NAG Library Routine Document

F08UTF (ZPBSTF)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{UPLO}$ – 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:     $\mathrm{N}$ – INTEGERInput

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

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

3:     $\mathrm{KB}$ – 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:     $\mathrm{BB}\left(\mathbf{LDBB},*\right)$ – COMPLEX (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 $n$ Hermitian 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:     $\mathrm{LDBB}$ – INTEGERInput

On entry: the first dimension of the array BB as declared in the (sub)program from which F08UTF (ZPBSTF) is called.

Constraint: $\mathbf{LDBB}\ge \mathbf{KB}+1$.

6:     $\mathrm{INFO}$ – 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.

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the factorization could not be completed, because the updated element $b\left(i,i\right)$ 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