Nsryjdtyk

This is my code. I want to iterate the function f(x) and its derivative matrix simultaneously both in matrix form. How can i do that?

import numpy as np

import sympy as sp



x=sp.Symbol('x')

k=

def m1(x):

    return 4*x**2 + 8*x

def m2(x):

    return 8*x**2 + 6*x

def m3(x):

    return x**2 + 10*x

def m4(x):

    return 10*x**2 + x







def dm1(x):

    return sp.diff(m1(x),x)

def dm2(x):

    return sp.diff(m2(x),x)

def dm3(x):

    return sp.diff(m3(x),x)

def dm4(x):

    return sp.diff(m4(x),x)



def f(x):

    return([[m1(x),m2(x)],[m3(x),m4(x)]]) # function matrix



def k(x):

    return ([[dm1(x),dm2(x)],[dm3(x),dm4(x)]]) # derivative matrix

import numpy as np

import sympy as sp



x=sp.Symbol('x')

k=

tol = 1e-3



def m1(x):

    return 4*x**2 + 8*x

def m2(x):

    return 8*x**2 + 6*x

def m3(x):

    return x**2 + 10*x

def m4(x):

    return 10*x**2 + x





def dm1(val):

    return m1(x).diff(x).subs(x,val)

def dm2(val):

    return m2(x).diff(x).subs(x,val)

def dm3(val):

    return m3(x).diff(x).subs(x,val)

def dm4(val):

    return m4(x).diff(x).subs(x,val)





def f(x):

    return [m1(x), m2(x), m3(x), m4(x)] # function matrix



def k(val):

    return [dm1(val), dm2(val), dm3(val), dm4(val)] # derivative list



x_bar = 5.

x_results = 



for i in range(0,4):

    h=1

    x_temp = x_bar

    print(x_temp)

    while (abs(h) > tol):

        h = -1.*f(x_temp)[i]/k(x_temp)[i]

        print(h)

        x_temp = x_temp + h

    x_results.append(x_temp)

print(x_results)

print(f(x_results[0]))

EDIT: the above solves every function individually and not all together for 1 variable like it would in linear seismic inversion, the following should solve it the correct way:

import numpy as np

import sympy as sp



x=sp.Symbol('x')

k=

tol = 1e-3



def m1(x):

    return 4*x**2 + 8*x

def m2(x):

    return 8*x**2 + 6*x

def m3(x):

    return x**2 + 10*x

def m4(x):

    return 10*x**2 + x





def dm1(val):

    return m1(x).diff(x).subs(x,val)

def dm2(val):

    return m2(x).diff(x).subs(x,val)

def dm3(val):

    return m3(x).diff(x).subs(x,val)

def dm4(val):

    return m4(x).diff(x).subs(x,val)





def f(x):

    return [m1(x), m2(x), m3(x), m4(x)] # function matrix



def k(val):

    return [dm1(val), dm2(val), dm3(val), dm4(val)] # derivative list



x_start = 5.

F = np.array(f(x_start))

dF = np.array(k(x_start))

dx = 1.

x_temp = x_start





while abs(dx) > tol:

    make_square = np.dot(np.transpose(dF),dF)

    print(make_square)

    print(type(dF))

    if make_square is not np.ndarray:

        inverse = 1/make_square

        #inverse = np.linalg.inv(make_square)

    else:

        inverse = np.linalg.inv(make_square)

        #inverse = 1/make_square

    inv_trans = np.dot(inverse,np.transpose(dF))

    dx = -1.*np.dot(inv_trans, F)

    print(dx)

    x_temp = x_temp + dx

    F = np.array(f(x_temp))

    dF = np.array(k(x_temp))

print(x_temp)