NAG Library Routine Document

F07QWF (ZSPTRI)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{UPLO}$ – CHARACTER(1)Input

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

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

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

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

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

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

2:     $\mathrm{N}$ – INTEGERInput

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

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

3:     $\mathrm{AP}\left(*\right)$ – COMPLEX (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 factorization of $A$ stored in packed form, as returned by F07QRF (ZSPTRF).

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:     $\mathrm{IPIV}\left(*\right)$ – INTEGER arrayInput

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

On entry: details of the interchanges and the block structure of $D$, as returned by F07QRF (ZSPTRF).

5:     $\mathrm{WORK}\left(\mathbf{N}\right)$ – COMPLEX (KIND=nag_wp) arrayWorkspace

6:     $\mathrm{INFO}$ – 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.

$\mathbf{INFO}>0$

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero. $D$ 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 (f07qwfe.f90)

10.2  Program Data

Program Data (f07qwfe.d)

10.3  Program Results

Program Results (f07qwfe.r)