NAG Library Routine Document

F07VUF (ZTBCON)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{NORM}$ – CHARACTER(1)Input

On entry: indicates whether ${\kappa }_1\left(A\right)$ or ${\kappa }_{\infty }\left(A\right)$ is estimated.

$\mathbf{NORM}=\text{'1'}$ or $\text{'O'}$

${\kappa }_1\left(A\right)$ is estimated.

$\mathbf{NORM}=\text{'I'}$

${\kappa }_{\infty }\left(A\right)$ is estimated.

Constraint: $\mathbf{NORM}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$.

2:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether $A$ is upper or lower triangular.

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

$A$ is upper triangular.

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

$A$ is lower triangular.

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

3:     $\mathrm{DIAG}$ – CHARACTER(1)Input

On entry: indicates whether $A$ is a nonunit or unit triangular matrix.

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

$A$ is a nonunit triangular matrix.

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

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

Constraint: $\mathbf{DIAG}=\text{'N'}$ or $\text{'U'}$.

4:     $\mathrm{N}$ – INTEGERInput

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

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

5:     $\mathrm{KD}$ – INTEGERInput

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

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

6:     $\mathrm{AB}\left(\mathbf{LDAB},*\right)$ – 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 $n$ triangular band matrix $A$.

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

If $\mathbf{DIAG}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

7:     $\mathrm{LDAB}$ – INTEGERInput

On entry: the first dimension of the array AB as declared in the (sub)program from which F07VUF (ZTBCON) is called.

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

8:     $\mathrm{RCOND}$ – REAL (KIND=nag_wp)Output

On exit: an estimate of the reciprocal of the condition number of $A$. RCOND is set to zero if exact singularity is detected or the estimate underflows. If RCOND is less than machine precision, $A$ is singular to working precision.

9:     $\mathrm{WORK}\left(2\times \mathbf{N}\right)$ – COMPLEX (KIND=nag_wp) arrayWorkspace

10:   $\mathrm{RWORK}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayWorkspace

11:   $\mathrm{INFO}$ – 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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f07vufe.f90)

10.2  Program Data

Program Data (f07vufe.d)

10.3  Program Results

Program Results (f07vufe.r)