# Interfacing to numpy/scipy¶

In some occasions or for some users it might be interesting to access NGSolve data from python in a fashion which is compatible with numpy and/or scipy. We give a few examples of possible use cases.

## Working with small vectors and dense matrices:¶

see [Vectors and matrices](ngspy-howto-linalg)

## Working with large vectors¶

You can get a “view” on an NGSolve-BaseVector using .FV() (which will give you a FlatVector) combined with .NumPy() which will give a numpy array which operates on the NGSolve-Vector-Data. For example the following works, assuming b to be an NGSolve-Vector:

```
b.FV().NumPy()[:] = abs(b.FV().NumPy()) - 1.0
```

which will give you the component-wise operation (absolute value minus one) applied on the vector b. During this operation data does not need to be copied.

## Working with sparse matrices¶

You can access the sparse matrix information of a BaseMatrix using

```
rows,cols,vals = a.mat.COO()
```

Note that a bilinear form with flag symmetric==True will only give you one half of the matrix. These information can be put into a standard scipy-matrix, e.g. with

```
import scipy.sparse as sp
A = sp.csr_matrix((vals,(rows,cols)))
```

You can use this, for instance, to examine the sparsity pattern of your matrix:

```
import matplotlib.pylab as plt
plt.spy(A)
plt.show()
```

or to compute the condition number (note that we export to a dense matrix here):

```
import numpy as np
np.linalg.cond(A.todense())
```

## Using iterative solvers from scipy¶

To use iterative solvers from scipy we have to wrap a LinearOperator around the NGSolve-matrix. The crucial component is the application of matrix vector product. Here is a very simple example where the scipy-cg-solver is used to solve the linear system (no preconditioner, no Dirichlet-dofs):

```
import scipy
import scipy.sparse.linalg
tmp1 = f.vec.CreateVector()
tmp2 = f.vec.CreateVector()
def matvec(v):
tmp1.FV().NumPy()[:] = v
tmp2.data = a.mat * tmp1
return tmp2.FV().NumPy()
A = scipy.sparse.linalg.LinearOperator( (a.mat.height,a.mat.width), matvec)
u.vec.FV().NumPy()[:], succ = scipy.sparse.linalg.cg(A, f.vec.FV().NumPy())
```

You can also use a sparse matrix format from python to run to previous example, see above. However, for preconditioning actions a sparse matrix is not necessarily set up such that the LinearOperator is often more useful.