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I'm looking to use a small numpy array to generate a curve that I can use to predict the height measurement at non-known points. I have several points that I am using to create a poly1d. I know it's possible, we use software that does it just fine at work, and when I used a different image as a tester, plugging the values into Excel and getting the polynomial, it worked fine, but I'm getting pretty drastic measurements on a different calibratable image, I get drastically different results.
Here is the image that I'm trying to measure.
The stick on the front of the pole contains known measurements. From bottom to top, they are 3'6" (42"), 6'6" (78"), 9' 8" (116"), 13' (156)
The picture has been through opencv undistort with a calibrated camera.
This is the function that actually performs the logic. x and y are gathered by cv2 EVENT_LBUTTONUP, and sent to this function.
Checking the lengths of the array is just to help me figure out why this isn't working, trying to generate a line to show the curve fit.
dist = self.firstClick-y
self.yData.append(dist)
if len(self.yData) > 4:
print(self.poly(dist))
if len(self.yData) == 4:
array = np.array(self.xData)
array = np.expand_dims(array, axis=0)
print(self.xData)
print(self.yData)
array=np.append(array, [self.yData], axis=0)
print(array)
x = array[:,0]
y = array[:,1]
self.poly = np.poly1d(np.polyfit(x, y, 2))
poly1d = np.poly1d(self.poly)
xp = np.linspace(-2, 20, 1)
_ = plt.plot(x, y, '.', xp, self.poly(xp), '-', xp, self.poly(xp), '--')
plt.ylim(0,200)
plt.show()
When I run this code, my values tend to quickly go into the tens of thousands when I'm attempting to collect the measurement at 18' 11", (the lowest wire).
Any help would be appreciated, I've been up all night trying to fit this curve.
Edit:
Sorry, I should have included the code used to display and scale the image.
self.img = cv2.imread(imagePath, cv2.IMREAD_ANYCOLOR)
self.scale_percent = 30
self.width = int(self.img.shape[1] * self.scale_percent/100)
self.height = int(self.img.shape[0] * self.scale_percent/100)
dsize = (self.width, self.height)
self.output = cv2.resize(self.img, dsize)
img = self.output
cv2.imshow('image', img)
cv2.setMouseCallback('image', self.click_event)
cv2.waitKey()
I just called this function to display the image and the below code to calibrate the values.
if self.firstClick == 0:
self.firstClick = y
cv2.putText(self.output, "Pole Base", (x, y), font, 1, (255, 255, 0), 2)
cv2.imshow('image', self.output)
elif self.firstClick != 0 and self.secondClick == 0:
self.secondClick = y
print("The difference in first and second clicks is", self.firstClick - self.secondClick)
first = self.firstClick - self.secondClick
inch = first/42
foot = inch*12
self.foot = foot
print("One foot is currently: ", foot)
self.firstLine = 3.5*12
self.secondLine = 6.5*12
self.thirdLine = 9.67*12
self.fourthLine = 13*12
self.xData = np.array([self.firstLine, self.secondLine, self.thirdLine, self.fourthLine])
self.yData.append(self.firstLine)
print(self.firstLine)
print(self.secondLine)
print(self.thirdLine)
print(self.fourthLine)
I have a pan-tilt-zoom camera (changing focal length over time). There is no idea about its base focal length (e.g. focal length in time point 0). However, It is possible to track the change in focal length between frame and another based on some known constraints and assumptions (Doing a SLAM).
If I assume a random focal length (in pixel unit), for example, 1000 pixel. Then, the new focal lengths are tracked frame by frame. Would I get correct results relatively? Would the results (focal lengths) in each frame be correct up to scale to the ground truth focal length?
For pan and tilt, assuming 0 at start would be valid. Although it is not correct, The estimated values of new tili-pan will be correct up to an offset. However, I suspect the estimated focal length will not be even correct up to scale or offset.. Is it correct or not?
For a quick short answer - if pan-tilt-zoom camera is approximated as a thin lens, then this is the relation between distance (z) and focal length (f):
This is just an approximation. Not fully correct. For more precise calculations, see the camera matrix. Focal length is an intrinsic parameter in the camera matrix. Even if not known, it can be calculated using some camera calibration method such as DLT, Zhang's Method and RANSAC. Once you have the camera matrix, focal length is just a small part of it. You get many more useful things along with it.
