SLAED3 finds the roots of the secular equation, as defined by the


 values in D, W, and RHO, between 1 and K.  It makes the


 appropriate calls to SLAED4 and then updates the eigenvectors by


 multiplying the matrix of eigenvectors of the pair of eigensystems


 being combined by the matrix of eigenvectors of the K-by-K system


 which is solved here.


 This code makes very mild assumptions about floating point


 arithmetic. It will work on machines with a guard digit in


 add/subtract, or on those binary machines without guard digits


 which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.


 It could conceivably fail on hexadecimal or decimal machines


 without guard digits, but we know of none.

K

          K is INTEGER


          The number of terms in the rational function to be solved by


          SLAED4.  K >= 0.

N

          N is INTEGER


          The number of rows and columns in the Q matrix.


          N >= K (deflation may result in N>K).

N1

          N1 is INTEGER


          The location of the last eigenvalue in the leading submatrix.


          min(1,N) <= N1 <= N/2.

D

          D is REAL array, dimension (N)


          D(I) contains the updated eigenvalues for


          1 <= I <= K.

Q

          Q is REAL array, dimension (LDQ,N)


          Initially the first K columns are used as workspace.


          On output the columns 1 to K contain


          the updated eigenvectors.

LDQ

          LDQ is INTEGER


          The leading dimension of the array Q.  LDQ >= max(1,N).

RHO

          RHO is REAL


          The value of the parameter in the rank one update equation.


          RHO >= 0 required.

DLAMDA

          DLAMDA is REAL array, dimension (K)


          The first K elements of this array contain the old roots


          of the deflated updating problem.  These are the poles


          of the secular equation. May be changed on output by


          having lowest order bit set to zero on Cray X-MP, Cray Y-MP,


          Cray-2, or Cray C-90, as described above.

Q2

          Q2 is REAL array, dimension (LDQ2, N)


          The first K columns of this matrix contain the non-deflated


          eigenvectors for the split problem.

INDX

          INDX is INTEGER array, dimension (N)


          The permutation used to arrange the columns of the deflated


          Q matrix into three groups (see SLAED2).


          The rows of the eigenvectors found by SLAED4 must be likewise


          permuted before the matrix multiply can take place.

CTOT

          CTOT is INTEGER array, dimension (4)


          A count of the total number of the various types of columns


          in Q, as described in INDX.  The fourth column type is any


          column which has been deflated.

W

          W is REAL array, dimension (K)


          The first K elements of this array contain the components


          of the deflation-adjusted updating vector. Destroyed on


          output.

S

          S is REAL array, dimension (N1 + 1)*K


          Will contain the eigenvectors of the repaired matrix which


          will be multiplied by the previously accumulated eigenvectors


          to update the system.

INFO

          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.


          > 0:  if INFO = 1, an eigenvalue did not converge

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee