NAG Library Routine Document

f07cdf (dgttrf)

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

Note: the dimension of the array dl 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 $\left(n-1\right)$ multipliers that define the matrix $L$ of the $LU$ factorization of $A$.

3:     $\mathbf{d}\left(*\right)$ – 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 upper triangular matrix $U$ from the $LU$ factorization of $A$.

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

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

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

On exit: is overwritten by the $\left(n-1\right)$ elements of the first superdiagonal of $U$.

5:     $\mathbf{du2}\left(\mathbf{n}-2\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: contains the $\left(n-2\right)$ elements of the second superdiagonal of $U$.

6:     $\mathbf{ipiv}\left(\mathbf{n}\right)$ – Integer arrayOutput

On exit: contains the $n$ pivot indices that define the permutation matrix $P$. At the $i$th step, row $i$ of the matrix was interchanged with row $\mathbf{ipiv}\left(i\right)$. $\mathbf{ipiv}\left(i\right)$ will always be either $i$ or $\left(i+1\right)$, $\mathbf{ipiv}\left(i\right)=i$ indicating that a row interchange was not performed.

7:     $\mathbf{info}$ – 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.

$\mathbf{info}>0$

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero. The factorization has been completed, but the factor $U$ is exactly singular, and division by zero will occur if it is used to solve a system of equations.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07cdfe.f90)

10.2

Program Data

Program Data (f07cdfe.d)

10.3

Program Results

Program Results (f07cdfe.r)