Visible to Intel only — GUID: GUID-6481BA8A-F9FB-410B-A080-BDE6457F97D1
Visible to Intel only — GUID: GUID-6481BA8A-F9FB-410B-A080-BDE6457F97D1
?pstrf
Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.
Syntax
call spstrf( uplo, n, a, lda, piv, rank, tol, work, info )
call dpstrf( uplo, n, a, lda, piv, rank, tol, work, info )
call cpstrf( uplo, n, a, lda, piv, rank, tol, work, info )
call zpstrf( uplo, n, a, lda, piv, rank, tol, work, info )
Include Files
- mkl.fi, lapack.f90
Description
The routine computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix. The form of the factorization is:
PT * A * P = UT * U, if uplo ='U' for real flavors,
PT * A * P = UH * U, if uplo ='U' for complex flavors,
PT * A * P = L * LT, if uplo ='L' for real flavors,
PT * A * P = L * LH, if uplo ='L' for complex flavors,
where P is a permutation matrix stored as vector piv, and U and L are upper and lower triangular matrices, respectively.
This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 3 BLAS.
Input Parameters
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of A is stored: 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. The order of matrix A; n≥ 0. |
a |
REAL for spstrf DOUBLE PRECISION for dpstrf COMPLEX for cpstrf DOUBLE COMPLEX for zpstrf. Array a, 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). |
work |
REAL for spstrf and cpstrf DOUBLE PRECISION for dpstrf and zpstrf. work(*) is a workspace array. The dimension of work is at least max(1,2*n). |
tol |
REAL for single precision flavors DOUBLE PRECISION for double precision flavors. User defined tolerance. If tol < 0, then n*ε*max(Ak,k), where ε is the machine precision, will be used (see Error Analysis for the definition of machine precision). The algorithm terminates at the (k-1)-st step, if the pivot ≤tol. |
lda |
INTEGER. The leading dimension of a; at least max(1, n). |
Output Parameters
a |
If info = 0, the factor U or L from the Cholesky factorization is as described in Description. |
piv |
INTEGER. Array, size at least max(1, n). The array piv is such that the nonzero entries are Ppiv(k),k (1 ≤k≤n). |
rank |
INTEGER. The rank of a given by the number of steps the algorithm completed. |
info |
INTEGER. If info = 0, the execution is successful. If info = -k, the k-th argument had an illegal value. If info > 0, the matrix A is either rank deficient with a computed rank as returned in rank, or is not positive semidefinite. |