Visible to Intel only — GUID: GUID-65301377-3A94-4C5E-BCF5-33691A0323FE
Visible to Intel only — GUID: GUID-65301377-3A94-4C5E-BCF5-33691A0323FE
?ppcon
Estimates the reciprocal of the condition number of a packed symmetric (Hermitian) positive-definite matrix.
Syntax
call sppcon( uplo, n, ap, anorm, rcond, work, iwork, info )
call dppcon( uplo, n, ap, anorm, rcond, work, iwork, info )
call cppcon( uplo, n, ap, anorm, rcond, work, rwork, info )
call zppcon( uplo, n, ap, anorm, rcond, work, rwork, info )
call ppcon( ap, anorm, rcond [,uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine estimates the reciprocal of the condition number of a packed symmetric (Hermitian) positive-definite matrix A:
κ1(A) = ||A||1 ||A-1||1 (since A is symmetric or Hermitian, κ∞(A) = κ1(A)).
An estimate is obtained for ||A-1||, and the reciprocal of the condition number is computed as rcond = 1 / (||A|| ||A-1||).
Before calling this routine:
compute anorm (either ||A||1 = maxjΣi |aij| or ||A||∞ = maxiΣj |aij|)
call ?pptrf to compute the Cholesky factorization of A.
Input Parameters
n |
INTEGER. The order of the matrix A; n≥ 0. |
ap, work |
REAL for sppcon DOUBLE PRECISION for dppcon COMPLEX for cppcon DOUBLE COMPLEX for zppcon. Arrays: ap(*), work(*). The array ap contains the packed factored matrix A, as returned by ?pptrf. The dimension of ap must be at least max(1,n(n+1)/2). The array work is a workspace for the routine. The dimension of work must be at least max(1, 3*n) for real flavors and max(1, 2*n) for complex flavors. |
anorm |
REAL for single precision flavors DOUBLE PRECISION for double precision flavors. The norm of the original matrix A (see Description). |
iwork |
INTEGER. Workspace array, size at least max(1, n). |
rwork |
REAL for cppcon DOUBLE PRECISION for zppcon. Workspace array, size at least max(1, n). |
Output Parameters
rcond |
REAL for single precision flavors DOUBLE PRECISION for double precision flavors. An estimate of the reciprocal of the condition number. The routine sets rcond =0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytime rcond is small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular. |
info |
INTEGER. If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value. |
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 ppcon 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
The computed rcond is never less than r (the reciprocal of the true condition number) and in practice is nearly always less than 10r. A call to this routine involves solving a number of systems of linear equations A*x = b; the number is usually 4 or 5 and never more than 11. Each solution requires approximately 2n2 floating-point operations for real flavors and 8n2 for complex flavors.