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))
def solve_rdft_improved(a, b, x):
(size, _) = a.shape
f = rdft.generate_f(size)
r = rdft.generate_random_r(size)
fr = f.dot(r)
ra = r.dot(a)
(x1, l, u, fra, frb, _) = rdft.rdft_lu_solver_with_lu(a, b, r)
x2 = np.array(x1)
x2 = iteration.iteration_another(a, l, u, fr, b, x2, linalg.cond(fra))
x2 = iteration.remove_imag(x2)
return (x2, fra, fr, ra, x1)
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))
def solve_rdft_improved(a,b,x): (size,_) = a.shape f = rdft.generate_f(size) r = rdft.generate_random_r(size) fr = f.dot(r) ra = r.dot(a) (x1, l, u, fra, frb, _) = rdft.rdft_lu_solver_with_lu(a,b,r) x2 = np.array(x1) x2 = iteration.iteration_another(a, l, u, fr, b, x2, linalg.cond(fra)) x2 = iteration.remove_imag(x2) return (x2, fra, fr, ra, x1)
def solve_rdft_givens(a, b, x):
(size, _) = a.shape
f = rdft.generate_f(size)
r = rdft.generate_r(size) ## === care === ##
g = givens.givens_generation(size)
fr = f.dot(r)
frg = fr.dot(g)
rg = r.dot(g)
(x1, l, u, fra, frb, _) = rdft.rdft_lu_solver_with_lu(a, b, rg)
x2 = np.array(x1)
x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(fra))
x2 = iteration.remove_imag(x2)
return (x2, x1)
def solve_rdft_givens(a,b,x): (size,_) = a.shape f = rdft.generate_f(size) r = rdft.generate_r(size) ## === care === ## g = givens.givens_generation(size) fr = f.dot(r) frg = fr.dot(g) rg = r.dot(g) (x1, l, u, fra, frb, _) = rdft.rdft_lu_solver_with_lu(a,b,rg) x2 = np.array(x1) x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(fra)) x2 = iteration.remove_imag(x2) return (x2, x1)
def solve_rdft_givens_both(a,b,x): (size,_) = a.shape f = rdft.generate_f(size) r = rdft.generate_r(size) g1 = givens.givens_generation(size) g2 = givens.givens_generation(size) fr = f.dot(r) frg = fr.dot(g1) frgb = frg.dot(b) ag = a.dot(g2) frgag = frg.dot(ag) (l,u) = lu.lu(frgag) y = lu.l_step(l,frgb) z = lu.u_step(u,y) x1 = g2.dot(z) x2 = np.array(x1) x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(frgag), g2) x2 = iteration.remove_imag(x2) return (x2, x1)
def solve_rdft_givens_both(a, b, x):
(size, _) = a.shape
f = rdft.generate_f(size)
r = rdft.generate_r(size)
g1 = givens.givens_generation(size)
g2 = givens.givens_generation(size)
fr = f.dot(r)
frg = fr.dot(g1)
frgb = frg.dot(b)
ag = a.dot(g2)
frgag = frg.dot(ag)
(l, u) = lu.lu(frgag)
y = lu.l_step(l, frgb)
z = lu.u_step(u, y)
x1 = g2.dot(z)
x2 = np.array(x1)
x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(frgag),
g2)
x2 = iteration.remove_imag(x2)
return (x2, x1)