Visible to Intel only — GUID: GUID-AFF3667B-1CCF-417D-996C-E754B5226614
Visible to Intel only — GUID: GUID-AFF3667B-1CCF-417D-996C-E754B5226614
?trcon
Estimates the reciprocal of the condition number of a triangular matrix.
Syntax
call strcon( norm, uplo, diag, n, a, lda, rcond, work, iwork, info )
call dtrcon( norm, uplo, diag, n, a, lda, rcond, work, iwork, info )
call ctrcon( norm, uplo, diag, n, a, lda, rcond, work, rwork, info )
call ztrcon( norm, uplo, diag, n, a, lda, rcond, work, rwork, info )
call trcon( a, rcond [,uplo] [,diag] [,norm] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine estimates the reciprocal of the condition number of a triangular matrix A in either the 1-norm or infinity-norm:
κ1(A) =||A||1 ||A-1||1 = κ∞(AT) = κ∞(AH)
κ∞ (A) =||A||∞ ||A-1||∞ =k1 (AT) = κ1 (AH) .
Input Parameters
norm |
CHARACTER*1. Must be '1' or 'O' or 'I'. If norm = '1' or 'O', then the routine estimates the condition number of matrix A in 1-norm. If norm = 'I', then the routine estimates the condition number of matrix A in infinity-norm. |
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates whether A is upper or lower triangular: If uplo = 'U', the array a stores the upper triangle of A, other array elements are not referenced. If uplo = 'L', the array a stores the lower triangle of A, other array elements are not referenced. |
diag |
CHARACTER*1. Must be 'N' or 'U'. If diag = 'N', then A is not a unit triangular matrix. If diag = 'U', then A is unit triangular: diagonal elements are assumed to be 1 and not referenced in the array a. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
a, work |
REAL for strcon DOUBLE PRECISION for dtrcon COMPLEX for ctrcon DOUBLE COMPLEX for ztrcon. The array a(lda,*) contains the matrix A. The second dimension of a must be at least max(1,n). 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. |
lda |
INTEGER. The leading dimension of a; lda≥ max(1, n). |
iwork |
INTEGER. Workspace array, size at least max(1, n). |
rwork |
REAL for ctrcon DOUBLE PRECISION for ztrcon. 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 trcon interface are as follows:
a |
Holds the matrix A of size (n, n). |
norm |
Must be '1', 'O', or 'I'. The default value is '1'. |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |
diag |
Must be 'N' or 'U'. The default value is 'N'. |
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 n2 floating-point operations for real flavors and 4n2 operations for complex flavors.