NAG Library Routine Document

f08uff (dpbstf)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{uplo}$ – Character(1)Input

On entry: indicates whether the upper or lower triangular part of $B$ is stored.

$\mathbf{uplo}=\text{'U'}$

The upper triangular part of $B$ is stored.

$\mathbf{uplo}=\text{'L'}$

The lower triangular part of $B$ is stored.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $B$.

Constraint: $\mathbf{n}\ge 0$.

3:     $\mathbf{kb}$ – IntegerInput

On entry: if $\mathbf{uplo}=\text{'U'}$, the number of superdiagonals, $k_b$, of the matrix $B$.

If $\mathbf{uplo}=\text{'L'}$, the number of subdiagonals, $k_b$, of the matrix $B$.

Constraint: $\mathbf{kb}\ge 0$.

4:     $\mathbf{bb}\left(\mathbf{ldbb},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array bb must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $n$ by $n$ symmetric positive definite band matrix $B$.

The matrix is stored in rows $1$ to $k_b+1$, more precisely,

• if $\mathbf{uplo}=\text{'U'}$, the elements of the upper triangle of $B$ within the band must be stored with element $B_{ij}$ in $\mathbf{bb}\left(k_b+1+i-j,j\right)\text{ for }\max \left(1,j-k_b\right)\le i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the elements of the lower triangle of $B$ within the band must be stored with element $B_{ij}$ in $\mathbf{bb}\left(1+i-j,j\right)\text{ for }j\le i\le \min \left(n,j+k_b\right)\text{.}$

On exit: $B$ is overwritten by the elements of its split Cholesky factor $S$.

5:     $\mathbf{ldbb}$ – IntegerInput

On entry: the first dimension of the array bb as declared in the (sub)program from which f08uff (dpbstf) is called.

Constraint: $\mathbf{ldbb}\ge \mathbf{kb}+1$.

6:     $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}>0$

The factorization could not be completed, because the updated element $b\left(〈\mathit{\text{value}}〉,〈\mathit{\text{value}}〉\right)$ would be the square root of a negative number. Hence $B$ is not positive definite. This may indicate an error in forming the matrix $B$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example