How to properly cast mpmath matrix to numpy ndarray ( and mpmath.mpf to float)
Question:
I’m working with mpmath python library to gain precision during some computations, but i need to cast the result in a numpy native type.
More precisely i need to cast an mpmath matrix (that contains mpf object types) in an numpy.ndarray (that contains float types).
I have solved the problem with a raw approach:
# My input Matrix:
matr = mp.matrix(
[[ '115.80200375', '22.80402473', '13.69453064', '54.28049263'],
[ '22.80402473', '86.14887381', '53.79999432', '42.78548627'],
[ '13.69453064', '53.79999432', '110.9695448' , '37.24270321'],
[ '54.28049263', '42.78548627', '37.24270321', '95.79388469']])
# multiple precision computation
D = MPDBiteration(matr)
# Create a new ndarray
Z = numpy.ndarray((matr.cols,matr.rows),dtype=numpy.float)
# I fill it pretty "manually"
for i in range(0,matr.rows):
for j in range(0,matr.cols):
Z[i,j] = D[i,j] # or float(D[i,j]) seems to work the same
My question is:
Is there a better/more elegant/easier/clever way to do it?
UPDATE:
Reading again and again the mpmath documentation I’ve found this very useful method: tolist() , it can be used as follows:
Z = np.array(matr.tolist(),dtype=np.float32)
It seems slightly better and elegant (no for loops needed)
Are there better ways to do it? Does my second solution round or chop extra digits?
Answers:
Your second method is to be preferred, but using np.float32 means casting numbers to single precision. For your matrix, this precision is too low: 115.80200375 becomes 115.80200195 due to truncation. You can set double precition explicitly with numpy.float64, or just pass Python’s float type as an argument, which means the same.
Z = numpy.array(matr.tolist(), dtype=float)
or, to keep the matrix structure,
Z = numpy.matrix(matr.tolist(), dtype=float)
You can do that when vectorizing a function (which is what we usually want to do anyway). The following example vectorizes and converts the theta function
import numpy as np
import mpmath as mpm
jtheta3_fn = lambda z,q: mpm.jtheta(n=3,z=z,q=q)
jtheta3_fn = np.vectorize(jtheta3_fn,otypes=(float,))
I’m working with mpmath python library to gain precision during some computations, but i need to cast the result in a numpy native type.
More precisely i need to cast an mpmath matrix (that contains mpf object types) in an numpy.ndarray (that contains float types).
I have solved the problem with a raw approach:
# My input Matrix:
matr = mp.matrix(
[[ '115.80200375', '22.80402473', '13.69453064', '54.28049263'],
[ '22.80402473', '86.14887381', '53.79999432', '42.78548627'],
[ '13.69453064', '53.79999432', '110.9695448' , '37.24270321'],
[ '54.28049263', '42.78548627', '37.24270321', '95.79388469']])
# multiple precision computation
D = MPDBiteration(matr)
# Create a new ndarray
Z = numpy.ndarray((matr.cols,matr.rows),dtype=numpy.float)
# I fill it pretty "manually"
for i in range(0,matr.rows):
for j in range(0,matr.cols):
Z[i,j] = D[i,j] # or float(D[i,j]) seems to work the same
My question is:
Is there a better/more elegant/easier/clever way to do it?
UPDATE:
Reading again and again the mpmath documentation I’ve found this very useful method: tolist() , it can be used as follows:
Z = np.array(matr.tolist(),dtype=np.float32)
It seems slightly better and elegant (no for loops needed)
Are there better ways to do it? Does my second solution round or chop extra digits?
Your second method is to be preferred, but using np.float32 means casting numbers to single precision. For your matrix, this precision is too low: 115.80200375 becomes 115.80200195 due to truncation. You can set double precition explicitly with numpy.float64, or just pass Python’s float type as an argument, which means the same.
Z = numpy.array(matr.tolist(), dtype=float)
or, to keep the matrix structure,
Z = numpy.matrix(matr.tolist(), dtype=float)
You can do that when vectorizing a function (which is what we usually want to do anyway). The following example vectorizes and converts the theta function
import numpy as np
import mpmath as mpm
jtheta3_fn = lambda z,q: mpm.jtheta(n=3,z=z,q=q)
jtheta3_fn = np.vectorize(jtheta3_fn,otypes=(float,))