NAG Library Function Document

nag_dgecon (f07agc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or Nag_ColMajor.

2:     norm – Nag_NormTypeInput

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

$\mathbf{norm}=\mathrm{Nag\_OneNorm}$

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

$\mathbf{norm}=\mathrm{Nag\_InfNorm}$

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

Constraint: $\mathbf{norm}=\mathrm{Nag\_OneNorm}$ or $\mathrm{Nag\_InfNorm}$.

3:     n – IntegerInput

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

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

4:     a[$\mathit{dim}$] – const doubleInput

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

The $\left(i,j\right)$th element of the matrix $A$ is stored in

• $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $LU$ factorization of $A$, as returned by nag_dgetrf (f07adc).

5:     pda – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

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

6:     anorm – doubleInput

On entry: if $\mathbf{norm}=\mathrm{Nag\_OneNorm}$, the $1$-norm of the original matrix $A$.

If $\mathbf{norm}=\mathrm{Nag\_InfNorm}$, the $\infty$-norm of the original matrix $A$.

anorm may be computed by calling nag_dge_norm (f16rac) with the same value for the argument norm.

anorm must be computed either before calling nag_dgetrf (f07adc) or else from a copy of the original matrix $A$ (see Section 9).

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

7:     rcond – double *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.

8:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

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

NE_INT

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

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

NE_INT_2

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

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.

NE_REAL

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

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07agce.c)

9.2  Program Data

Program Data (f07agce.d)

9.3  Program Results

Program Results (f07agce.r)