Here I am computing the distance d between two points A and B and the
derivatives of d towards the coordinates of A and B
import sympy as sp
sp.init_printing()
X_A=sp.symbols('X_A')
Y_A=sp.symbols('Y_A')
Z_A=sp.symbols('Z_A')
X_B=sp.symbols('X_B')
Y_B=sp.symbols('Y_B')
Z_B=sp.symbols('Z_B')
d=sp.sqrt((X_A-X_B)**2+(Y_A-Y_B)**2+(Z_A-Z_B)**2)
Q=sp.Matrix([d])
R=sp.Matrix([X_A,Y_A,Z_A,X_B,Y_B,Z_B])
dQ_dR=Q.jacobian(R)
J=sp.MatrixSymbol('J',1,6)
print sp.fcode(dQ_dR,J)
This yields the (valid) code:
J(1, 1) = (X_A - X_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 2) = (Y_A - Y_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 3) = (Z_A - Z_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 4) = (-X_A + X_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 5) = (-Y_A + Y_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 6) = (-Z_A + Z_B)/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
unfortunately, this could have been written much more efficiently:
overd=1.0/sqrt((X_A - X_B)**2 + (Y_A - Y_B)**2 + (Z_A
@ - Z_B)**2)
J(1, 1) = (X_A - X_B)*overd
J(1, 2) = (Y_A - Y_B)*overd
J(1, 3) = (Z_A - Z_B)*overd
J(1, 4) = (-X_A + X_B)*overd
J(1, 5) = (-Y_A + Y_B)*overd
J(1, 6) = (-Z_A + Z_B)*overd
or even
J(1, 4) = -J(1,1)
J(1, 5) = -J(1,2)
J(1, 6) = -J(1,3)
Is there any way to have sympy recognise the possible use of such
"temporary variables", or if not, at least enforce when you specify them?
Would you expect compiler optimisation to catch this?
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