Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using packed storage.
Syntax
FORTRAN 77:
call spptrf( uplo, n, ap, info )
call dpptrf( uplo, n, ap, info )
call cpptrf( uplo, n, ap, info )
call zpptrf( uplo, n, ap, info )
Fortran 95:
call pptrf( ap [, uplo] [,info] )
C:
lapack_int LAPACKE_<?>pptrf( int matrix_order, char uplo, lapack_int n, <datatype>* ap );
Include Files
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite packed matrix A:
| A = UT*U for real data, A = UH*U for complex data | if uplo='U' |
| A = L*LT for real data, A = L*LH for complex data | if uplo='L' |
where L is a lower triangular matrix and U is upper triangular.
Note
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of A is packed in the array ap, and how A is factored: If uplo = 'U', the array ap stores the upper triangular part of the matrix A, and A is factored as UH*U. If uplo = 'L', the array ap stores the lower triangular part of the matrix A; A is factored as L*LH. |
n |
INTEGER. The order of matrix A; n ≥ 0. |
ap |
REAL for spptrf DOUBLE PRECISION for dpptrf COMPLEX for cpptrf DOUBLE COMPLEX for zpptrf. Array, DIMENSION at least max(1, n(n+1)/2). The array ap contains either the upper or the lower triangular part of the matrix A (as specified by uplo) in packed storage (see Matrix Storage Schemes). |
Output Parameters
ap |
The upper or lower triangular part of A in packed storage is overwritten by the Cholesky factor U or L, as specified by uplo. |
info |
INTEGER. If info=0, the execution is successful. If info = -i, the i-th parameter had an illegal value. If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A. |
Fortran 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.
Specific details for the routine pptrf interface are as follows:
ap |
Holds the array A of size (n*(n+1)/2). |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |
Application Notes
If uplo = 'U', the computed factor U is the exact factor of a perturbed matrix A + E, where
c(n) is a modest linear function of n, and ε is the machine precision.
A similar estimate holds for uplo = 'L'.
The total number of floating-point operations is approximately (1/3)n3 for real flavors and (4/3)n3 for complex flavors.
After calling this routine, you can call the following routines:
to solve A*X = B |
|
to estimate the condition number of A |
|
to compute the inverse of A. |