NAG Library Function Document

nag_dptcon (f07jgc)

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:    $\mathbf{d}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, 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:    $\mathbf{e}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, 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:    $\mathbf{anorm}$ – doubleInput

On entry: the $1$-norm of the original matrix $A$, which may be computed as shown in Section 10. anorm must be computed either before calling nag_dpttrf (f07jdc) or else from a copy of the original matrix $A$.

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

5:    $\mathbf{rcond}$ – double *Output

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

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL

On entry, $\mathbf{anorm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{anorm}\ge 0.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07jgce.c)

10.2

Program Data

Program Data (f07jgce.d)

10.3

Program Results

Program Results (f07jgce.r)