DLAED9(3)

💅 DLAED9(3) — Library Functions Manual 💅

okay bestie, this is the manual page for DLAED9, and it’s giving “Fortran subroutine, dense matrix, secular equation, eigenvector updates” energy. Let’s get into it. 🦋

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaed9.f

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

       subroutine DLAED9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s,
           lds, info)

DLAED9 is used by DSTEDC. It finds the roots of the secular equation and updates the eigenvectors. It’s used when the original matrix is dense. 💅

🌸 Function/Subroutine Documentation 🌸

   subroutine DLAED9 (integer k, integer kstart, integer kstop, integer n,
       double precision, dimension( * ) d, double precision, dimension( ldq, *
       ) q, integer ldq, double precision rho, double precision, dimension( * )
       dlambda, double precision, dimension( * ) w, double precision,
       dimension( lds, * ) s, integer lds, integer info)

DLAED9 is used by DSTEDC. It finds the roots of the secular equation and updates the eigenvectors. It’s used when the original matrix is dense.

💖 Purpose 💖

DLAED9 finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP. It makes the appropriate calls to DLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors. That’s the whole plot. 🎀

🦋 Parameters 🦋

K

K is INTEGER. The number of terms in the rational function to be solved by DLAED4. K >= 0.

KSTART

KSTART is INTEGER. That’s the whole note, bestie. ✨

KSTOP

KSTOP is INTEGER. The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP, are to be computed. 1 <= KSTART <= KSTOP <= K.

N

N is INTEGER. The number of rows and columns in the Q matrix. N >= K (the source spells it delation, and yes, it may result in N > K). 🫶

D

D is DOUBLE PRECISION array, dimension (N). D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

Q

Q is DOUBLE PRECISION array, dimension (LDQ,N). That’s it, no extra lore. 💅

LDQ

LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max( 1, N ).

RHO

RHO is DOUBLE PRECISION. The value of the parameter in the rank one update equation. RHO >= 0 required.

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.

W

W is DOUBLE PRECISION array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector.

S

S is DOUBLE PRECISION 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

LDS is INTEGER. The leading dimension of S. LDS >= max( 1, K ).

INFO

INFO is INTEGER.

• = 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 👑

• 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 dlaed9.f.

😭 Author 😭

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie. Footer sign-off vibes: source/version is LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/dlaed9.f(3). Mwah 💋