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main.py
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main.py
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# coding: UTF-8
import math
import cmath
import random
import scipy.linalg as slinalg
import numpy.linalg as linalg
import numpy as np
import rdft
import lib_lu_solve as lib
import iteration
import partial_pivot as pp
#------------------------------------
# function definition
#------------------------------------
def generate_random_matrix(size, val_range):
r = np.zeros((size,size), dtype=np.complex128)
for i in range(0,size):
for j in range(0,size):
r[i,j] = random.uniform(-val_range,val_range)
return r
def generate_random_vector(size,val_range):
r = np.zeros(size, dtype=np.complex128)
for i in range(0,size):
r[i] = random.uniform(-val_range,val_range)
return r
def generate_linear_system(size,val_range):
a = generate_random_matrix(size,val_range)
x = generate_random_vector(size, val_range)
b = a.dot(x)
return (a, b, x)
def error(x1, x2):
dv = x1 - x2
d = linalg.norm(dv)
return d
#------------------------------------
# test code
#------------------------------------
def const_r():
for i in range(0, 50):
size = 200
mat = np.zeros((size,size))
r = rdft.generate_r(size) # use constant r
for j in range(0,size):
for k in range(0,size):
mat[j,k] = random.uniform(-100,100)
f = rdft.generate_f(size)
fr = f.dot(r)
fra = fr.dot(mat)
(a_maxcond,_,_) = rdft.get_leading_maxcond(mat)
(fra_maxcond,_,_) = rdft.get_leading_maxcond(fra)
a_cond = linalg.cond(mat)
fra_cond = linalg.cond(fra)
print("A: ", a_maxcond/a_cond)
print("FRA:", fra_maxcond/fra_cond)
def const_a(sample, size, rand_range):
result = []
mat = np.zeros((size,size))
for j in range(0,size):
for k in range(0,size):
mat[j,k] = random.uniform(-rand_range,rand_range)
for i in range(0, sample):
f = rdft.generate_f(size)
r = rdft.generate_r(size)
fr = f.dot(r)
fra = fr.dot(mat)
(a_maxcond,_,a_subcond) = rdft.get_leading_maxcond(mat)
(fra_maxcond,_,fra_subcond) = rdft.get_leading_maxcond(fra)
a_cond = linalg.cond(mat)
fra_cond = linalg.cond(fra)
result.append([mat, a_maxcond/a_cond, fra_maxcond/fra_cond, fra, a_subcond, fra_subcond])
#print("A: ", a_maxcond/a_cond)
#print("FRA:", fra_maxcond/fra_cond)
return result
def fourier_r(size):
r = np.zeros((size, size), dtype=complex)
for i in range(0,size):
r[i,i] = (cmath.rect(1,(-2.0*math.pi/size)*i*i))
return r
def iteration_checker(size, test_num, val_range, res_opt=0):
for i in range(0,test_num):
(a,b,x) = generate_linear_system(size, val_range)
a_float = np.array(a,dtype=np.float64)
b_float = np.array(b,dtype=np.float64)
x1 = []
l,u = [], []
(x1, l, u, fra, frb, fr) = rdft.rdft_lu_solver_with_lu(a,b)
x0 = x1
x1_after = np.array(x1)
x1_after = iteration.iteration(fra, l, u, frb, x1_after, linalg.cond(fra))
x1_after = iteration.remove_imag(x1_after)
(x2, pl, pu, swapped_a, swapped_b) = pp.solve(a_float,b_float)
x3 = iteration.iteration(swapped_a, pl, pu, swapped_b, x2, linalg.cond(a_float))
#x2 = lib.lu_solver(a,b)
#x2 = lib.direct_solver(a_float,b_float)
#x4 = lib.direct_lu_solver(a,b)
if res_opt == 1:
print("---error---")
print("cond:", linalg.cond(a))
print("[0] error", linalg.norm(b - a.dot(x0)))
print("[1] error", linalg.norm(b - a.dot(x1)))
#print("[2] error", linalg.norm(b - a.dot(x2)))
#print("[3] error", linalg.norm(b - a.dot(x3)))
elif res_opt == 2:
print(str(linalg.cond(a)) + " " +
str(linalg.norm(x - x0)) + " " +
str(linalg.norm(x - x1_before)) + " " +
str(linalg.norm(x - x1_after)) + " " +
str(linalg.norm(x - x5)) + " " +
str(linalg.norm(x - x2)) + " " +
str(linalg.norm(x - x3)))
elif res_opt == 3:
step = []
for j in x4_step:
step.append(linalg.norm(x - j))
print(str(linalg.cond(a)) + " " +
str(linalg.norm(x - x0)) + " " +
str(linalg.norm(x - x1_before)) + " " +
str(linalg.norm(x - x1_after)) + " " +
str(step) + " " +
str(linalg.norm(x - x2))) # partial pivot only
elif res_opt == 4:
print(str(linalg.cond(a)) + " " +
str(linalg.norm(x - x0)) + " " +
str(linalg.norm(x - x2)) + " " +
str(linalg.norm(x - x4))) # partial pivot only
elif res_opt != 1:
print("---error---")
print("cond:", linalg.cond(a))
print("[0] error", linalg.norm(x - x0))
print("[1] error", linalg.norm(x - x1_before)) # remove_imag => iteration
print("[2] error", linalg.norm(x - x1_after)) # iteration => remove_imag
print("[3] error", linalg.norm(x - x2))
#print("[4] error", linalg.norm(x - x3))
#print(x1)
# print("[4] error", linalg.norm(b - a.dot(x4))) # no need because the same result as [3]
#error_check(True)
# size, test_num, val_range, graph
#iteration_checker(100, 100, 100, 4)