NAG Library Routine Document

F08USF (ZHBGST)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     VECT – CHARACTER(1)Input

On entry: indicates whether $X$ is to be returned.

$\mathbf{VECT}=\text{'N'}$

$X$ is not returned.

$\mathbf{VECT}=\text{'V'}$

$X$ is returned.

Constraint: $\mathbf{VECT}=\text{'N'}$ or $\text{'V'}$.

2:     UPLO – CHARACTER(1)Input

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

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

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

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

3:     N – INTEGERInput

On entry: $n$, the order of the matrices $A$ and $B$.

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

4:     KA – INTEGERInput

On entry: if $\mathbf{UPLO}=\text{'U'}$, the number of superdiagonals, $k_a$, of the matrix $A$.

If $\mathbf{UPLO}=\text{'L'}$, the number of subdiagonals, $k_a$, of the matrix $A$.

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

5:     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: $\mathbf{KA}\ge \mathbf{KB}\ge 0$.

6:     AB(LDAB,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the upper or lower triangle of the $n$ by $n$ Hermitian band matrix $A$.

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

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

On exit: the upper or lower triangle of AB is overwritten by the corresponding upper or lower triangle of $C$ as specified by UPLO.

7:     LDAB – INTEGERInput

On entry: the first dimension of the array AB as declared in the (sub)program from which F08USF (ZHBGST) is called.

Constraint: $\mathbf{LDAB}\ge \mathbf{KA}+1$.

8:     BB(LDBB,$*$) – COMPLEX (KIND=nag_wp) arrayInput

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

On entry: the banded split Cholesky factor of $B$ as specified by UPLO, N and KB and returned by F08UTF (ZPBSTF).

9:     LDBB – INTEGERInput

On entry: the first dimension of the array BB as declared in the (sub)program from which F08USF (ZHBGST) is called.

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

10:   X(LDX,$*$) – COMPLEX (KIND=nag_wp) arrayOutput

Note: the second dimension of the array X must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{VECT}=\text{'V'}$ and at least $1$ if $\mathbf{VECT}=\text{'N'}$.

On exit: the $n$ by $n$ matrix $X=S^{-1}Q$, if $\mathbf{VECT}=\text{'V'}$.

If $\mathbf{VECT}=\text{'N'}$, X is not referenced.

11:   LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which F08USF (ZHBGST) is called.

Constraints:

• if $\mathbf{VECT}=\text{'V'}$, $\mathbf{LDX}\ge \max \left(1,\mathbf{N}\right)$;
• if $\mathbf{VECT}=\text{'N'}$, $\mathbf{LDX}\ge 1$.

12:   WORK(N) – COMPLEX (KIND=nag_wp) arrayWorkspace

13:   RWORK(N) – REAL (KIND=nag_wp) arrayWorkspace

14:   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.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f08usfe.f90)

9.2  Program Data

Program Data (f08usfe.d)

9.3  Program Results

Program Results (f08usfe.r)