NAG Library Routine Document
F07JRF (ZPTTRF) computes the modified Cholesky factorization of a complex by Hermitian positive definite tridiagonal matrix .
The routine may be called by its
F07JRF (ZPTTRF) factorizes the matrix
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
is a unit upper bidiagonal matrix.
- 1: – INTEGERInput
On entry: , the order of the matrix .
- 2: – REAL (KIND=nag_wp) arrayInput/Output
the dimension 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: – COMPLEX (KIND=nag_wp) arrayInput/Output
the dimension of the array E
must be at least
On entry: must contain the subdiagonal elements of the matrix .
: is overwritten by the
subdiagonal elements of the lower bidiagonal matrix
can also be regarded as containing the
superdiagonal elements of the upper bidiagonal matrix
- 4: – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The leading minor of order is not positive definite,
the factorization could not be completed.
The leading minor of order is not positive definite, the factorization was
completed, but .
The computed factorization satisfies an equation of the form
is the machine precision
Following the use of this routine, F07JSF (ZPTTRS)
can be used to solve systems of equations
, and F07JUF (ZPTCON)
can be used to estimate the condition number of
8 Parallelism and Performance
The total number of floating-point operations required to factorize the matrix is proportional to .
The real analogue of this routine is F07JDF (DPTTRF)
This example factorizes the Hermitian positive definite tridiagonal matrix
10.1 Program Text
Program Text (f07jrfe.f90)
10.2 Program Data
Program Data (f07jrfe.d)
10.3 Program Results
Program Results (f07jrfe.r)