagates across the entire problem in a single step. As an additional benefit, the matrix you construct should be sparse, which scipy has a module for.
Wikipedia: explicit and implicit methods
EDIT Example of an implicit method matching (roughly) your problem. This solution is linear, so it doesn't take into account the effect of the calculated displacement on the force. You would need to iterate (or use non-linear techniques) to calculate this. Hope it helps.
#!/usr/bin/python3
import matplotlib.pyplot as pp
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import scipy as sp
import scipy.sparse
import scipy.sparse.linalg
#------------------------------------------------------------------------------#
# Generate a grid of knots
nX = 10
nY = 10
x = np.linspace(-0.5, 0.5, nX)
y = np.linspace(-0.5, 0.5, nY)
x, y = np.meshgrid(x, y)
knots = list(zip(x.flatten(), y.flatten()))
# Create links between the knots
links = []
# Horizontal links
for i in range(0, nY):
for j in range(0, nX - 1):
links.append((i*nX + j, i*nX + j + 1))
# Vertical links
for i in range(0, nY - 1):
for j in range(0, nX):
links.append((i*nX + j, (i + 1)*nX + j))
# Create constraints. This dict takes a knot index as a key and returns the
# fixed z-displacement associated with that knot.
constraints = {
0 : 0.0,
nX - 1 : 0.0,
nX*(nY - 1): 0.0,
nX*nY - 1 : 1.0,
2*nX + 4 : 1.0,
}
#------------------------------------------------------------------------------#
# Matrix i-coordinate, j-coordinate and value
Ai = []
Aj = []
Ax = []
# Right hand side array
B = np.zeros(len(knots))
# Loop over the links
for link in links:
# Link geometry
displacement = np.array([ knots[1][i] - knots[0][i] for i in range(2) ])
distance = np.sqrt(displacement.dot(displacement))
# For each node
for i in range(2):
# If it is not a constraint, add the force associated with the link to
# the equation of the knot
if link[i] not in constraints:
Ai.append(link[i])
Aj.append(link[i])
Ax.append(-1/distance)
Ai.append(link[i])
Aj.append(link[not i])
Ax.append(+1/distance)
# If it is a constraint add a diagonal and a value
else:
Ai.append(link[i])
Aj.append(link[i])
Ax.append(+1.0)
B[link[i]] += constraints[link[i]]
# Create the matrix and solve
A = sp.sparse.coo_matrix((Ax, (Ai, Aj))).tocsr()
X = sp.sparse.linalg.lsqr(A, B)[0]
#------------------------------------------------------------------------------#
# Plot the links
fg = pp.figure()
ax = fg.add_subplot(111, projection='3d')
for link in links:
x = [ knots[i][0] for i in link ]
y = [ knots[i][1] for i in link ]
z = [ X[i] for i in link ]
ax.plot(x, y, z)
pp.show()

