NAG Library Routine Document

F07JRF (ZPTTRF)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

2:     D($*$) – 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:     E($*$) – 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:     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 $\mathbf{INFO}=-i$, the $i$th argument had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the leading minor of order $i$ is not positive definite. If $i<\mathbf{N}$, the factorization could not be completed, while if $i=\mathbf{N}$, the factorization was completed, but $\mathbf{D}\left(\mathbf{N}\right)\le 0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07jrfe.f90)

9.2  Program Data

Program Data (f07jrfe.d)

9.3  Program Results

Program Results (f07jrfe.r)