def LU_decomp(n):
h = 1 / (n + 1)
x = np.linspace(0, 1, n + 2)[1:-1]
q = h**2 * f(x)
A = tridiag(n)
t0 = time.time()
init = pylib()
LUdecomp = init.luDecomp(
A) # LU-decomp., pivot permutation, row interchange (+1/-1)
LUbacksub = init.luBackSubst(LUdecomp[0], LUdecomp[1], q)
T = time.time() - t0
return LUbacksub, T, x
v[1:-1], elapsed_time = TDCMA(f, n, runs)
# Write results to file
with open(DATADIR + "TDCMA.csv", 'a') as file:
file.write('{},{:.2e}\n'.format(n, elapsed_time))
# Run LU decomposition and back substitution
ns = [10**i for i in range(1, lu_exponent + 1)]
for n in ns:
algo_time = 0
for run in range(1, runs + 1):
h = 1. / (n + 1)
x = np.linspace(0, 1, n + 2)
u = f(x) * h**2
A = build_toeplitz(-1, 2, -1, n)
lib = pylib()
start = time.time()
A, index, t = lib.luDecomp(A)
lib.luBackSubst(A, index, u[1:-1])
algo_time += time.time() - start
average_algo_time = algo_time / float(runs)
# Write results to file
with open(DATADIR + "LU_timing.csv", 'a') as file:
file.write('{},{:.2e}\n'.format(n, average_algo_time))
# Write input parameters to file
with open(DATADIR + 'last_run.txt', 'w') as file:
file.write('exponent: {}\n'.format(exponent))
file.write('lu_exponent: {}\n'.format(lu_exponent))
file.write('runs: {}\n'.format(runs))
# coding=utf-8
# Code to test and demonstrate the adaptive-step rk4 found in the library.
#Written by Kyrre Ness Sjøbæk
import computationalLib, numpy
lib = computationalLib.pylib()
import math
def derivsSHM(y, t):
"""
Example derivs for solving SHM equation
x'' + x = 0
which can be expressed as two coupled diff eq's
for the variables x and v:
x' = v
v' = - x
Input:
- Array y[] which contains the values for x, v at time t
- Array t, the time to evaluate at (useful for external forces etc.)
I have chosen the following convention:
- y[0] = x(t)
- y[1] = v(t)
Output:
- Array containing the derivatives at point t,
same convention as with y[]:
return[0] = x'(t)
if len(sys.argv) == 1:
print "Number of integration points:"
n = int(sys.stdin.readline())
print "Integration limits (a, b)"
(a,b) = sys.stdin.readline().split(",")
a = int(a)
b = int(b)
elif len(sys.argv) == 4:
n = int(sys.argv[1])
a = int(sys.argv[2])
b = int(sys.argv[3])
else:
print "Usage: python", sys.argv[0], "N a b"
sys.exit(0)
#Definitions
m = pylib(inputcheck=False,cpp=False)
def integrand(x):
return 4./(1. + x*x)
#Integrate with Gaus-legendre!
(x,w) = m.gausLegendre(a,b,n)
int_gaus = numpy.sum(w*integrand(x))
#Final output
print "integration of f(x) 4/(1+x**2) from",a,"to",b,"with",n,"meshpoints:"
print "Gaus-legendre:", int_gaus
print "Trapezoidal: ", m.trapezoidal(a,b,n, integrand)
print "Simpson: ", m.simpson(a,b,n,integrand)
# coding=utf-8
#Simple matrix inversion example
#Translated to Python by Kyrre Ness Sjøbæk
import numpy, computationalLib, math
myLib = computationalLib.pylib(inputcheck=False, cpp=False)
A = numpy.array([[1,3,4],[3,4,6],[4,6,8]],numpy.double)
print "Initial matrix A:\n", A
#LU-decompose A
matr = A.copy()
(matr,index,d) = myLib.luDecomp(matr);
print "LU-decomposed matrix:\n", matr
print "Index array:\n", index
print "Parity:\n", d
#Invert A column-by-column:
Ainv = numpy.zeros((3,3),numpy.double)
for j in xrange(3):
col = numpy.zeros(3)
col[j] = 1;
Ainv[:,j] = myLib.luBackSubst(matr,index,col)
print "Inverse of A:\n", Ainv
#Test matrix inversion: AxAinv should be identity
test = True
ZERO = 1.0E-10
const_1 = -2.0 * const_2
orb_factor = orb_l * (orb_l + 1)
#Calculate array of potential values
V = numpy.zeros(max_step + 1, numpy.double)
for i in xrange(max_step + 1):
r = r_min + i * step
V[i] = potential(r) + orb_factor / r**2 #(include centrifugal term)
#Calculate elements of the matrix to be diagonalized
d = numpy.zeros(max_step, numpy.double) #diagonal elements
e = numpy.zeros(max_step, numpy.double) #off-diagonal elements
z = numpy.zeros(
(max_step, max_step),
numpy.double) #matrix for eigenvectors (only used as a dummy-argument to
#tqli() in the current version of this program)
for i in xrange(max_step):
d[i] = const_1 + V[i + 1]
e[i] = const_2
z[i, i] = 1 #(identity matrix)
#Diagonalize and obtain eigenvalues. The eigenvalues are stored in d.
