LAED9 - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void laed9(integer *k, integer *kstart, integer *kstop, integer *n, T *d, T *q, integer *ldq, T *rho, T *dlamda, T *w, T *s, integer *lds, integer *info)#

LAED9 used by sstedc. Finds the roots of the secular equation and

updates the eigenvectors. Used when the original matrix is dense.

Purpose:

 LAED9 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.
Parameters:
  • K[in]

    K is INTEGER

    The number of terms in the rational function to be solved by SLAED4. K >= 0.

  • KSTART[in] KSTART is INTEGER

  • KSTOP[in]

    KSTOP is INTEGER

    The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP are to be computed. 1 <= KSTART <= KSTOP <= K.

  • N[in]

    N is INTEGER

    The number of rows and columns in the Q matrix. N >= K (delation may result in N > K).

  • D[out]

    D is REAL array, dimension (N)

    D(I) contains the updated eigenvalues

    for KSTART <= I <= KSTOP.
  • Q[out] Q is REAL array, dimension (LDQ,N)

  • LDQ[in]

    LDQ is INTEGER

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

  • RHO[in]

    RHO is REAL

    The value of the parameter in the rank one update equation. RHO >= 0 required.

  • DLAMDA[in]

    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.

  • W[in]

    W is REAL array, dimension (K)

    The first K elements of this array contain the components of the deflation-adjusted updating vector.

  • S[out]

    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[in]

    LDS is INTEGER

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

  • INFO[out]

    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