SRC/slaed9.f(3)

💅 SRC/slaed9.f 💅

okay bestie, this is the Library Functions Manual page for SRC/slaed9.f, and it's giving “serious LAPACK subroutine” energy. Let's go. 🫶

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✨ NAME ✨

SRC/slaed9.f — that's the name, bestie. Manual name folded in: Library Functions Manual. 💖

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

       subroutine slaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s,
           lds, info)

• slaed9 — SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

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🦋 Function/Subroutine Documentation 🦋

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

🎯 Purpose

SLAED9 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 SLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.

🎀 Parameters 🎀

• K — K is INTEGER. The number of terms in the rational function to be solved by SLAED4. K >= 0.
• KSTART — KSTART is INTEGER.
• 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 (delation may result in N > K).
• D — D is REAL array, dimension (N). D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
• Q — Q is REAL array, dimension (LDQ,N).
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max( 1, N ).
• RHO — RHO is REAL. The value of the parameter in the rank one update equation. RHO >= 0 required.
• DLAMBDA — DLAMBDA is 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 — W is REAL array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector.
• S — S is 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 — 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.

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👑 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 slaed9.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay bestie, that's the whole page. Final footer vibe check: LAPACK Version 3.12.0 and source page SRC/slaed9.f(3). The footer doesn't list a date here, so I'm not inventing one — this is your cute sign-off. Mwah. 💋✨