The function may be called by the names: f07jrc, nag_lapacklin_zpttrf or nag_zpttrf.
f07jrc factorizes the matrix as
where is a unit lower bidiagonal matrix and is a diagonal matrix with positive diagonal elements. The factorization may also be regarded as having the form , where is a unit upper bidiagonal matrix.
1: – IntegerInput
On entry: , the order of the matrix .
2: – doubleInput/Output
Note: the dimension, dim, of the array d
must be at least
On entry: must contain the diagonal elements of the matrix .
On exit: is overwritten by the diagonal elements of the diagonal matrix from the factorization of .
3: – ComplexInput/Output
Note: the dimension, dim, of the array e
must be at least
On entry: must contain the subdiagonal elements of the matrix .
On exit: is overwritten by the subdiagonal elements of the lower bidiagonal matrix . (e can also be regarded as containing the superdiagonal elements of the upper bidiagonal matrix .)
4: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
The leading minor of order is not positive definite, the factorization was
completed, but .
The leading minor of order is not positive definite,
the factorization could not be completed.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The computed factorization satisfies an equation of the form
and is the machine precision.
Following the use of this function, f07jsc can be used to solve systems of equations , and f07juc can be used to estimate the condition number of .
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f07jrc is not threaded in any implementation.
The total number of floating-point operations required to factorize the matrix is proportional to .