NAG Library Routine Document

F07HVF (ZPBRFS)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored and how $A$ is to be factorized.

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

The upper triangular part of $A$ is stored and $A$ is factorized as $U^{\mathrm{H}}U$, where $U$ is upper triangular.

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

The lower triangular part of $A$ is stored and $A$ is factorized as $L{L}^{\mathrm{H}}$, where $L$ is lower triangular.

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

2:     N – INTEGERInput

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

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

3:     KD – INTEGERInput

On entry: $k_d$, the number of superdiagonals or subdiagonals of the matrix $A$.

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

4:     NRHS – INTEGERInput

On entry: $r$, the number of right-hand sides.

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

5:     AB(LDAB,$*$) – COMPLEX (KIND=nag_wp) arrayInput

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

On entry: the $n$ by $n$ original Hermitian positive definite band matrix $A$ as supplied to F07HRF (ZPBTRF).

6:     LDAB – INTEGERInput

On entry: the first dimension of the array AB as declared in the (sub)program from which F07HVF (ZPBRFS) is called.

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

7:     AFB(LDAFB,$*$) – COMPLEX (KIND=nag_wp) arrayInput

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

On entry: the Cholesky factor of $A$, as returned by F07HRF (ZPBTRF).

8:     LDAFB – INTEGERInput

On entry: the first dimension of the array AFB as declared in the (sub)program from which F07HVF (ZPBRFS) is called.

Constraint: $\mathbf{LDAFB}\ge \mathbf{KD}+1$.

9:     B(LDB,$*$) – COMPLEX (KIND=nag_wp) arrayInput

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

On entry: the $n$ by $r$ right-hand side matrix $B$.

10:   LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F07HVF (ZPBRFS) is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

11:   X(LDX,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the $n$ by $r$ solution matrix $X$, as returned by F07HSF (ZPBTRS).

On exit: the improved solution matrix $X$.

12:   LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which F07HVF (ZPBRFS) is called.

Constraint: $\mathbf{LDX}\ge \max \left(1,\mathbf{N}\right)$.

13:   FERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{FERR}\left(\mathit{j}\right)$ contains an estimated error bound for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,r$.

14:   BERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{BERR}\left(\mathit{j}\right)$ contains the component-wise backward error bound $\beta$ for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,r$.

15:   WORK($2\times \mathbf{N}$) – COMPLEX (KIND=nag_wp) arrayWorkspace

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

17:   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 $\mathbf{INFO}=-i$, the $i$th parameter 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 (f07hvfe.f90)

9.2  Program Data

Program Data (f07hvfe.d)

9.3  Program Results

Program Results (f07hvfe.r)