sympy

问题 Given the product of a matrix and a vector A.v with A of shape (m,n) and v of dim n, where m and n are symbols, I need to calculate the Derivative with respect to the matrix elements. I haven't found the way to use a proper vector, so I started with 2 MatrixSymbol : n, m = symbols('n m') j = tensor.Idx('j') i = tensor.Idx('i') l = tensor.Idx('l') h = tensor.Idx('h') A = MatrixSymbol('A', n,m) B = MatrixSymbol('B', m,1) C=A*B Now, if I try to derive with respect to one of A's elements with the

问题 In an expression like import sympy a = sympy.Symbol('a') b = sympy.Symbol('b') x = a + 2*b I'd like to swap a and b to retrieve b + 2*a . I tried y = x.subs([(a, b), (b, a)]) y = x.subs({a: b, b: a}) but neither works; the result is 3*a in both cases as b , for some reason, gets replaced first. Any hints? 回答1: There is a simultaneous argument you can pass to the substitution, which will ensure that all substitutions happen simultaneously and don't interfere with one another as they are doing

问题 I have a homogeneous solution to a simple second-order ODE, which when I try to solve for initial values using Sympy, returns the same solution. It should substitute for y(0) and y'(0) and yield a solution without constants, but does not. Here is the code to set up the equation (it is a spring balance equation, k = spring constant and m = mass). Some redundant symbols which I use elsewhere, sorry. %matplotlib inline from sympy import * m,k, x,t,s,T, omega,A,B = symbols('m k x t s T omega A B'

问题 If I plot a circle with this snippet from sympy import * x, y = symbols('x y') p1 = plot_implicit(Eq(x**2 +y**2, 1),aspect_ratio=(1.,1.)) I will get a figure window like this one Now the aspect ratio is not what I was expecting because I see an ellipse instead of a circle. Moreover, if I change the aspect ratio of the window (dragging the bottom-right corner of the window) I get also a change in the aspect ratio of the plot... The following image is what I get after dragging the corner in

问题 In sympy I have an integral which returns a Piecewise object, e.g. In [2]: from sympy.abc import x,y,z In [3]: test = exp(-x**2/z**2) In [4]: itest = integrate(test,(x,0,oo)) In [5]: itest Out[5]: ⎧ ___ ⎪ ╲╱ π ⋅z │ ⎛ 1 ⎞│ π ⎪ ─────── for │periodic_argument⎜──────────────, ∞⎟│ ≤ ─ ⎪ 2 │ ⎜ 2 ⎟│ 2 ⎪ │ ⎝polar_lift (z) ⎠│ ⎪ ⎪∞ ⎪⌠ ⎨⎮ 2 ⎪⎮ -x ⎪⎮ ─── ⎪⎮ 2 ⎪⎮ z ⎪⎮ ℯ dx otherwise ⎪⌡ ⎪0 ⎩ I would like to extract just the first branch of this piecewise equation, in other words, I would like to be able to

问题 Helle I want to do some summation on a numpy array like this import numpy as np import sympy as sy import cv2 i, j = sy.symbols('i j', Integer=True) #next read some grayscale image to create a numpy array of pixels a = cv2.imread(filename) b = sy.summation(sy.summation(a[i][j], (i,0,1)), (j,0,1)) #double summation but I'm facing with an error. is it possible to handle numpy symbols as numpy arrays'indexes? if not can you sugest me a solution? Thanks. 回答1: You can't use numpy object directly

问题 I want to get rid of an extra substitution which sympy makes when differentiating a user defined composite function. The code is t = Symbol('t') u = Function('u') f = Function('f') U = Symbol('U') pprint(diff(f(u(t),t),t)) The output is: d d ⎛ d ⎞│ ──(f(u(t), t)) + ──(u(t))⋅⎜───(f(ξ₁, t))⎟│ dt dt ⎝dξ₁ ⎠│ξ₁=u(t) I guess it does this because you can't differentiate w.r.t u(t), so this is ok. What I want to do next is to substitute u(t) with an other variable say U and then get rid of the extra

问题 I have a vector X which I created like this: from sympy import * x1 = Symbol('x1') x2 = Symbol('x2') x3 = Symbol('x3') X = Matrix([x1, x2, x3]) Then I also have a matrix myMat which just contains ones: myMat = ones(3, 3) Matrix([ [1, 1, 1], [1, 1, 1], [1, 1, 1]]) Now I would like to replace the diagonal of the matrix by my vector X ; my desired outcome looks like this: Matrix([ [x1, 1, 1], [1, x2, 1], [1, 1, x3]]) I can of course do it in a for-loop like this: for ind, el in enumerate(X):

问题 I am using the following code in sympy : from sympy.physics.secondquant import F, Fd, NO, Commutator from sympy import symbols a, b, c, d = symbols("a,b,c,d") comm = NO(Commutator( Fd(a) * F(b), Fd(c) * F(d) ).doit()) print(comm) # gives me 0 Clearly, this should not be zero. Well, maybe I do not understand sympy . Here is what I want to calculate: [F†_a F_b, F†_c F_d] with not necessarily equal indices a, b, c and d. 来源： https://stackoverflow.com/questions/52227318/does-sympy-give-me-wrong

问题 I have the following issue: I want to lambdify a sympy expression containing parametric integrals like Integral(tanh(a*x),(x,0,1)) . I tried to do a manual implementation like here. What we want is essentially that the integral gets converted to something like: lambda theta: quad(lambda x: g(x,theta), a,b)[0] where g = sp.lambdify((x,param), f, modules='numpy')) Consider the following MWE: import sympy as sp import numpy as np from scipy.integrate import quad def integral_as_quad(function,