OpenCV has an inbuilt implementation of Zhang's method. (Look at this documentation for explanations, but code is old and unusable. New up-to-date code below.) You need to take some pictures of a chess board through your camera. Here is some helper code:
import cv2
from matplotlib import pyplot as plt
import numpy as np
from glob import glob
from scipy import linalg
x,y = np.meshgrid(range(6),range(8))
world_points=np.hstack((x.reshape(48,1),y.reshape(48,1),np.zeros((48,1)))).astype(np.float32)
_3d_points=[]
_2d_points=[]
img_paths=glob('./*.JPG') #get paths of all checkerboard images
for path in img_paths:
im=cv2.imread(path)
ret, corners = cv2.findChessboardCorners(im, (6,8))
if ret: #add points only if checkerboard was correctly detected:
_2d_points.append(corners) #append current 2D points
_3d_points.append(world_points) #3D points are always the same
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(_3d_points, _2d_points, (im.shape[1],im.shape[0]), None, None)
print ("Ret:\n",ret)
print ("Mtx:\n",mtx)
print ("Dist:\n",dist)
You might want Undistortion: Correcting for Radial Distortion
# termination criteria
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
# prepare object points, like (0,0,0), (1,0,0), (2,0,0) ....,(6,5,0)
objp = np.zeros((6*8,3), np.float32)
objp[:,:2] = np.mgrid[0:6,0:8].T.reshape(-1,2)
# Arrays to store object points and image points from all the images.
objpoints = [] # 3d point in real world space
imgpoints = [] # 2d points in image plane.
for fname in img_paths:
img = cv2.imread(fname)
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
# Find the chess board corners
ret, corners = cv2.findChessboardCorners(gray, (6,8),None)
# If found, add object points, image points (after refining them)
if ret == True:
objpoints.append(objp)
cv2.cornerSubPix(gray,corners,(11,11),(-1,-1),criteria)
imgpoints.append(corners)
if 'IMG_5456.JPG' in fname:
plt.figure(figsize=(20,10))
img_vis=img.copy()
cv2.drawChessboardCorners(img_vis, (6,8), corners, ret)
plt.imshow(img_vis)
plt.show()
#Calibration
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1],None,None)
# Reprojection Error
tot_error = 0
for i in range(len(objpoints)):
imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(imgpoints[i],imgpoints2, cv2.NORM_L2)/len(imgpoints2)
tot_error += error
print ("Mean Reprojection error: ", tot_error/len(objpoints))
# undistort
mapx,mapy = cv2.initUndistortRectifyMap(mtx,dist,None,newcameramtx,(w,h),5)
dst = cv2.remap(img,mapx,mapy,cv2.INTER_LINEAR)
# crop the image
x,y,w,h = roi
dst = dst[y:y+h, x:x+w]
plt.figure(figsize=(20,10))
#cv2.drawChessboardCorners(dst, (6,8), corners, ret)
plt.imshow(dst)
plt.show()
# Reprojection Error
tot_error = 0
for i in range(len(objpoints)):
imgpoints2, _ = cv2.projectPoints(objpoints[i], rvecs[i], tvecs[i], mtx, dist)
error = cv2.norm(imgpoints[i],imgpoints2, cv2.NORM_L2)/len(imgpoints2)
tot_error += error
print ("Mean Reprojection error: ", tot_error/len(objpoints))
I have an image with dimensions 1024*1024 stored in a HDF5 file, which is treated as a data cube of slice thickness 1, (so that stored dimension is 1024*1024*1) . I used the Niermann HDF5 plug-in (https://github.com/niermann/gms_plugin_hdf5) to import the data. After importing, the data cube became 1*1024*1024, and displayed as 1 pixel wide, 1024 pixels hight and 1024 slices images.
Before considering re-implement the plug-in, I'd like to ask, is there any way to "reshape" the data (like in "Numpy.reshape"), so that the dimensions can be properly treated?
Thanks!
