NAG Library Routine Document

f07gjf  (dpptri)

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:     $\mathbf{ap}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array ap must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$.

On entry: the Cholesky factor of $A$ stored in packed form, as returned by f07gdf (dpptrf).

On exit: the factorization is overwritten by the $n$ by $n$ matrix $A^{-1}$.

More precisely,

• if $\mathbf{uplo}=\text{'U'}$, the upper triangle of $A^{-1}$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the lower triangle of $A^{-1}$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

4:     $\mathbf{info}$ – 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 (f07gjfe.f90)

10.2

Program Data

Program Data (f07gjfe.d)

10.3

Program Results

Program Results (f07gjfe.r)