NAG C Library Function Document

nag_dpotrf (f07fdc)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     order – Nag_OrderTypeInput

On entry: the order parameter specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order $=$ Nag_RowMajor. See Section 2.2.1.4 of the Essential Introduction for a more detailed explanation of the use of this parameter.

Constraint: order $=$ Nag_RowMajor or Nag_ColMajor.

2:     uplo – Nag_UploType Input

On entry: indicates whether the upper or lower triangular part of $A$ is stored and how $A$ is factorized, as follows:

• if  $=$ Nag_Upper, the upper triangular part of $A$ is stored and $A$ is factorized as $U^{\mathit{T}}U$, where $U$ is upper triangular;
• if  $=$ Nag_Lower, the lower triangular part of $A$ is stored and $A$ is factorized as $L{L}^{\mathit{T}}$, where $L$ is lower triangular.

Constraint:  $=$ Nag_Upper or Nag_Lower.

3:     n – Integer Input

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

Constraint: .

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

Note: the dimension, dim, of the array a must be at least .

If order $=$ Nag_ColMajor, the $\left(i,j\right)$th element of the matrix $A$ is stored in  and if order $=$ Nag_RowMajor, the $\left(i,j\right)$th element of the matrix $A$ is stored in .

On entry: the $n$ by $n$ symmetric positive-definite matrix $A$. If  $=$ Nag_Upper, the upper triangle of $A$ must be stored and the elements of the array below the diagonal are not referenced; if  $=$ Nag_Lower, the lower triangle of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the upper or lower triangle of $A$ is overwritten by the Cholesky factor $U$ or $L$ as specified by uplo.

5:     pda – Integer Input

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

Constraint: .

6:     fail – NagError *Input/Output

The NAG error parameter (see the Essential Introduction).

6  Error Indicators and Warnings

NE_INT

On entry, .
Constraint: .

On entry, .
Constraint: .

NE_INT_2

On entry, , .
Constraint: .

NE_POS_DEF

The leading minor of order $〈\mathit{\text{value}}〉$ is not positive-definite and the factorization could not be completed. Hence $A$ itself is not positive-definite. This may indicate an error in forming the matrix $A$. To factorize a symmetric matrix which is not positive-definite, call nag_dsytrf (f07mdc) instead.

NE_ALLOC_FAIL

Memory allocation failed.

NE_BAD_PARAM

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

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 consult NAG for assistance.

7  Accuracy

8  Further Comments

• nag_dpotrs (f07fec) to solve $AX=B$;
• nag_dpocon (f07fgc) to estimate the condition number of $A$;
• nag_dpotri (f07fjc) to compute the inverse of $A$.

9  Example

9.1  Program Text

9.2  Program Data

9.3  Program Results