If you don't like icol, irow and these expressions, another elegant solution is to just use the streaming object.
image ReShape3D( image input, number sx, number sy, number sz )
{
// Perform testing
number nPix=1
for ( number d=0; d<input.ImageGetNumDimensions(); d++ )
nPix *= input.ImageGetDimensionsize(d)
if ( sx*sy*sz < nPix ) Throw( "Input image larger than provided shape." )
if ( sx*sy*sz > nPix ) Throw( "Input image smaller than provided shape." )
image reShaped := input.Imageclone()
reShaped.ImageResize(3,sx,sy,sz)
object dStream = NewStreamFromBuffer(0)
ImageWriteImageDataToStream(input,dStream,0)
dStream.StreamSetPos(0,0)
ImageReadImageDataFromStream(reShaped,dStream,0)
return reshaped
}
Image before := RealImage("Before",4,10,20,30)
before = random()
Image after := ReShape3D( before,20,10,30 )
before.ShowImage()
after.ShowImage()
If your input/output array sizes do not match in dimension (such that slice would not work), then you can also 'stream' the data into and out of 1D using the following:
number sx = 4
number sy = 5
number sz = 2
image oneLine := RealImage( "1D",4, sx*sy*sz )
oneLine = icol
oneLine.ShowImage()
image reShape1Dto3D := RealImage( "1D->3D", 4, sx, sy, sz )
reShape1Dto3D = oneLine[icol + iwidth*irow + iwidth*iheight*iplane, 0 ]
reShape1Dto3D.ShowImage()
image reShape3Dto1D := RealImage( "3D->1D", 4, sx*sy*sz )
reShape3Dto1D[icol + iwidth*irow + iwidth*iheight*iplane, 0 ] = reShape1Dto3D
reShape3Dto1D.ShowImage()
The trick here is, that you can address a single value in an image expression using square-brackets. In a 3D image by [X,Y,Z], in a 2D image by [X,Y], and in a 1D images as [X,0]. [*]
The internal variables icol, irow, iplane are replaced by X,Y,Z coordinate of the evaluated expression, whereas iwidth, iheight and idepth are replaced by the dimension sizes of the evaluated expression.
What is the evaluated expression's size? It becomes defined by the only image of "known size" in the line - either left or right side, so that
reShape1Dto3D = oneLine[ icol + iwidth*irow + iwidth*iheight*iplane, 0 ]
becomes a loop over X/Y/Z of all pixels of reShape1Dto3D an the lefthand side of the expression. For each triplet (X/Y/Z) the value is taken from the computed position of oneLine.
Exactly the same is used in
reShape3Dto1D[ icol + iwidth*irow + iwidth*iheight*iplane, 0 ] = reShape1Dto3D
but here the loop is again over the size of reShape1Dto3D, because that is the image of "known size" in the line, even if it is on the righthand side.
* Higher dimensionality is not supported in this way, as [T,L,B,R] is already used for sub-areas.
After few more trial with the examples in "DM scripting handbook", a method is figured out:
image out = in.slice2(0,0,0, 1,1024,1, 2,1024,1)
that is, the output 2d image in the x-y take the projection of y-z plane of the input image using Slice2() command.
I have a bit of code (displayed below) that is supposed to display the stimulus for 10 frames. We need pretty exact display times, so using number of frames is a must instead of core.wait(xx) as the display time won't be as precise.
Instead of drawing the stimuli, and leaving it for another 9 frames - the stimuli is re-drawn for every frame.
# Import what is needed
import numpy as np
from psychopy import visual, event, core, logging
from math import sin, cos
import random, math
win = visual.Window(size=(1366, 768), fullscr=True, screen=0, allowGUI=False, allowStencil=False,
monitor='testMonitor', color=[0,0,0], colorSpace='rgb',
blendMode='avg', useFBO=True,
units='deg')
### Definitions of libraries
'''Parameters :
numpy - python package of numerical computations
visual - where all visual stimulus live
event - code to deal with mouse + keyboard input
core - general function for timing & closing the program
logging - provides function for logging error and other messages to one file
random - options for creating arrays of random numbers
sin & cos - for geometry and trigonometry
math - mathematical operations '''
# this is supposed to record all frames
win.setRecordFrameIntervals(True)
win._refreshThreshold=1/65.0+0.004 #i've got 65Hz monitor and want to allow 4ms tolerance
#set the log module to report warnings to the std output window (default is errors only)
logging.console.setLevel(logging.WARNING)
nIntervals=5
# Create space variables and a window
lineSpaceX = 0.55
lineSpaceY = 0.55
patch_orientation = 45 # zero is vertical, going anti-clockwise
surround_orientation = 90
#Jitter values
g_posJitter = 0.05 #gaussian positional jitter
r_posJitter = 0.05 #random positional jitter
g_oriJitter = 5 #gaussian orientation jitter
r_oriJitter = 5 #random orientation jitter
#create a 1-Dimentional array
line = np.array(range(38)) #with values from (0-37) #possibly not needed 01/04/16 DK
#Region where the rectangular patch would appear
#x_rand=random.randint(1,22) #random.randint(Return random integers from low (inclusive) to high (exclusive).
