Question

import pandas as pd
import numpy as np
import statsmodels.api as sm
from pandas.tools.plotting import scatter_matrix

# First we will load the mtcars dataset and do a scatterplot matrix

mtcars = sm.datasets.get_rdataset('mtcars')
df = pd.DataFrame(mtcars.data)
scatter_matrix(df[[0,2,3,4,5]], alpha=0.3, figsize=(8, 8), diagonal='kde', marker='o');

# Next we will do the 3D mesh

xgv = np.arange(-1.5, 1.5, 0.1)
ygv = np.arange(-3, 3, 0.1)
[X,Y] = np.meshgrid(xgv, ygv)
V = np.exp(-(X**2 + Y**2))

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, V, rstride=1, cstride=1, cmap=plt.cm.jet, linewidth=0.25)
plt.title('Gridded Data Set');

# And finally, the matrix manipulations

import scipy

A = np.reshape(np.arange(1, 5), (2,2))
b = np.array([36, 88])
ans = scipy.linalg.solve(A, b)
P, L, U = scipy.linalg.lu(A)
Q, R = scipy.linalg.qr(A)
D, V = scipy.linalg.eig(A)
print 'ans =\n', ans, '\n'
print 'L =\n', L, '\n'
print "U =\n", U, '\n'
print "P = \nPermutation Matrix\n", P, '\n'
print 'Q =\n', Q, '\n'
print "R =\n", R, '\n'
print 'V =\n', V, '\n'
print "D =\nDiagonal matrix\n", np.diag(abs(D)), '\n'

ans =
[ 16.  10.]

L =
[[ 1.          0.        ]
 [ 0.33333333  1.        ]]

U =
[[ 3.          4.        ]
 [ 0.          0.66666667]]

P =
Permutation Matrix
[[ 0.  1.]
 [ 1.  0.]]

Q =
[[-0.31622777 -0.9486833 ]
 [-0.9486833   0.31622777]]

R =
[[-3.16227766 -4.42718872]
 [ 0.         -0.63245553]]

V =
[[-0.82456484 -0.41597356]
 [ 0.56576746 -0.90937671]]

D =
Diagonal matrix
[[ 0.37228132  0.        ]
 [ 0.          5.37228132]]