Generate coordinates inside Polygon

I want to bin the values of polygons to a fine regular grid.
For instance, I have the following coordinates:
data = 2.353
data_lats = np.array([57.81000137, 58.15999985, 58.13000107, 57.77999878])
data_lons = np.array([148.67999268, 148.69999695, 148.47999573, 148.92999268])
My regular grid looks like this:
delta = 0.25
grid_lons = np.arange(-180, 180, delta)
grid_lats = np.arange(90, -90, -delta)
llx, lly = np.meshgrid( grid_lons, grid_lats )
rows = lly.shape[0]
cols = llx.shape[1]
grid = np.zeros((rows,cols))
Now I can find the grid pixel that corresponds to the center of my polygon very easily:
centerx, centery = np.mean(data_lons), np.mean(data_lats)
row = int(np.floor( centery/delta ) + (grid.shape[0]/2))
col = int(np.floor( centerx/delta ) + (grid.shape[1]/2))
grid[row,col] = data
However, there are probably a couple of grid pixels that still intersect with the polygon. Hence, I would like to generate a bunch of coordinates inside my polygon (data_lons, data_lats) and find their corresponding grid pixel as before. Do you a suggestion to generate the coordinates randomly or systematically? I failed, but am still trying.
Note: One data set contains around ~80000 polygons so it has to be really fast (a couple of seconds). That is also why I chose this approach, because it does not account the area of overlap... (like my earlier question Data binning: irregular polygons to regular mesh which is VERY slow)
I worked on a quick and dirty solution by simply calculating the coordinates between corner pixels. Take a look:
dlats = np.zeros((data_lats.shape[0],4))+np.nan
dlons = np.zeros((data_lons.shape[0],4))+np.nan
idx = [0,1,3,2,0] #rearrange the corner pixels
for cc in range(4):
dlats[:,cc] = np.mean((data_lats[:,idx[cc]],data_lats[:,idx[cc+1]]), axis=0)
dlons[:,cc] = np.mean((data_lons[:,idx[cc]],data_lons[:,idx[cc+1]]), axis=0)
data_lats = np.column_stack(( data_lats, dlats ))
data_lons = np.column_stack(( data_lons, dlons ))
Thus, the red dots represent the original corners - the blue ones the intermediate pixels between them.
I can do this one more time and include the center pixel (geo[:,[4,9]])
dlats = np.zeros((data.shape[0],8))
dlons = np.zeros((data.shape[0],8))
for cc in range(8):
dlats[:,cc] = np.mean((data_lats[:,cc], geo[:,4]), axis=0)
dlons[:,cc] = np.mean((data_lons[:,cc], geo[:,9]), axis=0)
data_lats = np.column_stack(( data_lats, dlats, geo[:,4] ))
data_lons = np.column_stack(( data_lons, dlons, geo[:,9] ))
This works really nice, and I can assign each point directly to its corresponding grid pixel like this:
row = np.floor( data_lats/delta ) + (llx.shape[0]/2)
col = np.floor( data_lons/delta ) + (llx.shape[1]/2)
However the final binning now takes ~7sec!!! How can I speed this code up:
for ii in np.arange(len(data)):
for cc in np.arange(data_lats.shape[1]):
final_grid[row[ii,cc],col[ii,cc]] += data[ii]
final_grid_counts[row[ii,cc],col[ii,cc]] += 1
You'll need to test the following approach to see if it is fast enough. First, you should modify all your lats and lons into, to make them (possibly fractional) indices into your grid:
idx_lats = (data_lats - lat_grid_start) / lat_grid step
idx_lons = (data_lons - lon_grid_start) / lon_grid step
Next, we want to split your polygons into triangles. For any convex polygon, you could take the center of the polygon as one vertex of all triangles, and then the vertices of the polygon in consecutive pairs. But if your polygon are all quadrilaterals, it is going to be faster to divide them into only 2 triangles, using vertices 0, 1, 2 for the first, and 0, 2, 3 for the second.
To know if a certain point is inside a triangle, I am going to use the barycentric coordinates approach described here. This first function checks whether a bunch of points are inside a triangle:
def check_in_triangle(x, y, x_tri, y_tri) :
A = np.vstack((x_tri[0], y_tri[0]))
lhs = np.vstack((x_tri[1:], y_tri[1:])) - A
rhs = np.vstack((x, y)) - A
uv = np.linalg.solve(lhs, rhs)
# Equivalent to (uv[0] >= 0) & (uv[1] >= 0) & (uv[0] + uv[1] <= 1)
return np.logical_and(uv >= 0, axis=0) & (np.sum(uv, axis=0) <= 1)
Given a triangle by its vertices, you can get the lattice points inside it, by running the above function on the lattice points in the bounding box of the triangle:
def lattice_points_in_triangle(x_tri, y_tri) :
x_grid = np.arange(np.ceil(np.min(x_tri)), np.floor(np.max(x_tri)) + 1)
y_grid = np.arange(np.ceil(np.min(y_tri)), np.floor(np.max(y_tri)) + 1)
x, y = np.meshgrid(x_grid, y_grid)
x, y = x.reshape(-1), y.reshape(-1)
idx = check_in_triangle(x, y, x_tri, y_tri)
return x[idx], y[idx]
And for a quadrilateral, you simply call this last function twice :
def lattice_points_in_quadrilateral(x_quad, y_quad) :
return map(np.concatenate,
zip(lattice_points_in_triangle(x_quad[:3], y_quad[:3]),
lattice_points_in_triangle(x_quad[[0, 2, 3]],
y_quad[[0, 2, 3]])))
If you run this code on your example data, you will get two empty arrays returned: that's because the order of the quadrilateral points is a surprising one: indices 0 and 1 define one diagonal, 2 and 3 the other. My function above was expecting the vertices to be ordered around the polygon. If you really are doing things this other way, you need to change the second call to lattice_points_in_triangle inside lattice_points_in_quadrilateral so that the indices used are [0, 1, 3] instead of [0, 2, 3].
And now, with that change :
>>> idx_lats = (data_lats - (-180) ) / 0.25
>>> idx_lons = (data_lons - (-90) ) / 0.25
>>> lattice_points_in_quadrilateral(idx_lats, idx_lons)
[array([952]), array([955])]
If you change the resolution of your grid to 0.1:
>>> idx_lats = (data_lats - (-180) ) / 0.1
>>> idx_lons = (data_lons - (-90) ) / 0.1
>>> lattice_points_in_quadrilateral(idx_lats, idx_lons)
[array([2381, 2380, 2381, 2379, 2380, 2381, 2378, 2379, 2378]),
array([2385, 2386, 2386, 2387, 2387, 2387, 2388, 2388, 2389])]
Timing wise this approach is going to be, in my system, about 10x too slow for your needs:
In [8]: %timeit lattice_points_in_quadrilateral(idx_lats, idx_lons)
1000 loops, best of 3: 269 us per loop
So you are looking at over 20 sec. to process your 80,000 polygons.

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