#y_rand=random.randint(1,25)
x_rand=random.randint(6,13) #random.randint(Return random integers from low (inclusive) to high (inclusive).
y_rand=random.randint(6,16)
#rectangular patch dimensions
width=15
height=12
message = visual.TextStim(win,pos=(0.0,-12.0),text='...Press SPACE to continue...')
fixation = visual.TextStim(win, pos=(0.0,0.0), text='X')
# Initialize clock to record response time
rt_clock = core.Clock()
#Nested loop to draw anti-aliased lines on grid
#create a function for this
def myStim():
for x in xrange(1,33): #32x32 grid. When x is 33 will not execute loop - will stop
for y in xrange(1,33): #When y is 33 will not execute loop - will stop
##Define x & y value (Gaussian distribution-positional jitter)
x_pos = (x-32/2-1/2 )*lineSpaceX + random.gauss(0,g_posJitter) #random.gauss(mean,s.d); -1/2 is to center even-numbered stimuli; 32x32 grid
y_pos = (y-32/2-1/2 )*lineSpaceY + random.gauss(0,g_posJitter)
if (x >= x_rand and x < x_rand+width) and (y >= y_rand and y < y_rand+height): # note only "=" on one side
Line_Orientation = random.gauss(patch_orientation,g_oriJitter) #random.gauss(mean,s.d) - Gaussian func.
else:
Line_Orientation = random.gauss(surround_orientation,g_oriJitter) #random.gauss(mean,s.d) - Gaussian func.
#Line_Orientation = random.gauss(Line_Orientation,g_oriJitter) #random.gauss(mean,s.d) - Gaussian func.
#stimOri = random.uniform(xOri - r_oriJitter, xOri + r_oriJitter) #random.uniform(A,B) - Uniform func.
visual.Line(win, units = "deg", start=(0,0), end=(0.0,0.35), pos=(x_pos,y_pos), ori=Line_Orientation, autoLog=False).draw() #Gaussian func.
for frameN in range (10):
myStim()
win.flip()
print x_rand, y_rand
print keys, rt #display response and reaction time on screen output window
I have tried to use the following code to keep it displayed (by not clearing the buffer). But it just draws over it several times.
for frameN in range(10):
myStim()
win.flip(clearBuffer=False)
I realize that the problem could be because I have .draw() in the function that I have defined def myStim():. However, if I don't include the .draw() within the function - I won't be able to display the stimuli.
Thanks in advance for any help.
If I understand correctly, the problem you are facing is that you have to re-draw the stimulus on every flip, but your current drawing function also recreates the entire (random) stimulus, so:
the stimulus changes on each draw between flips, although you need it to stay constant, and
you get a (on some systems quite massive) performance penalty by re-creating the entire stimulus over and over again.
What you want instead is: create the stimulus once, in its entirety, before presentation; and then have this pre-generated stimulus drawn on every flip.
Since your stimulus consists of a fairly large number of visual elements, I would suggest using a class to store the stimulus in one place.
Essentially, you would replace your myStim() function with this class (note that I stripped out most comments, re-aligned the code a bit, and simplified the if statement):
class MyStim(object):
def __init__(self):
self.lines = []
for x in xrange(1, 33):
for y in xrange(1, 33):
x_pos = ((x - 32 / 2 - 1 / 2) * lineSpaceX +
random.gauss(0, g_posJitter))
y_pos = ((y - 32 / 2 - 1 / 2) * lineSpaceY +
random.gauss(0, g_posJitter))
if ((x_rand <= x < x_rand + width) and
(y_rand <= y < y_rand + height)):
Line_Orientation = random.gauss(patch_orientation,
g_oriJitter)
else:
Line_Orientation = random.gauss(surround_orientation,
g_oriJitter)
current_line = visual.Line(
win, units="deg", start=(0, 0), end=(0.0, 0.35),
pos=(x_pos, y_pos), ori=Line_Orientation,
autoLog=False
)
self.lines.append(current_line)
def draw(self):
[line.draw() for line in self.lines]
What this code does on instantiation is in principle identical to your myStim() function: it creates a set of (random) lines. But instead of drawing them onto the screen right away, they are all collected in the list self.lines, and will remain there until we actually need them.
