SLAED9(3)

💅 SLAED9(3) — Library Functions Manual 💅

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaed9.f

That’s the file path, bestie. No cap.

✨ SYNOPSIS ✨

🛠 Functions/Subroutines 🛠

The one and only: SLAED9, and here’s the synopsis in all its exact-character glory:

subroutine SLAED9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s,
    lds, info)

SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

🛠 Function/Subroutine Documentation 🛠

Full signature tea, copied exactly so nobody has to guess:

subroutine SLAED9 (integer k, integer kstart, integer kstop, integer n,
    real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real
    rho, real, dimension( * ) dlambda, real, dimension( * ) w, real,
    dimension( lds, * ) s, integer lds, integer info)

SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

🎯 Purpose: 🎯

Okay so here’s the mission, lowkey iconic: SLAED9 finds the roots of the secular equation — the one defined by the values in D, Z, and RHO — between KSTART and KSTOP. It makes the appropriate calls to SLAED4, then stores the new matrix of eigenvectors so it can be used in calculating the next level of Z vectors. 💫

🧸 Parameters 🧸

• K — INTEGER. The number of terms in the rational function to be solved by SLAED4. Constraint: K >= 0.
• KSTART — INTEGER. That’s literally it in the source, bestie.
• KSTOP — INTEGER. The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP, are to be computed. Constraint: 1 <= KSTART <= KSTOP <= K.
• N — INTEGER. The number of rows and columns in the Q matrix. Constraint: N >= K (delation may result in N > K).
• D — REAL array, dimension (N). D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
• Q — REAL array, dimension (LDQ,N). No extra description in the source, so we’re not inventing one. ✨
• LDQ — INTEGER. The leading dimension of the array Q. Constraint: LDQ >= max( 1, N ).
• RHO — REAL. The value of the parameter in the rank one update equation. Constraint: RHO >= 0 required.
• DLAMBDA — REAL 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.
• W — REAL array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector.
• S — REAL array, dimension (LDS, K). Will contain the eigenvectors of the repaired matrix which will be stored for subsequent Z vector calculation and multiplied by the previously accumulated eigenvectors to update the system.
• LDS — INTEGER. The leading dimension of S. Constraint: LDS >= max( 1, K ).
• INFO — INTEGER. Status tea:
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = 1, an eigenvalue did not converge.

👑 Author 👑

The author squad is:

• 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 154 of file slaed9.f. 📍

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole manual page, bestie! Footer source/version: LAPACK Version 3.12.0. Footer path: /home/abui...RC/slaed9.f(3). No date line was on the footer, so no invented date — just version and path, periodt. 💖