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 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_getinfo(a, b, x, sample):
mat = np.array(a)
(size, _) = a.shape
result = []
a_cond = linalg.cond(mat)
(a_maxcond, _, a_subcond) = rdft.get_leading_maxcond(mat)
for i in range(0, sample):
# RDFT solve
(x1, fra, fr, ra, x1_orig) = solve_rdft(a, b, x)
(fra_maxcond, _, fra_subcond) = rdft.get_leading_maxcond(fra)
fra_cond = linalg.cond(fra)
err_rdft_iter = linalg.norm(x1 - x)
err_rdft = linalg.norm(x1_orig - x)
# RDFT improved solve
(x1_imp, fra_imp, fr_imp, ra_imp,
x1_imp_orig) = solve_rdft_improved(a, b, x)
(fra_maxcond_imp, _, fra_subcond_imp) = rdft.get_leading_maxcond(fra)
fra_cond_imp = linalg.cond(fra_imp)
err_rdft_imp_iter = linalg.norm(x1_imp - x)
err_rdft_imp = linalg.norm(x1_imp_orig - x)
# RDFT givens solve
(x5_imp, x5_imp_orig) = solve_rdft_givens(a, b, x)
err_rdft_givens_iter = linalg.norm(x5_imp - x)
err_rdft_givens = linalg.norm(x5_imp_orig - x)
# RDFT givens solve
(x7_imp, x7_imp_orig) = solve_rdft_givens_both(a, b, x)
err_rdft_givens_both_iter = linalg.norm(x7_imp - x)
err_rdft_givens_both = linalg.norm(x7_imp_orig - x)
# GAUSS solve
(x2, ga, _, x2_orig) = solve_gauss(a, b, x)
(ga_maxcond, _, ga_subcond) = rdft.get_leading_maxcond(fra)
ga_cond = linalg.cond(ga)
err_gauss_iter = linalg.norm(x2 - x)
err_gauss = linalg.norm(x2_orig - x)
# Partial Pivot
a_float = np.array(a, dtype=np.float64)
b_float = np.array(b, dtype=np.float64)
(x3, pl, pu, swapped_a, swapped_b) = pp.solve(a_float, b_float)
err_pp = linalg.norm(x3 - x)
##x3_i = iteration.iteration(swapped_a, pl, pu, swapped_b, x3, linalg.cond(a_float))
#result make
result.append(
([
a_maxcond / a_cond, fra_maxcond / fra_cond, fra, a_subcond,
fra_subcond, fr, ra, err_rdft_iter, err_rdft,
err_rdft_imp_iter, err_rdft_imp
], [err_rdft_givens_iter, err_rdft_givens
], [err_rdft_givens_both_iter, err_rdft_givens_both],
[ga_maxcond / ga_cond, ga, ga_subcond, err_gauss_iter,
err_gauss], [err_pp]))
return result
def solve_getinfo(a,b,x,sample):
mat = np.array(a)
(size,_) = a.shape
result = []
a_cond = linalg.cond(mat)
(a_maxcond,_,a_subcond) = rdft.get_leading_maxcond(mat)
for i in range(0, sample):
# RDFT solve
(x1, fra, fr, ra, x1_orig) = solve_rdft(a,b,x)
(fra_maxcond,_,fra_subcond) = rdft.get_leading_maxcond(fra)
fra_cond = linalg.cond(fra)
err_rdft_iter = linalg.norm(x1-x)
err_rdft = linalg.norm(x1_orig-x)
# RDFT improved solve
(x1_imp, fra_imp, fr_imp, ra_imp, x1_imp_orig) = solve_rdft_improved(a,b,x)
(fra_maxcond_imp,_,fra_subcond_imp) = rdft.get_leading_maxcond(fra)
fra_cond_imp = linalg.cond(fra_imp)
err_rdft_imp_iter = linalg.norm(x1_imp-x)
err_rdft_imp = linalg.norm(x1_imp_orig-x)
# RDFT givens solve
(x5_imp, x5_imp_orig) = solve_rdft_givens(a,b,x)
err_rdft_givens_iter = linalg.norm(x5_imp-x)
err_rdft_givens = linalg.norm(x5_imp_orig-x)
# RDFT givens solve
(x7_imp, x7_imp_orig) = solve_rdft_givens_both(a,b,x)
err_rdft_givens_both_iter = linalg.norm(x7_imp-x)
err_rdft_givens_both = linalg.norm(x7_imp_orig-x)
# GAUSS solve
(x2, ga, _, x2_orig) = solve_gauss(a,b,x)
(ga_maxcond,_,ga_subcond) = rdft.get_leading_maxcond(fra)
ga_cond = linalg.cond(ga)
err_gauss_iter = linalg.norm(x2-x)
err_gauss = linalg.norm(x2_orig-x)
# Partial Pivot
a_float = np.array(a,dtype=np.float64)
b_float = np.array(b,dtype=np.float64)
(x3, pl, pu, swapped_a, swapped_b) = pp.solve(a_float,b_float)
err_pp = linalg.norm(x3-x)
##x3_i = iteration.iteration(swapped_a, pl, pu, swapped_b, x3, linalg.cond(a_float))
#result make
result.append(([a_maxcond/a_cond, fra_maxcond/fra_cond, fra, a_subcond, fra_subcond, fr, ra, err_rdft_iter, err_rdft,err_rdft_imp_iter,err_rdft_imp],[err_rdft_givens_iter,err_rdft_givens],[err_rdft_givens_both_iter,err_rdft_givens_both],[ga_maxcond/ga_cond, ga, ga_subcond, err_gauss_iter, err_gauss],[err_pp]))
return result
