NAG Library Routine Document

f07jgf (dptcon)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

2:     $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

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

On entry: must contain the $n$ diagonal elements of the diagonal matrix $D$ from the $LD{L}^{\mathrm{T}}$ factorization of $A$.

3:     $\mathbf{e}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

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

On entry: must contain the $\left(n-1\right)$ subdiagonal elements of the unit lower bidiagonal matrix $L$. (e can also be regarded as the superdiagonal of the unit upper bidiagonal matrix $U$ from the $U^{\mathrm{T}}DU$ factorization of $A$.)

4:     $\mathbf{anorm}$ – Real (Kind=nag_wp)Input

On entry: the $1$-norm of the original matrix $A$, which may be computed by calling f06rpf with its argument $\mathbf{norm}=\text{'1'}$. anorm must be computed either before calling f07jdf (dpttrf) or else from a copy of the original matrix $A$.

Constraint: $\mathbf{anorm}\ge 0.0$.

5:     $\mathbf{rcond}$ – Real (Kind=nag_wp)Output

On exit: the reciprocal condition number, $1/{\kappa }_1\left(A\right)=1/\left({‖A‖}_1{‖A^{-1}‖}_1\right)$.

6:     $\mathbf{work}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayWorkspace

7:     $\mathbf{info}$ – 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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07jgfe.f90)

10.2

Program Data

Program Data (f07jgfe.d)

10.3

Program Results

Program Results (f07jgfe.r)