NAG C Library Function Document

nag_dpptrf (f07gdc)

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

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

On entry: the symmetric positive-definite matrix $A$, packed by rows or columns. The storage of elements $a_{ij}$ depends on the order and uplo parameters as follows:

• if order $=$ Nag_ColMajor and uplo $=$ Nag_Upper,
            $a_{ij}$ is stored in , for $i\le j$;
• if order $=$ Nag_ColMajor and uplo $=$ Nag_Lower,
            $a_{ij}$ is stored in , for $i\ge j$;
• if order $=$ Nag_RowMajor and uplo $=$ Nag_Upper,
            $a_{ij}$ is stored in , for $i\le j$;
• if order $=$ Nag_RowMajor and uplo $=$ Nag_Lower,
            $a_{ij}$ is stored in , for $i\ge j$.

On exit: the upper or lower triangle of $A$ is overwritten by the Cholesky factor $U$ or $L$ as specified by uplo, using the same packed storage format as described above.

5:     fail – NagError *Input/Output

The NAG error parameter (see the Essential Introduction).

6  Error Indicators and Warnings

NE_INT

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_dsptrf (f07pdc) 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_dpptrs (f07gec) to solve $AX=B$;
• nag_dppcon (f07ggc) to estimate the condition number of $A$;
• nag_dpptri (f07gjc) to compute the inverse of $A$.

9  Example

9.1  Program Text

9.2  Program Data

9.3  Program Results