SLAED2(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 SLAED2(3) — like, the slaed2.f page, bestie 💅

ok so real talk, this is the manual page for slaed2.f(3) — a LAPACK library function page, and honestly? she's doing a LOT. let's get into it ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaed2.f

like yes that's literally the whole name, it's a whole path, she's got main character energy and a very long address 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SLAED2 (k, n, n1, d, q, ldq, indxq, rho, z, dlambda, w, q2,
    indx, indxc, indxp, coltyp, info)

SLAED2 used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

💜 Function/Subroutine Documentation 💜

subroutine SLAED2 (integer k, integer n, integer n1, real, dimension( * ) d,
    real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq,
    real rho, real, dimension( * ) z, real, dimension( * ) dlambda, real,
    dimension( * ) w, real, dimension( * ) q2, integer, dimension( * ) indx,
    integer, dimension( * ) indxc, integer, dimension( * ) indxp, integer,
    dimension( * ) coltyp, integer info)

SLAED2 used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

🌈 Purpose:

!> !> SLAED2 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 entry in the !> Z vector. For each such occurrence the order of the related secular !> equation problem is reduced by one. !>

so basically she's out here merging two eigenvalue sets into one sorted set, then trying to shrink the problem — deflation can happen two ways: two or more eigenvalues being close together, or a tiny entry in the Z vector. every time that happens, the order of the related secular equation problem goes down by one. slay 🔥

🎀 Parameters 🎀

  • K — !> K is INTEGER / !> The number of non-deflated eigenvalues, and the order of the / !> related secular equation. 0 <= K <=N. / !> — so like, how many eigenvalues survived the deflation, and the order of the secular equation she's working with. bounds: 0 <= K <=N. 🫶
  • N — !> N is INTEGER / !> The dimension of the symmetric tridiagonal matrix. N >= 0. / !> — the dimension of the symmetric tridiagonal matrix, N >= 0. ✨
  • N1 — !> N1 is INTEGER / !> The location of the last eigenvalue in the leading sub-matrix. / !> min(1,N) <= N1 <= N/2. / !> — where the last eigenvalue sits in the leading sub-matrix. bounds: min(1,N) <= N1 <= N/2. 💖
  • D — !> D is REAL 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. / !> — REAL array, dimension (N). on the way in she's holding the eigenvalues of the two submatrices getting combined; on the way out she's holding the trailing (N-K) updated eigenvalues (the deflated ones, bestie) sorted into increasing order. 🌸
  • Q — !> Q is REAL array, dimension (LDQ, N) / !> On entry, Q contains the eigenvectors of two submatrices in / !> the two square blocks with corners at (1,1), (N1,N1) / !> and (N1+1, N1+1), (N,N). / !> On exit, Q contains the trailing (N-K) updated eigenvectors / !> (those which were deflated) in its last N-K columns. / !> — REAL array, dimension (LDQ, N). entry: eigenvectors of two submatrices in the two square blocks with corners at (1,1), (N1,N1) and (N1+1, N1+1), (N,N). exit: the trailing (N-K) updated eigenvectors (the deflated ones) live in her last N-K columns. 👑
  • LDQ — !> LDQ is INTEGER / !> The leading dimension of the array Q. LDQ >= max(1,N). / !> — INTEGER, the leading dimension of the array Q. must be 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 N1 added to their / !> values. Destroyed on exit. / !> — INTEGER array, dimension (N). the permutation that separately sorts the two sub-problems in D into ascending order. ⚠️ important note: elements in the second half of this permutation must first have N1 added to their values. Destroyed on exit. 💀
  • RHO — !> RHO is REAL / !> 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 / !> SLAED3. / !> — REAL. entry: the off-diagonal element associated with the rank-1 cut that originally split the two submatrices now being recombined. exit: RHO has been modified to the value required by SLAED3. 🔥
  • Z — !> Z is REAL 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 have been destroyed by the updating / !> process. / !> — REAL array, dimension (N). entry: the updating vector (last row of the first sub-eigenvector matrix + first row of the second sub-eigenvector matrix). exit: the contents of Z have been destroyed by the updating process 😭 she does not survive the vibe check.
  • DLAMBDA — !> DLAMBDA is REAL array, dimension (N) / !> A copy of the first K eigenvalues which will be used by / !> SLAED3 to form the secular equation. / !> — REAL array, dimension (N). a copy of the first K eigenvalues, which SLAED3 will use to form the secular equation. 🍓
  • W — !> W is REAL array, dimension (N) / !> The first k values of the final deflation-altered z-vector / !> which will be passed to SLAED3. / !> — REAL array, dimension (N). the first k values of the final deflation-altered z-vector, which gets passed to SLAED3. 🧚
  • Q2 — !> Q2 is REAL array, dimension (N1**2+(N-N1)**2) / !> A copy of the first K eigenvectors which will be used by / !> SLAED3 in a matrix multiply (SGEMM) to solve for the new / !> eigenvectors. / !> — REAL array, dimension (N1**2+(N-N1)**2). a copy of the first K eigenvectors that SLAED3 will use in a matrix multiply (SGEMM) to solve for the new eigenvectors. ✨
  • INDX — !> INDX is INTEGER array, dimension (N) / !> The permutation used to sort the contents of DLAMBDA into / !> ascending order. / !> — INTEGER array, dimension (N). the permutation used to sort the contents of DLAMBDA into ascending order. 💜
  • INDXC — !> INDXC is INTEGER array, dimension (N) / !> The permutation used to arrange the columns of the deflated / !> Q matrix into three groups: the first group contains non-zero / !> elements only at and above N1, the second contains / !> non-zero elements only below N1, and the third is dense. / !> — INTEGER array, dimension (N). the permutation that arranges the columns of the deflated Q matrix into three groups: group one has non-zero elements only at and above N1, group two has non-zero elements only below N1, and group three is dense. 🌈
  • 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. / !> — 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. 🎀
  • COLTYP — !> COLTYP is INTEGER array, dimension (N) / !> During execution, a label which will indicate which of the / !> following types a column in the Q2 matrix is: / !> 1 : non-zero in the upper half only; / !> 2 : dense; / !> 3 : non-zero in the lower half only; / !> 4 : deflated. / !> On exit, COLTYP(i) is the number of columns of type i, / !> for i=1 to 4 only. / !> — INTEGER array, dimension (N). during execution it's a label telling you which type a column in the Q2 matrix is: 1 = non-zero in the upper half only, 2 = dense, 3 = non-zero in the lower half only, 4 = deflated. on exit, COLTYP(i) is the number of columns of type i, for i=1 to 4 only. 🔥
  • INFO — !> INFO is INTEGER / !> = 0: successful exit. / !> < 0: if INFO = -i, the i-th argument had an illegal value. / !> — INTEGER. = 0: successful exit, we love a win 💖. < 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

Modified by Francoise Tisseur, University of Tennessee

⭐ Definition ⭐

Definition at line 210 of file slaed2.f.

💫 Author 💫

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ok that's the whole page, no cap 🫶 and for the cute sign-off: this is LAPACK, Version 3.12.0, dated /home/abui...RC/slaed2.f(3) — periodt, go merge some eigenvalues bestie 💅✨

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