laed9(3)

💅 laed9(3) 💅

Okay bestie, the manual name is laed9(3), and the vibe is D&C step: secular equation. Buckle up. 🎀

✨ NAME ✨

laed9 — laed9: D&C step: secular equation 💖

🦋 SYNOPSIS 🦋

🎀 Functions 🎀

• subroutine dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info) — DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
• 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.

💅 Detailed Description 💅

This is the top-level docs area, and then Function Documentation takes over below. The actual subroutine tea starts in a sec. 🫶

🌸 Function Documentation 🌸

💖 subroutine dlaed9 💖

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

🎯 Purpose 🎯

Okay so 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 quest, bestie. ✨

🧚 Parameters 🧚

• K — INTEGER. The number of terms in the rational function to be solved by DLAED4. K >= 0.
• KSTART — INTEGER. The original just gives the type here, no extra description. 💅
• KSTOP — INTEGER. The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP are to be computed. 1 <= KSTART <= KSTOP <= K.
• N — INTEGER. The number of rows and columns in the Q matrix. N >= K (delation may result in N > K).
• D — DOUBLE PRECISION array, dimension (N). D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
• Q — DOUBLE PRECISION array, dimension (LDQ,N). That's the whole note for Q, bestie.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max( 1, N ).
• RHO — DOUBLE PRECISION. The value of the parameter in the rank one update equation. RHO >= 0 required.
• DLAMBDA — 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 — DOUBLE PRECISION array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector.
• S — 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 — INTEGER. The leading dimension of S. LDS >= max( 1, K ).
• INFO — 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 📌

Definition at line 154 of file dlaed9.f.

---

💜 subroutine slaed9 💜

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 🎯

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. Iconic math behavior, fr fr. 🌈

🧚 Parameters 🧚

• K — INTEGER. The number of terms in the rational function to be solved by SLAED4. K >= 0.
• KSTART — INTEGER. Again, the original just gives the type, no extra lore. 🫶
• KSTOP — INTEGER. The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP are to be computed. 1 <= KSTART <= KSTOP <= K.
• N — INTEGER. The number of rows and columns in the Q matrix. 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). That's the whole note for Q.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max( 1, N ).
• RHO — REAL. The value of the parameter in the rank one update equation. 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. LDS >= max( 1, K ).
• INFO — 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 📌

Definition at line 154 of file slaed9.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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And that's the tea, bestie: this footer is serving LAPACK Version 3.12.0 and the page is laed9(3). Slay. 💖✨