DLAED8(3)

💅 DLAED8(3) — Library Functions Manual 💅

okay so welcome to DLAED8(3), bestie — this is a page from the Library Functions Manual, and it's all about one very specific LAPACK routine. Buckle up, because this is giving linear algebra main character energy. 💅

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaed8.f — that's the exact source file path this page is named after, no cap.

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

       subroutine DLAED8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z,
           dlambda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx,
           info)
           DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular
           equation. Used when the original matrix is dense.

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💖 Function/Subroutine Documentation 💖

   subroutine DLAED8 (integer icompq, integer k, integer n, integer qsiz,
       double precision, dimension( * ) d, double precision, dimension( ldq, *
       ) q, integer ldq, integer, dimension( * ) indxq, double precision rho,
       integer cutpnt, double precision, dimension( * ) z, double precision,
       dimension( * ) dlambda, double precision, dimension( ldq2, * ) q2,
       integer ldq2, double precision, dimension( * ) w, integer, dimension( *
       ) perm, integer givptr, integer, dimension( 2, * ) givcol, double
       precision, dimension( 2, * ) givnum, integer, dimension( * ) indxp,
       integer, dimension( * ) indx, integer info)

DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

🎯 Purpose 🎯

Okay so here's the tea: DLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: 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. Periodt. 💅

🧾 Parameters 🧾

• ICOMPQ — INTEGER. = 0: compute eigenvalues only. = 1: compute eigenvectors of the original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. 🎀
• K — INTEGER. The number of non-deflated eigenvalues, and the order of the related secular equation.
• N — INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
• QSIZ — INTEGER. The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
• D — DOUBLE PRECISION array, dimension (N). On entry, the eigenvalues of the two submatrices to be combined. On exit, the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order.
• Q — DOUBLE PRECISION array, dimension (LDQ,N). If ICOMPQ = 0, Q is not referenced. Otherwise, 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).
• INDXQ — INTEGER array, dimension (N). 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.
• RHO — DOUBLE PRECISION. On entry, the off-diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined. On exit, RHO has been modified to the value required by DLAED3.
• CUTPNT — INTEGER. The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= CUTPNT <= N.
• Z — DOUBLE PRECISION array, dimension (N). On entry, Z contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). On exit, the contents of Z are destroyed by the updating process.

Heads up, bestie: on exit, the contents of Z are destroyed by the updating process. 😭

• DLAMBDA — DOUBLE PRECISION array, dimension (N). A copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.
• Q2 — DOUBLE PRECISION array, dimension (LDQ2,N). If ICOMPQ = 0, Q2 is not referenced. Otherwise, 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). The first k values of the final deflation-altered z-vector and will be passed to DLAED3.
• PERM — INTEGER array, dimension (N). The permutations (from deflation and sorting) to be applied to each eigenblock.
• GIVPTR — INTEGER. 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.
• INDXP — INTEGER array, dimension (N). The permutation used to place deflated values of D at the end of the array. INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues.
• INDX — INTEGER array, dimension (N). The permutation used to sort the contents of D into ascending order.
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Vibe check on INFO: < 0 means an argument was illegal, and INFO = -i tells you it was the i-th one. 👀

💌 Author 💌

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

🫶 Contributors 🫶

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

📌 Definition 📌

Definition at line 240 of file dlaed8.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 — the footer is giving LAPACK Version 3.12.0, the abbreviated path /home/abui...RC/dlaed8.f(3), and no printed date, so I can't give you a calendar day, sorry 🫶. It also says it was generated automatically by Doxygen for LAPACK from the source code. 🎀✨