# luļ

Syntax

lu(obj, [permute=false])

Arguments

obj is a matrix with no NULL values.

permute is a Boolean value. The default value is false.

Details

Compute pivoted LU decomposition of a matrix.

If permute is false, return 3 matrices (L, U and P) with obj = PāLU. P is a permutation matrix, L is a lower triangular matrix with unit diagonal elements, and U is an upper triangular matrix.

If permute is true, return 2 matrices (L and U) with obj = L*U.

Examples

```\$ A = matrix([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]);

\$ P, L, U = lu(A);
\$ P;
```

#0

#1

#2

#3

0

0

1

0

0

0

0

1

1

0

0

0

0

1

0

0

```\$ L;
```

#0

#1

#2

#3

1

0

0

0

0.875

1

0

0

0.25

0.72

1

0

0.625

0.12

0.233871

1

```\$ U;
```

#0

#1

#2

#3

8

2

6

4

0

6.25

0.75

4.5

0

0

4.96

0.76

0

0

0

0.782258

```\$ L, U = lu(A, true);
\$ L;
```

#0

#1

#2

#3

0.25

0.72

1

0

0.625

0.12

0.233871

1

1

0

0

0

0.875

1

0

0

```\$ U;
```

#0

#1

#2

#3

8

2

6

4

0

6.25

0.75

4.5

0

0

4.96

0.76

0

0

0

0.782258