NAG Library Function Document

nag_zsytri (f07nwc)

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 $\mathrm{Nag\_ColMajor}$.

2:     uplo – Nag_UploTypeInput

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

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

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

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

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

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

3:     n – IntegerInput

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

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

4:     a[$\mathit{dim}$] – ComplexInput/Output

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

On entry: details of the factorization of $A$, as returned by nag_zsytrf (f07nrc).

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

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangle of $A^{-1}$ is stored in the upper triangular part of the array.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangle of $A^{-1}$ is stored in the lower triangular part of the array.

5:     pda – IntegerInput

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

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

6:     ipiv[$\mathit{dim}$] – const IntegerInput

Note: the dimension, dim, 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 nag_zsytrf (f07nrc).

7:     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_SINGULAR

$d\left(⟨\mathit{\text{value}}⟩,⟨\mathit{\text{value}}⟩\right)$ 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 (f07nwce.c)

10.2  Program Data

Program Data (f07nwce.d)

10.3  Program Results

Program Results (f07nwce.r)