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

Constraint: $n \geq 0$ .
2: $d [\dim]$ – doubleInput/Output: Note: the dimension, dim, of the array d must be at least $\max (1, n)$ .

On entry: must contain the $n$ diagonal elements of the matrix $A$ .

On exit: is overwritten by the $n$ diagonal elements of the diagonal matrix $D$ from the $L D L^{T}$ factorization of $A$ .
3: $e [\dim]$ – doubleInput/Output: Note: the dimension, dim, of the array e must be at least $\max (1, n - 1)$ .

On entry: must contain the $(n - 1)$ subdiagonal elements of the matrix $A$ .

On exit: is overwritten by the $(n - 1)$ subdiagonal elements of the lower bidiagonal matrix $L$ . (e can also be regarded as containing the $(n - 1)$ superdiagonal elements of the upper bidiagonal matrix $U$ .)
4: $fail$ – NagError *Input/Output: The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_MAT_NOT_POS_DEF: The leading minor of order $n$ is not positive definite, the factorization was completed, but $d [n - 1] \leq 0$ .

The leading minor of order $〈value〉$ is not positive definite, the factorization could not be completed.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7 Accuracy

The computed factorization satisfies an equation of the form

A + E = L D L^{T},

where

{‖E‖}_{\infty} = O (ε) {‖A‖}_{\infty}

and

ε

is the machine precision.

Following the use of this function, nag_dpttrs (f07jec) can be used to solve systems of equations

A X = B

, and nag_dptcon (f07jgc) can be used to estimate the condition number of

A

nag_dpttrf (f07jdc) is not threaded in any implementation.

The total number of floating-point operations required to factorize the matrix

A

is proportional to

n

The complex analogue of this function is nag_zpttrf (f07jrc).

This example factorizes the symmetric positive definite tridiagonal matrix

A

given by

A = (\begin{array}{r} 4.0 & - 2.0 & 0 & 0 & 0 \\ - 2.0 & 10.0 & - 6.0 & 0 & 0 \\ 0 & - 6.0 & 29.0 & 15.0 & 0 \\ 0 & 0 & 15.0 & 25.0 & 8.0 \\ 0 & 0 & 0 & 8.0 & 5.0 \end{array}) .