DLAED9 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 DLAED4 and then stores the new matrix of


 eigenvectors for use in calculating the next level of Z vectors.

K

          K is INTEGER


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


          DLAED4.  K >= 0.

KSTART

          KSTART is INTEGER

KSTOP

          KSTOP is INTEGER


          The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP


          are to be computed.  1 <= KSTART <= KSTOP <= K.

N

          N is INTEGER


          The number of rows and columns in the Q matrix.


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

D

          D is DOUBLE PRECISION array, dimension (N)


          D(I) contains the updated eigenvalues


          for KSTART <= I <= KSTOP.

Q

          Q is DOUBLE PRECISION array, dimension (LDQ,N)

LDQ

          LDQ is INTEGER


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

RHO

          RHO is DOUBLE PRECISION


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


          RHO >= 0 required.

DLAMBDA

          DLAMBDA is DOUBLE PRECISION 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.

W

          W is DOUBLE PRECISION array, dimension (K)


          The first K elements of this array contain the components


          of the deflation-adjusted updating vector.

S

          S is DOUBLE PRECISION array, dimension (LDS, 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.

LDS

          LDS is INTEGER


          The leading dimension of S.  LDS >= max( 1, K ).

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.

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

 SLAED9 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 and then stores the new matrix of


 eigenvectors for use in calculating the next level of Z vectors.

K

          K is INTEGER


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


          SLAED4.  K >= 0.

KSTART

          KSTART is INTEGER

KSTOP

          KSTOP is INTEGER


          The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP


          are to be computed.  1 <= KSTART <= KSTOP <= K.

N

          N is INTEGER


          The number of rows and columns in the Q matrix.


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

D

          D is REAL array, dimension (N)


          D(I) contains the updated eigenvalues


          for KSTART <= I <= KSTOP.

Q

          Q is REAL array, dimension (LDQ,N)

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.

DLAMBDA

          DLAMBDA 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.

W

          W is REAL array, dimension (K)


          The first K elements of this array contain the components


          of the deflation-adjusted updating vector.

S

          S is REAL array, dimension (LDS, 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.

LDS

          LDS is INTEGER


          The leading dimension of S.  LDS >= max( 1, K ).

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.

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA