ZLAED8(3)

🎀 NAME

You're on the ZLAED8(3) page in the Library Functions Manual — header path says /home/abui...RC/zlaed8.f(3). The source file this page is all about is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaed8.f

No cap, that's the exact path, bestie. 💅

✨ SYNOPSIS

🦋 Functions/Subroutines

       subroutine ZLAED8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlambda, q2,
           ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)
           ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular
           equation. Used when the original matrix is dense.

🦋 Function/Subroutine Documentation

   subroutine ZLAED8 (integer k, integer n, integer qsiz, complex*16,
       dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) d,
       double precision rho, integer cutpnt, double precision, dimension( * )
       z, double precision, dimension( * ) dlambda, complex*16, dimension(
       ldq2, * ) q2, integer ldq2, double precision, dimension( * ) w, integer,
       dimension( * ) indxp, integer, dimension( * ) indx, integer, dimension(
       * ) indxq, integer, dimension( * ) perm, integer givptr, integer,
       dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum,
       integer info)
       ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation.
       Used when the original matrix is dense.

🍓 Purpose

ZLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. Deflation can happen in two ways, bestie: when two or more eigenvalues are close together, or if there is a tiny element in the Z vector. For each such occurrence, the order of the related secular equation problem is reduced by one. That's the whole glow-up. ✨

🌸 Parameters

• K — INTEGER. Contains the number of non-deflated eigenvalues. This is the order of the related secular equation.
• N — INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
• QSIZ — INTEGER. The dimension of the unitary matrix used to reduce the dense or band matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
• Q — COMPLEX*16 array, dimension (LDQ,N). On entry, Q contains the eigenvectors of the partially solved system which has been previously updated in matrix multiplies with other partially solved eigensystems. On exit, Q contains the trailing (N-K) updated eigenvectors (those which were deflated) in its last N-K columns.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max( 1, N ).
• D — DOUBLE PRECISION array, dimension (N). On entry, D contains the eigenvalues of the two submatrices to be combined. On exit, D contains the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order.
• RHO — DOUBLE PRECISION. Contains the off diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined. RHO is modified during the computation to the value required by DLAED3.
• CUTPNT — INTEGER. Contains the location of the last eigenvalue in the leading sub-matrix. MIN(1,N) <= CUTPNT <= N.
• Z — DOUBLE PRECISION array, dimension (N). On input this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). The contents of Z are destroyed during the updating process. 😭
• DLAMBDA — DOUBLE PRECISION array, dimension (N). Contains a copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.
• Q2 — COMPLEX*16 array, dimension (LDQ2,N). If ICOMPQ = 0, Q2 is not referenced. Otherwise, contains a copy of the first K eigenvectors which will be used by DLAED7 in a matrix multiply (DGEMM) to update the new eigenvectors.
• LDQ2 — INTEGER. The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
• W — DOUBLE PRECISION array, dimension (N). This will hold the first k values of the final deflation-altered z-vector and will be passed to DLAED3.
• INDXP — INTEGER array, dimension (N). This will contain the permutation used to place deflated values of D at the end of the array. On output INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues.
• INDX — INTEGER array, dimension (N). This will contain the permutation used to sort the contents of D into ascending order.
• INDXQ — INTEGER array, dimension (N). This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that elements in the second half of this permutation must first have CUTPNT added to their values in order to be accurate.
• PERM — INTEGER array, dimension (N). Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
• GIVPTR — INTEGER. Contains the number of Givens rotations which took place in this subproblem.
• GIVCOL — INTEGER array, dimension (2, N). Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
• GIVNUM — DOUBLE PRECISION array, dimension (2, N). Each number indicates the S value to be used in the corresponding Givens rotation.
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 225 of file zlaed8.f.

💜 Author

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