Visible to Intel only — GUID: GUID-15A9E907-2600-430B-BF11-DFA0A375711B
Visible to Intel only — GUID: GUID-15A9E907-2600-430B-BF11-DFA0A375711B
?potrf
Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
Syntax
call spotrf( uplo, n, a, lda, info )
call dpotrf( uplo, n, a, lda, info )
call cpotrf( uplo, n, a, lda, info )
call zpotrf( uplo, n, a, lda, info )
call potrf( a [, uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite 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.
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
- uplo
-
CHARACTER*1.Must be 'U' or 'L'.
Indicates whether the upper or lower triangular part of A is stored and how A is factored:
If uplo = 'U', the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.
If uplo = 'L', the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.
- n
-
INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.
- a
-
REAL for spotrf
DOUBLE PRECISION for dpotrf
COMPLEX for cpotrf
DOUBLE COMPLEX for zpotrf.
Array, size (lda,*). The array a contains either the upper or the lower triangular part of the matrix A (see uplo). The second dimension of a must be at least max(1, n).
- lda
-
INTEGER. The leading dimension of a.
Output Parameters
- a
-
The upper or lower triangular part of a 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.
LAPACK 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 LAPACK 95 Interface Conventions.
Specific details for the routine potrf interface are as follows:
a |
Holds the matrix A of size (n, n). |
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 or (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. |