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今天给大家介绍一个实用的在线小工具，矩阵微积分在线生成 Python/Latex 代码。
链接：
http://www.matrixcalculus.org/matrixCalculus
Python代码如下：
"""
d/dx x'*A*x + c*sin(y)'*x = 2*A*x+c*sin(y)
A is a matrix
c is a scalar
y is a vector
x is a vector
"""
from __future__ import division, print_function, absolute_import
import numpy as np
def fAndG(A, c, x, y):
assert(type(A) == np.ndarray)
dim = A.shape
assert(len(dim) == 2)
A_rows = dim[0]
A_cols = dim[1]
if type(c) == np.ndarray:
dim = c.shape
assert(dim == (1, ))
assert(type(x) == np.ndarray)
dim = x.shape
assert(len(dim) == 1)
x_rows = dim[0]
assert(type(y) == np.ndarray)
dim = y.shape
assert(len(dim) == 1)
y_rows = dim[0]
assert(A_cols == x_rows == y_rows == A_rows)
t_0 = np.dot(A, x)
t_1 = np.sin(y)
functionValue = (np.dot(x, t_0) + (c * np.dot(t_1, x)))
gradient = ((2 * t_0) + (c * t_1))
return functionValue, gradient
def generateRandomData():
A = np.random.randn(3, 3)
c = np.random.randn(1)
x = np.random.randn(3)
y = np.random.randn(3)
return A, c, x, y
if __name__ == '__main__':
A, c, x, y = generateRandomData()
functionValue, gradient = fAndG(A, c, x, y)
print('functionValue = ', functionValue)
print('gradient = ', gradient)
Latex代码如下：
\documentclass[12pt]{article}
\usepackage{amsmath,amsthm,amssymb}
\begin{document}
function:
\begin{align*}
f = x^\top \cdot A\cdot x+c\cdot \sin(y)^\top \cdot x
\end{align*}
gradient:
\begin{align*}
\frac{\partial f}{\partial x} = 2\cdot A\cdot x+c\cdot \sin(y)
\end{align*}
\end{document}
