Visible to Intel only — GUID: GUID-9008BB8C-906A-471D-97E0-BD2571527325
Visible to Intel only — GUID: GUID-9008BB8C-906A-471D-97E0-BD2571527325
?larrj
Performs refinement of the initial estimates of the eigenvalues of the matrix T.
Syntax
call slarrj( n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info )
call dlarrj( n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info )
Include Files
- mkl.fi
Description
Given the initial eigenvalue approximations of T, this routine does bisection to refine the eigenvalues of T, w(ifirst-offset) through w(ilast-offset), to more accuracy. Initial guesses for these eigenvalues are input in w, the corresponding estimate of the error in these guesses in werr. During bisection, intervals [a,b] are maintained by storing their mid-points and semi-widths in the arrays w and werr respectively.
Input Parameters
- n
-
INTEGER. The order of the matrix T.
- d
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Array, DIMENSION (n).
Contains n diagonal elements of the matrix T.
- e2
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Array, DIMENSION (n-1).
Contains (n-1) squared sub-diagonal elements of the T.
- ifirst
-
INTEGER.
The index of the first eigenvalue to be computed. - ilast
-
INTEGER.
The index of the last eigenvalue to be computed. - rtol
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Tolerance for the convergence of the bisection intervals. An interval [a,b] is considered to be converged if (b-a) ≤ rtol*max(|a|,|b|).
- offset
-
INTEGER.
Offset for the arrays w and werr, that is the ifirst-offset through ilast-offset elements of these arrays are to be used. - w
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Array, DIMENSION (n).
On input, w(ifirst-offset) through w(ilast-offset) are estimates of the eigenvalues of L*D*LT indexed ifirst through ilast.
- werr
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Array, DIMENSION (n).
On input, werr(ifirst-offset) through werr(ilast-offset) are the errors in the estimates of the corresponding elements in w.
- work
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
Workspace array, DIMENSION (2*n).
- iwork
-
INTEGER.
Workspace array, DIMENSION (2*n).
- pivmin
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
The minimum pivot in the Sturm sequence for the matrix T.
- spdiam
-
REAL for slarrj
DOUBLE PRECISION for dlarrj
The spectral diameter of the matrix T.
Output Parameters
- w
-
On exit, contains the refined estimates of the eigenvalues.
- werr
-
On exit, contains the refined errors in the estimates of the corresponding elements in w.
- info
-
INTEGER.
Now it is not used and always is set to 0.