Developer Reference for Intel® oneAPI Math Kernel Library for C
?tpcon
Estimates the reciprocal of the condition number of a packed triangular matrix.
Syntax
lapack_int LAPACKE_stpcon ( intmatrix_layout , charnorm , charuplo , chardiag , lapack_intn , const float*ap , float*rcond );
lapack_int LAPACKE_dtpcon ( intmatrix_layout , charnorm , charuplo , chardiag , lapack_intn , const double*ap , double*rcond );
lapack_int LAPACKE_ctpcon ( intmatrix_layout , charnorm , charuplo , chardiag , lapack_intn , const lapack_complex_float*ap , float*rcond );
lapack_int LAPACKE_ztpcon ( intmatrix_layout , charnorm , charuplo , chardiag , lapack_intn , const lapack_complex_double*ap , double*rcond );
Include Files
mkl.h
Description
stpcon dtpcon ctpcon ztpcon tpcon
The routine estimates the reciprocal of the condition number of a packed triangular matrix A in either the 1-norm or infinity-norm:
\(\kappa_{1}(A) = ||A||_{1} ||A^{-1}||_{1} = \kappa_{\infty}(A^{T}) = \kappa_{\infty}(A^{H})\)
\(\kappa_{\infty}(A) = ||A||_{\infty} ||A^{-1}||_{\infty} = \kappa_{1}(A^{T}) = \kappa_{1}(A^{H})\) .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
norm
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
Must be ‘U’ or ‘L’ . Indicates whether A is upper or lower triangular:
If uplo = 'U' , the array ap stores the upper triangle of A in packed form.
If uplo = 'L' , the array ap stores the lower triangle of A in packed form.
diag
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 ap .
n
The order of the matrix A ; n ≥ 0.
ap , work
The array ap(*) contains the packed matrix A . The dimension of ap must be at least max(1, n(n+1)/2).
iwork
Workspace array, size at least max(1, n) .
rwork
Workspace array, size at least max(1, n) .
Output Parameters
rcond
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.
Return Values
This function returns a value info .
If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.
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 10 r . 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 \(n^{2}\) floating-point operations for real flavors and \(4n^{2}\) operations for complex flavors.