I've discovered few typical mistakes that people often do in matlab/gnu octave/python code. Maybe mistake is strong word, not mistakes, but suboptimal usage of environment capabilities (yes, I know mistake sounds better :)). Since I am familiar with python more that mathab, I'll provide few snippets written on python with numpy and scipy libraries, but idea remains the same in matlab also.

### Grid functions.

We need setup geometry and some initial data:

```
import numpy as np
from scitools.numpyutils import meshgrid
h = 0.1
L = H = 1.
x = np.arange(0, L, h)
y = np.arange(0, H, h)
u_analytical = lambda x, y: 2*x + np.exp(y)
```

` `

```
u1 = np.zeros( (len(x), len(y) ) )
for i, x_val in enumerate( x ):
for j, y_val in enumerate( y ):
u1[i][j] = u_analytical(x_val, y_val)
```

` `

```
(xx, yy) = meshgrid(x, y, sparse=False, indexing='ij')
u1_ = u_analytical(xx, yy)
```

### Sparse matrices

First you should use sparse matrices, they rock! Second you should carefully choose sparse matrix format. As example why it should be done I'll quote documentation:Each sparse format has certain advantages and disadvantages. For instance, adding new non-zero entries to aIt is not very hard to choose correct sparse matrix format, especially in numerical computations, where in most cases you know all valuable information about your matrix before computation.lil_matrixis fast, however changing the sparsity pattern of acsr_matrixrequires a significant amount of work. On the other hand, operations such as matrix-vector multiplication and matrix-matrix arithmetic are much faster withcsr_matrixthanlil_matrix. A good strategy is to construct matrices using one format and then convert them to another that is better suited for efficient computation.

The saddest thing is that I saw bad written code in examples given by teachers in their numerical courses.