NAG Library Routine Document
F07FDF (DPOTRF) computes the Cholesky factorization of a real symmetric positive definite matrix.
||N, LDA, INFO
The routine may be called by its
F07FDF (DPOTRF) forms the Cholesky factorization of a real symmetric positive definite matrix either as if or if , where is an upper triangular matrix and is lower triangular.
Demmel J W (1989) On floating-point errors in Cholesky LAPACK Working Note No. 14 University of Tennessee, Knoxville
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
- 1: UPLO – CHARACTER(1)Input
: specifies whether the upper or lower triangular part of
is stored and how
is to be factorized.
- The upper triangular part of is stored and is factorized as , where is upper triangular.
- The lower triangular part of is stored and is factorized as , where is lower triangular.
- 2: N – INTEGERInput
On entry: , the order of the matrix .
- 3: A(LDA,) – REAL (KIND=nag_wp) arrayInput/Output
the second dimension of the array A
must be at least
symmetric positive definite matrix
- If , the upper triangular part of must be stored and the elements of the array below the diagonal are not referenced.
- If , the lower triangular part of must be stored and the elements of the array above the diagonal are not referenced.
: the upper or lower triangle of
is overwritten by the Cholesky factor
as specified by UPLO
- 4: LDA – INTEGERInput
: the first dimension of the array A
as declared in the (sub)program from which F07FDF (DPOTRF) is called.
- 5: INFO – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
If , the th parameter 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 and the factorization could not be completed. Hence
itself is not positive definite. This may indicate an error in forming the matrix
. To factorize a
matrix which is not positive definite, call
, the computed factor
is the exact factor of a perturbed matrix
is a modest linear function of
is the machine precision
, a similar statement holds for the computed factor
. It follows that
The total number of floating point operations is approximately .
A call to F07FDF (DPOTRF) may be followed by calls to the routines:
The complex analogue of this routine is F07FRF (ZPOTRF)
This example computes the Cholesky factorization of the matrix
9.1 Program Text
Program Text (f07fdfe.f90)
9.2 Program Data
Program Data (f07fdfe.d)
9.3 Program Results
Program Results (f07fdfe.r)