computationalLib.pylib(cpp=False).tqli(d, e, z)
#Sort the eigenvalues (smallest to largest)
d = numpy.msort(d)
#Output to file
output()
# coding=utf-8
# Code to test and demonstrate ODE solvers in the library.
# In order to use rk2 or euler instead of rk4, just change rk4 -> rk2
# or rk4 -> euler in the library function calls
#Written by Kyrre Ness Sjøbæk
import computationalLib, numpy
lib = computationalLib.pylib()
def derivsSHM(y,t):
"""
Example derivs for solving SHM equation
x'' + x = 0
which can be expressed as two coupled diff eq's
for the variables x and v:
x' = v
v' = - x
Input:
- Array y[] which contains the values for x, v at time t
- Array t, the time to evaluate at (useful for external forces etc.)
I have chosen the following convention:
- y[0] = x(t)
- y[1] = v(t)
Output:
- Array containing the derivatives at point t,
same convention as with y[]:
return[0] = x'(t)
return[1] = v'(t)
step = (r_max - r_min) / max_step
const_2 = -1.0 / step**2
const_1 = -2.0 * const_2
orb_factor = orb_l * (orb_l + 1)
#Calculate array of potential values
V = numpy.zeros(max_step+1,numpy.double)
for i in xrange(max_step+1):
r = r_min + i*step
V[i] = potential(r) + orb_factor/r**2 #(include centrifugal term)
#Calculate elements of the matrix to be diagonalized
d = numpy.zeros(max_step,numpy.double) #diagonal elements
e = numpy.zeros(max_step,numpy.double) #off-diagonal elements
z = numpy.zeros((max_step,max_step),numpy.double) #matrix for eigenvectors (only used as a dummy-argument to
#tqli() in the current version of this program)
for i in xrange(max_step):
d[i] = const_1 + V[i+1]
e[i] = const_2
z[i,i] = 1 #(identity matrix)
#Diagonalize and obtain eigenvalues. The eigenvalues are stored in d.
computationalLib.pylib(cpp=False).tqli(d,e,z)
#Sort the eigenvalues (smallest to largest)
d = numpy.msort(d)
#Output to file
output()
# coding=utf-8
#Simple matrix inversion example
#Translated to Python by Kyrre Ness Sjøbæk
import numpy, computationalLib, math
myLib = computationalLib.pylib(inputcheck=False, cpp=False)
A = numpy.array([[1, 3, 4], [3, 4, 6], [4, 6, 8]], numpy.double)
print "Initial matrix A:\n", A
#LU-decompose A
matr = A.copy()
(matr, index, d) = myLib.luDecomp(matr)
print "LU-decomposed matrix:\n", matr
print "Index array:\n", index
print "Parity:\n", d
#Invert A column-by-column:
Ainv = numpy.zeros((3, 3), numpy.double)
for j in xrange(3):
col = numpy.zeros(3)
col[j] = 1
Ainv[:, j] = myLib.luBackSubst(matr, index, col)
print "Inverse of A:\n", Ainv
#Test matrix inversion: AxAinv should be identity
test = True
ZERO = 1.0E-10
