Visible to Intel only — GUID: GUID-A60855D6-C482-422E-87FF-4D4B6AFD77EE
Visible to Intel only — GUID: GUID-A60855D6-C482-422E-87FF-4D4B6AFD77EE
?larrf
Finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.
Syntax
call slarrf( n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info )
call dlarrf( n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info )
Include Files
- mkl.fi
Description
Given the initial representation L*D*LT and its cluster of close eigenvalues (in a relative measure), w(clstrt), w(clstrt+1), ... w(clend), the routine ?larrf finds a new relatively robust representation
L*D*LT - σi*I = L(+)*D(+)*L(+)T
such that at least one of the eigenvalues of L(+)*D*(+)*L(+)T is relatively isolated.
Input Parameters
- n
-
INTEGER. The order of the matrix (subblock, if the matrix is splitted).
- d
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION (n). The n diagonal elements of the diagonal matrix D.
- l
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION (n-1).
The (n-1) subdiagonal elements of the unit bidiagonal matrix L.
- ld
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION (n-1).
The n-1 elements Li*Di.
- clstrt
-
INTEGER. The index of the first eigenvalue in the cluster.
- clend
-
INTEGER. The index of the last eigenvalue in the cluster.
- w
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION ≥ (clend -clstrt+1). The eigenvalue approximations of L*D*LT in ascending order. w(clstrt) through w(clend) form the cluster of relatively close eigenvalues.
- wgap
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION ≥ (clend -clstrt+1). The separation from the right neighbor eigenvalue in w.
- werr
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION ≥ (clend -clstrt+1). On input, werr contains the semiwidth of the uncertainty interval of the corresponding eigenvalue approximation in w.
- spdiam
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Estimate of the spectral diameter obtained from the Gerschgorin intervals.
- clgapl, clgapr
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster.
- pivmin
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
The minimum pivot allowed in the Sturm sequence.
- work
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Workspace array, DIMENSION (2*n).
Output Parameters
- wgap
-
On output, the gaps are refined.
- sigma
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
The shift used to form L(+)*D*(+)*L(+)T.
- dplus
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION (n). The n diagonal elements of the diagonal matrix D(+).
- lplus
-
REAL for slarrf
DOUBLE PRECISION for dlarrf
Array, DIMENSION (n). The first (n-1) elements of lplus contain the subdiagonal elements of the unit bidiagonal matrix L(+).