# Linear Algebra

## Overview

LLA works with matrices, that is arrays of rank 2, with all numerical values. Categorical variables could be integer coded if you need to.

## Basic Usage

`lla`

requires a BLAS and LAPACK shared library. These may be available via
your operating systems package manager, or you can download OpenBLAS, which includes precompiled binaries for MS Windows.

#### Note

LLA relies on CFFI to locate the BLAS & LAPPACK shared library. In most cases, this means CFFI will use the system default search paths. If you encounter errors in loading the library, consult the CFFI documentation. For MS Windows, the certain way to successfully load the DLL is to ensure that the library is on the`PATH`

.
You can also configure the path by setting the `cl-user::*lla-configuration*`

variable like so:

```
(defvar *lla-configuration*
'(:libraries ("s:/src/lla/lib/libopenblas.dll")))
```

Use the location specific to your system.

To load `lla`

:

```
(asdf:load-system :lla)
(use-package 'lla) ;access to the symbols
```

## Examples

To make working with matrices easier, we’re going to use the matrix-shorthand library. Load it like so:

```
(asdf:load-system :num-utils)
(use-package :num-utils.matrix-shorthand)
```

### Matrix Multiplication

`mm`

is the matrix multiplication function. It is generic and can operate on both regular arrays and ‘wrapped’ array types, e.g. hermitian or triangular. In this example we’ll multiple an array by a vector. `mx`

is the short-hand way of defining a matrix, and `vec`

a vector.

```
(let ((a (mx 'lla-double
(1 2)
(3 4)
(5 6)))
(b2 (vec 'lla-double 1 2)))
(mm a b2))
; #(5.0d0 11.0d0 17.0d0)
```

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