dstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.
?laed3finds the roots of the secular equation, as defined by the values in
rho, between 1 and
It makes the appropriate calls to
?laed4and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the
ksystem 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 none are known.
- INTEGER. The number of terms in the rational function to be solved by?laed4().k≥0
- INTEGER. The number of rows and columns in theqmatrix.(deflation may result inn≥k).n>k
- INTEGER. The location of the last eigenvalue in the leading sub-matrix;min(1,n) ≤n1≤n/2.
- REALforslaed3DOUBLE PRECISIONfordlaed3.Array. The second dimension ofq(ldq, *)qmust be at leastmax(1,.n)Initially, the firstkcolumns of this array are used as workspace.
- INTEGER. The leading dimension of the arrayq;.ldq≥max(1,n)
- REALforslaed3DOUBLE PRECISIONfordlaed3.The value of the parameter in the rank one update equation.required.rho≥0
- REALforslaed3DOUBLE PRECISIONfordlaed3.Arrays:.dlamda(k),q2(ldq2, *),w(k)The firstkelements of the arraydlamdacontain the old roots of the deflated updating problem. These are the poles of the secular equation.The firstkcolumns of the arrayq2contain the non-deflated eigenvectors for the split problem. The second dimension ofq2must be at leastmax(1,.n)The firstkelements of the arraywcontain the components of the deflation-adjusted updating vector.
- INTEGER. Array, dimension (n).The permutation used to arrange the columns of the deflatedqmatrix into three groups (see?laed2).The rows of the eigenvectors found by?laed4must be likewise permuted before the matrix multiply can take place.
- INTEGER. Array, dimension (4).A count of the total number of the various types of columns inq, as described inindx. The fourth column type is any column which has been deflated.
- REALforslaed3DOUBLE PRECISIONfordlaed3.Workspace 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.
- REALforslaed3DOUBLE PRECISIONfordlaed3.Array, dimension at least