SymPy : creating a numpy function from diagonal matrix that takes a numpy array

The creation of a numeric 3 by 3 matrix from a numeric vector is not really a SymPy thing, since no symbols are involved. Consider the following, where the argument d is an array holding the diagonal elements.

def mat(d):    return np.diag(d-4) + 4

The above function returns a 2d NumPy array. To return a SymPy matrix instead, use

def mat(d):    return sp.Matrix(np.diag(d-4) + 4)

When d has extremely small values, the subtraction followed by addition may cause loss of precision: for example, (1e-20 - 4) + 4 evaluates to zero. A safer alternative is

def mat(d):    diagmat = np.diag(d)     return diagmat + np.fromfunction(lambda i, j: (i != j)*4, diagmat.shape)

you can .subs() float values into the respective symbols:

import sympy as spimport numpy as npx1 = sp.Symbol('x1')x2 = sp.Symbol('x2')x3 = sp.Symbol('x3')X = sp.Matrix([x1, x2, x3])myM = 4 * sp.ones(3, 3)smyM=sp.diag(*X) + myM - sp.diag(*np.diag(myM))fcoefs = [(a, f) for a, f in (zip([x1, x2, x3], np.array([0.1,0.2,0.3])))]fmyM = smyM.subs(fcoefs)smyMOut[105]: Matrix([[x1,  4,  4],[ 4, x2,  4],[ 4,  4, x3]])fmyMOut[106]: Matrix([[0.1,   4,   4],[  4, 0.2,   4],[  4,   4, 0.3]])

seems to be a fine sympy.matrices.dense.MutableDenseMatrix Matrix after:

fmyM @ myMOut[107]: Matrix([[32.4, 32.4, 32.4],[32.8, 32.8, 32.8],[33.2, 33.2, 33.2]])

may need conversion to a np.array for full use with numpy

below is some of my code showing more of the pattern I used:

def ysolv(coeffs):    x,y,a,b,c,d,e = symbols('x y a b c d e')    ellipse = a*y**2 + b*x*y + c*x + d*y + e - x**2    y_sols = solve(ellipse, y)    print(*y_sols, sep='\n')    num_coefs = [(a, f) for a, f in (zip([a,b,c,d,e], coeffs))]    y_solsf0 = y_sols[0].subs(num_coefs)    y_solsf1 = y_sols[1].subs(num_coefs)    f0 = lambdify([x], y_solsf0)    f1 = lambdify([x], y_solsf1)    return f0, f1f0, f1 = ysolv(t[0])y0 = [f0(x) for x in xs]y1 = [f1(x) for x in xs]...    

from: https://stackoverflow.com/a/41232062/6876009 (yes, my "feeloutXrange" there is a hack so bad it had to be shown)