NAG Library Function Document

nag_real_cholesky (f03aec)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     n – IntegerInput

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

Constraint: $\mathbf{n}\ge 1$.

2:     a[$\mathbf{n}\times \mathbf{tda}$] – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix $A$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{tda}+j-1\right]$.

On entry: the upper triangle of the $n$ by $n$ positive definite symmetric matrix $A$. The elements of the array below the diagonal need not be set.

On exit: the sub-diagonal elements of the lower triangular matrix $L$. The upper triangle of $A$ is unchanged.

3:     tda – IntegerInput

On entry: the stride separating matrix column elements in the array a.

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

4:     p[n] – doubleOutput

On exit: the reciprocals of the diagonal elements of $L$.

5:     detf – double *Output

6:     dete – Integer *Output

On exit: the determinant of $A$ is given by $\mathbf{detf}\times {2.0}^{\mathbf{dete}}$. It is given in this form to avoid overflow or underflow.

7:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{tda}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$.

NE_INT_ARG_LT

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 1$.

NE_NOT_POS_DEF

The matrix is not positive definite, possibly due to rounding errors. The factorization could not be completed. detf and dete are set to zero.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f03aece.c)

10.2  Program Data

Program Data (f03aece.d)

10.3  Program Results

Program Results (f03aece.r)