Visible to Intel only — GUID: GUID-B2B87717-0636-47DE-AB61-9AEAC094BD65
Visible to Intel only — GUID: GUID-B2B87717-0636-47DE-AB61-9AEAC094BD65
?laed9
Used by sstedc/dstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
Syntax
call slaed9( k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info )
call dlaed9( k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info )
Include Files
- mkl.fi
Description
The routine finds the roots of the secular equation, as defined by the values in d, z, and rho, between kstart and kstop. It makes the appropriate calls to slaed4/dlaed4 and then stores the new matrix of eigenvectors for use in calculating the next level of z vectors.
Input Parameters
- k
-
INTEGER. The number of terms in the rational function to be solved by slaed4/dlaed4 (k≥ 0).
- kstart, kstop
-
INTEGER. The updated eigenvalues lambda(i),
kstart ≤ i ≤ kstop are to be computed.
1 ≤ kstart ≤ kstop ≤ k.
- n
-
INTEGER. The number of rows and columns in the Q matrix. n≥k (deflation may result in n > k).
- q
-
REAL for slaed9
DOUBLE PRECISION for dlaed9.
Workspace array, dimension (ldq, *).
The second dimension of q must be at least max(1, n).
- ldq
-
INTEGER. The leading dimension of the array q; ldq≥ max(1, n).
- rho
-
REAL for slaed9
DOUBLE PRECISION for dlaed9
The value of the parameter in the rank one update equation. rho≥ 0 required.
- dlamda, w
-
REAL for slaed9
DOUBLE PRECISION for dlaed9
Arrays, dimension (k) each. The first k elements of the array dlamda(*) contain the old roots of the deflated updating problem. These are the poles of the secular equation.
The first k elements of the array w(*) contain the components of the deflation-adjusted updating vector.
- lds
-
INTEGER. The leading dimension of the output array s; lds≥ max(1, k).
Output Parameters
- d
-
REAL for slaed9
DOUBLE PRECISION for dlaed9
Array, dimension (n). Elements in d(i) are not referenced for 1 ≤ i < kstart or kstop < i ≤ n.
- s
-
REAL for slaed9
DOUBLE PRECISION for dlaed9.
Array, dimension (lds, *) .
The second dimension of s must be at least max(1, k). Will contain the eigenvectors of the repaired matrix which will be stored for subsequent z vector calculation and multiplied by the previously accumulated eigenvectors to update the system.
- dlamda
-
On exit, the value is modified to make sure all dlamda(i) - dlamda(j) can be computed with high relative accuracy, barring overflow and underflow.
- w
-
Destroyed on exit.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value. If info = 1, the eigenvalue did not converge.