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Jupyter notebook version added
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‎ch06/Program_6.2_eigh.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 6.2: Diagonalization of triatomic systems (eigh.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"import numpy as np\n",
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"from scipy.linalg import eigh # Hermitian eigenvalue solver\n",
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"\n",
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"k = 1.0\n",
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"m1, m2, m3 = 1./4., 2./5., 1./4.\n",
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"A = np.array([[k, -k, 0], [-k, 2*k, -k], [0, -k, k]])\n",
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"B = np.array([[m1, 0, 0], [0, m2, 0], [0, 0, m3]])\n",
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"\n",
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"lamb, u = eigh(A, B) # eigenvalues and eigenvectors \n",
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"print (np.sqrt(lamb)) # print omega"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎ch06/Program_6.3_stringfdm.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 6.3: String under external forces (stringfdm.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"from scipy.linalg import solve # SciPy linear eqn solver\n",
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"import numpy as np, matplotlib.pyplot as plt\n",
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"%matplotlib notebook\n",
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"\n",
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"N, u0, uN= 20, 0., 0. # number of intervals, boundary values\n",
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"x = np.linspace(0., 1., N+1) # grid\n",
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"h, T, f = x[1]-x[0], 1.0, -1.0 # bin size, tension, load\n",
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"\n",
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"A = np.diag([-2.]*(N-1)) # diagonal \n",
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"A += np.diag([1.]*(N-2),1) + np.diag([1.]*(N-2),-1) # off diagonals\n",
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" \n",
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"B = np.array([-h*h*f/T]*(N-1)) # B matrix\n",
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"B[0], B[-1] = B[0]-u0, B[-1]-uN # boundary values, just in case\n",
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"\n",
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"u = solve(A, B) # solve \n",
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"u = np.insert(u, [0, N-1], [u0, uN]) # insert BV at 1st and last pos \n",
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"\n",
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"plt.plot(x, u, label='$f=-1$'), plt.legend(loc='center') # legend \n",
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"plt.xlabel('$x$'), plt.ylabel('$u$'), plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎ch06/Program_6.6_stringfun.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 6.6: Standing waves on a string (stringfun.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"from scipy.linalg import eigh # Hermitian eigenvalue solver\n",
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"import numpy as np, matplotlib.pyplot as plt\n",
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"%matplotlib notebook\n",
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"\n",
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"N = 20 # number of intervals\n",
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"h, s = 1./N, 5 # bin size, skip\n",
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"\n",
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"A = np.diag([-2.]*(N-1)) # diagonal\n",
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"A += np.diag([1.]*(N-2),1) + np.diag([1.]*(N-2),-1) # off diagonals\n",
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"\n",
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"A = -A/(h*h) # solve $-h^{-2} A X = k^2 X$\n",
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"lamb, u = eigh(A) # so eigenvalues lamb = k^2\n",
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"\n",
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"x, sty = np.linspace(0.,1., s*N + 1), ['o','^','s','v']\n",
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"fig, f, pi = plt.figure(), np.sin, np.pi # some aliases\n",
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"print (2*pi/np.sqrt(lamb[:len(sty)])) # wavelength \n",
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"\n",
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"for i in range(1, len(sty)+1):\n",
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" ui = np.insert(u[:,i-1], [0, N-1], [0., 0.]) # insert BV\n",
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" plt.plot(x, f(i*pi*x)*ui[1]/f(i*pi*x[s])) # normalize soln\n",
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" plt.plot(x[::s], ui, sty[i-1], label=repr(i))\n",
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" \n",
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"plt.xlabel('$x$'), plt.ylabel('$u$')\n",
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"plt.legend(loc='lower right'), plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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