NAG Library Routine Document

f07jrf (zpttrf)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

2:     $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) arrayInput/Output

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

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 $LD{L}^{\mathrm{H}}$ factorization of $A$.

3:     $\mathbf{e}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

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

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

On exit: is overwritten by the $\left(n-1\right)$ subdiagonal elements of the lower bidiagonal matrix $L$. (e can also be regarded as containing the $\left(n-1\right)$ superdiagonal elements of the upper bidiagonal matrix $U$.)

4:     $\mathbf{info}$ – 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.

$\mathbf{info}>0\hspace{0.17em}\text{and}\hspace{0.17em}\mathbf{info}<\mathbf{n}$

The leading minor of order $〈\mathit{\text{value}}〉$ is not positive definite, the factorization could not be completed.

$\mathbf{info}>0\hspace{0.17em}\text{and}\hspace{0.17em}\mathbf{info}=\mathbf{n}$

The leading minor of order $n$ is not positive definite, the factorization was completed, but $\mathbf{d}\left(\mathbf{n}\right)\le 0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07jrfe.f90)

10.2

Program Data

Program Data (f07jrfe.d)

10.3

Program Results

Program Results (f07jrfe.r)