NAG Library Routine Document

f07fjf  (dpotri)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{uplo}$ – Character(1)Input

On entry: specifies how $A$ has been factorized.

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

$A=U^{\mathrm{T}}U$, where $U$ is upper triangular.

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

$A=L{L}^{\mathrm{T}}$, where $L$ is lower triangular.

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

2:     $\mathbf{n}$ – IntegerInput

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

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

3:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

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

On entry: the upper triangular matrix $U$ if $\mathbf{uplo}=\text{'U'}$ or the lower triangular matrix $L$ if $\mathbf{uplo}=\text{'L'}$, as returned by f07fdf (dpotrf).

On exit: $U$ is overwritten by the upper triangle of $A^{-1}$ if $\mathbf{uplo}=\text{'U'}$; $L$ is overwritten by the lower triangle of $A^{-1}$ if $\mathbf{uplo}=\text{'L'}$.

4:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f07fjf (dpotri) is called.

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

5:     $\mathbf{info}$ – 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.

$\mathbf{info}>0$

Diagonal element $〈\mathit{\text{value}}〉$ of the Cholesky factor is zero; the Cholesky factor is singular and the inverse of $A$ cannot be computed.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07fjfe.f90)

10.2

Program Data

Program Data (f07fjfe.d)

10.3

Program Results

Program Results (f07fjfe.r)