I would like to use scipy.interpolate.interp2d or scipy.interpolate.RectBivariateSpline to interpolate a 2D image, but would like for the interpolation to be monotonic.
Is there an equivalent function that assures monotonicity or a way to force interp2d or RectBivariateSpline to return monotonic interpolations?
I believe I am looking for something similar to PchipInterpolator, but for 2D (or n-dimensional).
The first question is: How do you define monotonicity in 2D (and in higher dimensions)? It seems to be not unique. I searched and found this paper: Piecewise polynomial monotonic interpolation of 2D gridded data (https://hal.inria.fr/hal-01059532/document). Maybe this helps.
The function RectBivariateSpline in scipy is wrapped around fitpack (as I remember, but maybe not). If that is the case, then it wouldn't be monotonic, it is b-spline-based.
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I have a 1-D numpy array of positions(basically an eye-gaze data).
I want to apply sgolay function of matlab in python.
Though i have already seen scipy's savgol_filter and savgol_coeffs,i am not able to understand how to implement it as i am not well versed in it's mathematics.
I have also seen that there is a confusion about whether savgol_filter or savgol_coeffs of python is equivalent to matlab's sgolay function.
I want to differentiate the numpy array once to get velocity and then from velocity array differentiate it again to get acceleration.
The whole procedure is attached in this image
I need to do a Fourier transform of a map in Python. Fast Fourier Transforms expect periodic boundary conditions, but the input map is not periodic. So I need to apply an input filter/weight slowly tapering the map toward zero at the edges. Are there libraries for doing this in python?
My favorite function to apodize a map is the generalized Gaussian (also called 'Super-Gaussian' which is a Gaussian whose exponent is raised to a power P. By setting P to, say, 4 or 6 you get a flat-top pulse which falls off smoothly, which is good for FFT applications where sharp edges always create ripples in conjugate space.
The generalized Gaussian is available on Scipy. Here is a minimal code (Python 3) to apodize a 2D array with a generalized Gaussian. As noted in previous comments, there are dozens of functions which would work just as well.
import numpy as np
from scipy.signal import general_gaussian
# A 128x128 array
array = np.random.rand(128,128)
# Define a general Gaussian in 2D as outer product of the function with itself
window = np.outer(general_gaussian(128,6,50),general_gaussian(128,6,50))
# Multiply
ap_array = window*array
Such tapering is often referred to as a "window".
Scipy has many window functions.
You can use numpy.expand_dims to create the 2D window you want.
Regarding Stefan's comment, apparently the numpy team thinks that including more than arrays was a mistake. I would stick to using scipy for signal processing. Watch out, as they moved quite a bit of functions around in their 1.0 release so older documentation is, well, quite old.
As a final note: a "filter" is typically reserved for multiplications you apply in the Frequency domain, not spatial domain.
Given some coordinates in 3D (x-, y- and z-axes), what I would like to do is to get a polynomial (fifth order). I know how to do it in 2D (for example just in x- and y-direction) via numpy. So my question is: Is it possible to do it also with the third (z-) axes?
Sorry if I missed a question somewhere.
Thank you.
Numpy has functions for multi-variable polynomial evaluation in the polynomial package -- polyval2d, polyval3d -- the problem is getting the coefficients. For fitting, you need the polyvander2d, polyvander3d functions that create the design matrices for the least squares fit. The multi-variable polynomial coefficients thus determined can then be reshaped and used in the corresponding evaluation functions. See the documentation for those functions for more details.
I have a 3D array that I need to integrate numerically using Python. My array is a function of wavelength, depth and time. It is data that I have modelled numerically using another software package and don't have an analytical form of the function, just the 3d array output from the other package. I need to find the triple integral of this array. In Matlab I use trapz(my_array, 3) where 3 is the ndims to integrate over. The Scipy trapz only seems to work on a single integral.
I think I may have 2 options but I am I need some advice.
opt 1. use 3d interpolation in scipy that returns a function handle, do these exist? the 1d version returns a function, and then use scipy.integrate.tplquad to do the integration over the interpolated function where I use the max and in values in my array as the integration limits.
opt 2. use three nested trapz calls like this suggestion for 2d I found on another site. --> sp.trapz(sp.trapz(f, y[np.newaxis,:], axis=1), x, axis=0))
Can't quite get my head around to make either work. Any help/advice would be appreciated. I need to make sure that my integration error is as low as possible.
A recent immigrant to Python and scientific computing with Python. This is a question to avoid any duplication of code that might already exist.
I have a field that is sampled as a function of x and y in a regular grid. I would want to interpolate the data to obtain not only the value of the field at any point on the grid, but also the first and second derivatives. If I interpolate it with bicubic interpolation using interp2d, I can obtain the value of the field.
Does anyone have a suggestion on how to obtain the first and second derivatives of the field using an EXISTING numpy or scipy function?
Thanks!
The scipy.interpolate.interp2d.__call__ method has options dx and dy to evaluate higher derivatives at point (at least since version 0.14.0).