Cara menggunakan python fast interpolation

Introduction to Natural Language Processing in Python

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There are several general facilities available in SciPy for interpolation and smoothing for data in 1, 2, and higher dimensions. The choice of a specific interpolation routine depends on the data: whether it is one-dimensional, is given on a structured grid, or is unstructured. One other factor is the desired smoothness of the interpolator. In short, routines recommended for interpolation can be summarized as follows:

kind

routine

continuity

comment

1D

linear

piecewise continuous

comes from numpy

cubic spline

2nd derivative

monotone cubic spline

1st derivative

non-overshooting

non-cubic spline

(k-1)th derivative

k=3 is equivalent to

nearest

kind=’nearest’, ‘previous’, ‘next’

N-D curve

nearest, linear, spline

(k-1)th derivative

use N-dim y array

N-D regular (rectilinear) grid

nearest

method=’nearest’

linear

method=’linear’

splines

2nd derivatives

method=’cubic’, ‘quintic’

monotone splines

1st derivatives

method=’pchip’

N-D scattered

nearest

alias:

linear

cubic (2D only)

1st derivatives

radial basis function

For data smoothing, for 1- and 2-D data using cubic splines, based on the FORTRAN library FITPACK.

Additionally, routines are provided for interpolation / smoothing using with several kernels.

Futher details are given in the links below.

• 1-D interpolation
• Piecewise polynomials and splines
• Smoothing splines
• Multivariate data interpolation on a regular grid (RegularGridInterpolator)
• Scattered data interpolation (numpy.interp1)
• Extrapolation tips and tricks

Given a masked NumPy array of dimensionality (frames, points, 2) representing a video of frames frames, where in each frame points (x, y) points are being tracked.

I would like to interpolate this video from frames frames to any number of frames, very fast, hopefully with a cubic spline, but any other continuous interpolation will work OK too.

The naive solution I have implemented splits the array into 2 arrays of dimensions (frames, points) for the X array and Y array. Then, I transpose the array to (points, frames). For each row (single point over-time) I map it to an index and value, so the array (frames, points, 2)0 becomes:

(frames, points, 2)1

I feed this to a (frames, points, 2)2, and run on my new array which is for example (frames, points, 2)3 and get a new (frames, points, 2)4 array that I then convert back to NumPy.

This process removes the masks for intermittent frames (which is fine with me).

Current performance: Small array of shape (frames, points, 2)5 to (frames, points, 2)6

• Cubic interpolation 0.115 seconds
• Linear interpolation 0.112 seconds

Note!

This is a masked array, like (frames, points, 2)0. so it is important to incorporate the masks in the interpolation in order to not have 0 values (the data array looks like (frames, points, 2)8!