I want to optimize x computation based on C, D, and b using sympy and Theano.
However, I have two problems:
1.
I cannot replace (simplify/subs,...) C*DT by G. For instance,
C(0,0)*DT(0,0)+C(0,1)*DT(1,0)must be replaced by G(0,0), since G=C*DT.
2.
I cannot convert final computed x as a Theano function, since it
produces Error:
TypeError: unhashable type: 'MutableDenseMatrix'
My code:
import sympyfrom sympy import *
n, m = 2, 2
C = sympy.Matrix(n, m, lambda i, j: sympy.var('C%d_%d' % (i, j)))
D = sympy.Matrix(n, m, lambda i, j: sympy.var('D%d_%d' % (i, j)))
b = sympy.Matrix(n, 1, lambda i, j: sympy.var('b%d_%d' % (i, j)))
DT = D.transpose()
CDT = C * DT
G = sympy.Matrix(n, n, lambda i, j: sympy.var('G%d_%d' % (i, j)))
# does not work, no change in CDT# CDT.subs(CDT,G)
x=sympy.Matrix(n, 1, lambda i, j:0)
F=sympy.Matrix(n, m, lambda i, j:0)
v=sympy.Matrix(m, 1, lambda i, j:0)
s=sympy.Matrix(1, n, lambda i, j:0)
y=sympy.Matrix(n, 1, lambda i, j:1)
t=sympy.Matrix(1, m, lambda i, j:0)
w = symbols('w')
z = symbols('z')
zeroHelper = Matrix([0])
z = (C.row(0)*transpose(D[0,:]))[0]
x[0,0] = b[0,0]/z
F[0, :]=C[0, :]/z
v = transpose(D[1, :])
y[0] = (-F[0, :]*v)[0]
s[0] = (C[1, :]*DT[:, 0])[0]
for i in range(1, n-1):
print "step: %d" % i
t=C[i, :]-s[0,0:i]*F[0:i, :]
z+=(t*v)[0]
w=b[i,0]-(s[0,0:i]*x[0:i,0])[0]
x[0:i+1,0] += w/z*y[0:i+1,0]
F[0:i+1, :]+= y[0:i+1,0]*t/z
v=DT[:, 0:i+2]*zeroHelper.col_join(y[0:i+1,0])
y[0:i+1,0]=zeroHelper.col_join(y[0:i,0])-F[0:i+1, :]*v
s[0,0:i+1]=zeroHelper.row_join(s[0,0:i])+C[i+1, :]*DT[:, 0:i+1]
t = C[n-1, :] - s[0, 0:n-1] * F[0:n-1, :]
z += (t * v)[0]
w = b[n-1, 0] - (s[0, 0:n-1] * x[0:n-1, 0])[0]
x[0:n , 0] += w / z * y[0:n , 0]
x=sympy.simplify(x)
print (x)
# produces Error
func=theano_function([C,D,b],[x],dtypes={C:'float64',D:'float64',b:'float64'})
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