SRC/dlaed8.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

okay bestie, welcome to the <pink>SRC/dlaed8.f</pink> page — aka SRC/dlaed8.f(3) in the <purple>Library Functions Manual</purple>. This is the whole dlaed8 situation, and it is lowkey iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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.

🫶 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 bestie, DLAED8 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: 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 — ICOMPQ is INTEGER. = 0: compute eigenvalues only. = 1: compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. 🎀
  • K — K is INTEGER. The number of non-deflated eigenvalues, and the order of the related secular equation.
  • N — N is INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
  • QSIZ — QSIZ is INTEGER. The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
  • D — D is 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 — Q is 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 — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
  • INDXQ — INDXQ is 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 — RHO is 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 — CUTPNT is INTEGER. The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= CUTPNT <= N.
  • Z — Z is 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. 😭
  • DLAMBDA — DLAMBDA is DOUBLE PRECISION array, dimension (N). A copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.
  • Q2 — Q2 is 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 — LDQ2 is INTEGER. The leading dimension of the array Q2. LDQ2 >= max(1,N).
  • W — W is DOUBLE PRECISION array, dimension (N). The first k values of the final deflation-altered z-vector and will be passed to DLAED3. 🌸
  • PERM — PERM is INTEGER array, dimension (N). The permutations (from deflation and sorting) to be applied to each eigenblock.
  • GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem.
  • GIVCOL — GIVCOL is INTEGER array, dimension (2, N). Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
  • GIVNUM — GIVNUM is DOUBLE PRECISION array, dimension (2, N). Each number indicates the S value to be used in the corresponding Givens rotation.
  • INDXP — INDXP is 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 — INDX is INTEGER array, dimension (N). The permutation used to sort the contents of D into ascending order.
  • INFO — INFO is 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.

🫶 Contributors:

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

Definition at line 240 of file dlaed8.f.

💅 Author 💅

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okay bestie, that's the whole beautiful manual-page vibe check 💖 — this one is from LAPACK Version 3.12.0, source SRC/dlaed8.f(3). slay, bye! 💅✨🎀

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