The draw() method traverses through this list, element by element (that is, line by line), and calls every line's draw() method. Note that the stimuli do not have to be re-created every time we want to draw the whole set, but instead we just draw the already pre-created lines!
To get this working in practice, you first need to instantiate the MyStim class:
myStim = MyStim()
Then, whenever you want to present the stimulus, all you have to do is
myStim.draw()
win.flip()
Here is the entire, modified code that should get you started:
import numpy as np
from psychopy import visual, event, core, logging
from math import sin, cos
import random, math
win = visual.Window(size=(1366, 768), fullscr=True, screen=0, allowGUI=False, allowStencil=False,
monitor='testMonitor', color=[0,0,0], colorSpace='rgb',
blendMode='avg', useFBO=True,
units='deg')
# this is supposed to record all frames
win.setRecordFrameIntervals(True)
win._refreshThreshold=1/65.0+0.004 #i've got 65Hz monitor and want to allow 4ms tolerance
#set the log module to report warnings to the std output window (default is errors only)
logging.console.setLevel(logging.WARNING)
nIntervals=5
# Create space variables and a window
lineSpaceX = 0.55
lineSpaceY = 0.55
patch_orientation = 45 # zero is vertical, going anti-clockwise
surround_orientation = 90
#Jitter values
g_posJitter = 0.05 #gaussian positional jitter
r_posJitter = 0.05 #random positional jitter
g_oriJitter = 5 #gaussian orientation jitter
r_oriJitter = 5 #random orientation jitter
x_rand=random.randint(6,13) #random.randint(Return random integers from low (inclusive) to high (inclusive).
y_rand=random.randint(6,16)
#rectangular patch dimensions
width=15
height=12
message = visual.TextStim(win,pos=(0.0,-12.0),text='...Press SPACE to continue...')
fixation = visual.TextStim(win, pos=(0.0,0.0), text='X')
# Initialize clock to record response time
rt_clock = core.Clock()
class MyStim(object):
def __init__(self):
self.lines = []
for x in xrange(1, 33):
for y in xrange(1, 33):
x_pos = ((x - 32 / 2 - 1 / 2) * lineSpaceX +
random.gauss(0, g_posJitter))
y_pos = ((y - 32 / 2 - 1 / 2) * lineSpaceY +
random.gauss(0, g_posJitter))
if ((x_rand <= x < x_rand + width) and
(y_rand <= y < y_rand + height)):
Line_Orientation = random.gauss(patch_orientation,
g_oriJitter)
else:
Line_Orientation = random.gauss(surround_orientation,
g_oriJitter)
current_line = visual.Line(
win, units="deg", start=(0, 0), end=(0.0, 0.35),
pos=(x_pos, y_pos), ori=Line_Orientation,
autoLog=False
)
self.lines.append(current_line)
def draw(self):
[line.draw() for line in self.lines]
myStim = MyStim()
for frameN in range(10):
myStim.draw()
win.flip()
# Clear the screen
win.flip()
print x_rand, y_rand
core.quit()
Please do note that even with this approach, I am dropping frames on a 3-year-old laptop computer with relatively weak integrated graphics chip. But I suspect a modern, fast GPU would be able to handle this amount of visual objects just fine. In the worst case, you could pre-create a large set of stimuli, save them as a bitmap file via win.saveMovieFrames(), and present them as a pre-loaded SimpleImageStim during your actual study.
