DLAED3(3)

💅 DLAED3(3) 💅

okay so real talk: this page lives in the Library Functions Manual (the LAPACK one, bestie, not some random manual), and it's all about one very specific little workhorse subroutine. buckle up 🎀

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✨ NAME ✨

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaed3.f — yeah that's the whole NAME section, it's literally just the file path, slay 💀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DLAED3 (k, n, n1, d, q, ldq, rho, dlambda, q2, indx, ctot, w,
    s, info)

DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. no cap, that's the whole vibe ✨

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🌸 Function/Subroutine Documentation 🌸

subroutine DLAED3 (integer k, integer n, integer n1, double precision,
    dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq,
    double precision rho, double precision, dimension( * ) dlambda, double
    precision, dimension( * ) q2, integer, dimension( * ) indx, integer,
    dimension( * ) ctot, double precision, dimension( * ) w, double
    precision, dimension( * ) s, integer info)

DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. (yes it's the same sentence twice, the manpage said it twice, so we say it twice 💖)

🎯 Purpose 🎯

DLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to DLAED4 and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the K-by-K system which is solved here.

like, it's giving "solve the math, then fix up the eigenvectors" energy 👑

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🔥 Parameters 🔥

• K — K is INTEGER. The number of terms in the rational function to be solved by DLAED4. K >= 0. (so zero is allowed, bestie, but nothing negative 🙈)
• N — N is INTEGER. The number of rows and columns in the Q matrix. N >= K (deflation may result in N>K). lowkey important: deflation can make N bigger than K, that's not a bug, that's the vibe check passing ⭐
• N1 — N1 is INTEGER. The location of the last eigenvalue in the leading submatrix. min(1,N) <= N1 <= N/2. okay so that's the range, memorize it fr fr 📏
• D — D is DOUBLE PRECISION array, dimension (N). D(I) contains the updated eigenvalues for 1 <= I <= K. fresh eigenvalues, iconic ✨
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,N). Initially the first K columns are used as workspace. On output the columns 1 to K contain the updated eigenvectors. so it starts as scratch space and leaves as glow-up eigenvectors 💅
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N). don't you dare go smaller 🚨
• RHO — RHO is DOUBLE PRECISION. The value of the parameter in the rank one update equation. RHO >= 0 required. non-negative or it's a no from me 🙅‍♀️
• DLAMBDA — DLAMBDA is DOUBLE PRECISION 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. poles!! very main character math 🧚
• Q2 — Q2 is DOUBLE PRECISION array, dimension (LDQ2*N). The first K columns of this matrix contain the non-deflated eigenvectors for the split problem. no notes, iconic array 🫶
• INDX — INDX is INTEGER array, dimension (N). The permutation used to arrange the columns of the deflated Q matrix into three groups (see DLAED2). The rows of the eigenvectors found by DLAED4 must be likewise permuted before the matrix multiply can take place. like, you gotta shuffle everything the same way or it's chaos 😭
• CTOT — CTOT is INTEGER array, dimension (4). A count of the total number of the various types of columns in Q, as described in INDX. The fourth column type is any column which has been deflated. four slots, four column types, keep up bestie 🍓
• W — W is DOUBLE PRECISION array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector. Destroyed on output. ⚠️ literally destroyed, so don't come crying to me when your W is gone, it said so 💀
• S — S is DOUBLE PRECISION array, dimension (N1 + 1)*K. Will contain the eigenvectors of the repaired matrix which will be multiplied by the previously accumulated eigenvectors to update the system. repaired matrix!!! she's healing 💜
• INFO — INFO is INTEGER. here's the whole mood board:
  • = 0: successful exit. we love to see it ✅
  • < 0: if INFO = -i, the i-th argument had an illegal value. oops, somebody passed something cursed 😬
  • > 0: if INFO = 1, an eigenvalue did not converge. 🚩🚩 not the convergence failure

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👑 Author 👑

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

the whole squad showed up for this one 🌈

🎀 Contributors: 🎀

• Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
• Modified by Francoise Tisseur, University of Tennessee

shoutout to the contributors, we see you and we appreciate you 🫶💖

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Definition at line 175 of file dlaed3.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. robot-generated and still cute, iykyk 🤖✨

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okay so that's the whole page bestie, and for the sign-off: this is LAPACK Version 3.12.0, and the file is /home/abui...RC/dlaed3.f(3) — the same page we started on, full circle, periodt 💅🎀🌸