CODEWITHSUNDEEP
python-2.7sympy
MarcoMag
MarcoMag

Reputation: 651

How can we multiply all the entries of a Sympy symbolic matrix by another symbol?

I am currently working on sympy symbolic expressions that involve Matrices. I would like to know if it is possible to multiply one such matrix by another symbol. In other words, I would like all the lines of the matrix Bn_Ksi in the following to be multiplied by gN This is what I wanted to try with

    B_Ksi  = (1 / H_KsiKSi) * ( Bt + gN * Bn_Ksi )

The problem comes from:

    ipdb> gN * Bn_Ksi
    *** TypeError: can't multiply sequence by non-int of type 'Symbol'

I also tried using mul and got:

    ipdb> gN.__mul__(Bn_Ksi[1])
    NotImplemented

Here is the part of my code allowing to get the error:

from sympy import *


x, y , Alpha, Ksi = symbols("x y Alpha Ksi")
x1x, x1y, x2x, x2y, x3x, x3y  = symbols("x1x x1y x2x x2y x3x x3y")

N, nx, ny   =  symbols("N nx ny")

# gap function and penalty stiffness 
gN, kpenN = symbols("gN, kpenN")



S = Matrix([x, y])
x1 = Matrix([x1x, x1y])
x2 = Matrix([x2x, x2y])
x3 = Matrix([x3x, x3y])

N = Matrix([nx, ny])


# control points
b0 = x2 + 0.5 * (x1 - x2)
#b3
b3 = x2 + 0.5 * (x3 - x2)
#b1
b1 = b0 + (x2- b0) * Alpha
#b2
b2 = x2 + (b3 - x2) * ( 1 - Alpha)



# Berstein polynomials
# B1 
B0 =  (1./8.) * ((1 - Ksi)**3)
# B1
B1 = (3./8.) * (1 - Ksi)**2 *  (1 + Ksi)
# B3
B2 =  (3./8.) * (1 - Ksi) * (1 + Ksi)**2
#B4
B3 = (1./8.) *(1 + Ksi)**3

# Berstein polynomials first order derivative
B0_Ksi = diff(B0, Ksi)
B1_Ksi = diff(B1, Ksi)
B2_Ksi = diff(B2, Ksi)
B3_Ksi = diff(B3, Ksi)


x_interp = b0 * B0 +  b1 * B1 + b2 * B2 + b3 * B3


# first order derivative 
x_Ksi = diff(x_interp, Ksi)
#second order derivative
x_KsiKsi = diff(x_interp, Ksi, 2)


Bn  = Matrix([N, -B0 * N, -B1 * N, -B2 * N, -B3 * N])

Bn_Ksi  = Matrix([0, B0_Ksi * N, B1_Ksi * N, B2_Ksi * N, B3_Ksi * N])

Bt      = Matrix([x_Ksi, -B0_Ksi * x_Ksi, B1_Ksi * x_Ksi, B2_Ksi * x_Ksi, B3_Ksi * x_Ksi])


H_KsiKSi = x_Ksi.dot(x_Ksi) - gN * N.dot(x_KsiKsi)

B_Ksi  = (1 / H_KsiKSi) * ( Bt + gN * Bn_Ksi )

I am a beginner in sympy and Python in a general way, so I hope that the answer is not pointless. Thanks in advance for your help

Upvotes: 1

Views: 1395

Answers (1)

asmeurer
asmeurer

Reputation: 91580

The elements of your matrix Bn_Ksk are matrices. SymPy Matrix objects are designed to hold scalars, not other matrices. You should either flatten the matrix to contain scalars, or use sympy.BlockMatrix if you want a block matrix (matrix of matrices).

Upvotes: 2

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