I have a conditional probability of z for the given m, p(z|m), where the coefficients are chosen in order that integral over z in the limit of [0,1.5] and m in the range of [18:28] would be equal to one.
def p(z,m):
if (m<21.25):
E = { 'ft':0.55, 'alpha': 2.99, 'z0':0.191, 'km':0.089, 'kt':0.25 }
S = { 'ft':0.39, 'alpha': 2.15, 'z0':0.121, 'km':0.093, 'kt':-0.175 }
I={ 'ft':0.06, 'alpha': 1.77, 'z0':0.045, 'km':0.096, 'kt':-0.9196 }
Evalue=E['ft']*np.exp(-1*E['kt']*(m-18))*z**E['alpha']*np.exp(-1*(z/(E['z0']+E['km']*(m-18)))**E['alpha'])
Svalue=S['ft']*np.exp(-1*S['kt']*(m-18))*z**S['alpha']*np.exp(-1*(z/(S['z0']+S['km']*(m-18)))**S['alpha'])
Ivalue=I['ft']*np.exp(-1*I['kt']*(m-18))*z**I['alpha']*np.exp(-1*(z/(I['z0']+I['km']*(m-18)))**I['alpha'])
value=Evalue+Svalue+Ivalue
elif(m>=21.25):
E = { 'ft':0.25, 'alpha': 1.957, 'z0':0.321, 'km':0.196, 'kt':0.565 }
S = { 'ft':0.61, 'alpha': 1.598, 'z0':0.291, 'km':0.167, 'kt':0.155 }
I = { 'ft':0.14, 'alpha': 0.964, 'z0':0.170, 'km':0.129, 'kt':0.1759 }
Evalue=E['ft']*np.exp(-1*E['kt']*(m-18))*z**E['alpha']*np.exp(-1*(z/(E['z0']+E['km']*(m-18)))**E['alpha'])
Svalue=S['ft']*np.exp(-1*S['kt']*(m-18))*z**S['alpha']*np.exp(-1*(z/(S['z0']+S['km']*(m-18)))**S['alpha'])
Ivalue=I['ft']*np.exp(-1*I['kt']*(m-18))*z**I['alpha']*np.exp(-1*(z/(I['z0']+I['km']*(m-18)))**I['alpha'])
value=Evalue+Svalue+Ivalue
return value
I would like to draw a sample from this distribution, therefore I made a grid points in z and m plane to estimate the cumulative distribution, the cumulative integral over m reaches to one but the cumulative integral over z doesn't give me one in the edge. I don't know why it won't get converged to one?!!
grid_m = np.linspace(18, 28, 1000)
grid_z = np.linspace(0, 1.5, 1000)
dz = np.diff(grid_z[:2])
# get cdf on grid, use cumtrapz
prob_zgm=np.empty((grid_z.shape[0], grid_m.shape[0]),float)
for i in range(grid_z.shape[0]):
for j in range(grid_m.shape[0]):
prob_zgm[i,j]=p(grid_z[i],grid_m[j])
pr = np.column_stack((np.zeros(prob_zgm.shape[0]),prob_zgm))
dm = np.diff(grid_m[:2])
cdf_zgm = integrate.cumtrapz(pr, dx=dm, axis=1)
cdf = integrate.cumtrapz(pr, dx=dz, axis=0)
Which assumption might cause this inconsistency or I compute something wrongly?
Update: The cumulative distribution cdf_zgm is shown as
In the rest, in order to get the inverse of the probability, it is the approach I have used:
# fix bounds of cdf_zgm
cdf_zgm[:, 0] = 0
cdf_zgm[:, -1] = 1
#Interpolate the data using a linear spline to "grid_q" samples
grid_q = np.linspace(0, 1, 200)
grid_qm = np.empty((len(grid_m), len(grid_q)), float)
for i in range(len(grid_m)):
grid_qm[i] = interpolate.interp1d(cdf_zgm[i], grid_z)(grid_q)
# build 2d interpolation for z as function of (q,m)
z_interp = interpolate.interp2d(grid_q, grid_m, grid_qm)
#sample magnitude
ng=20000
r = dist_m.rvs(ng)
rvs_u = np.random.rand(ng)
rvs_z = np.asarray([z_interp(rvs_u[i], r[i]) for i in range(len(rvs_u))]).ravel()
Is it right approach to fix the boundaries of CDF to one?
I don't know what's wrong with that code. But here are a couple of different ideas to try:
(1) Just sum the array elements instead of trying to compute the numerical integrals. It is simpler that way. (Summing the array elements is essentially computing a rectangle rule approximation, which as it turns out, is actually more accurate than the trapezoidal rule.)
(2) Instead of trying to create a whole 2-d array at once, write a function which creates just a 1-d slice of p(z | m) for a given value of m. Then just sum those elements to get the cumulative probability.