NAG Library Routine Document

F07FDF (DPOTRF)

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

1:   UPLO – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored and how $A$ is to be factorized.

$\mathbf{UPLO}=\text{'U'}$

The upper triangular part of $A$ is stored and $A$ is factorized as $U^{\mathrm{T}}U$, where $U$ is upper triangular.

$\mathbf{UPLO}=\text{'L'}$

The lower triangular part of $A$ is stored and $A$ is factorized as $L{L}^{\mathrm{T}}$, where $L$ is lower triangular.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

2:   N – INTEGERInput

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

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

3:   A(LDA,$*$) – REAL (KIND=nag_wp) arrayInput/Output

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

On entry: the $n$ by $n$ symmetric positive definite matrix $A$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the upper or lower triangle of $A$ is overwritten by the Cholesky factor $U$ or $L$ as specified by UPLO.

4:   LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F07FDF (DPOTRF) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

5:   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 parameter 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 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 matrix which is not positive definite, call F07MDF (DSYTRF) instead.

7 Accuracy

8 Further Comments

9 Example

9.1 Program Text

Program Text (f07fdfe.f90)

9.2 Program Data

Program Data (f07fdfe.d)

9.3 Program Results

Program Results (f07fdfe.r)