SRC/dlaed3.f(3)

💅 NAME

SRC/dlaed3.f — okay hi bestie, this is the Library Functions Manual page for SRC/dlaed3.f(3), and it is literally all about the DLAED3 routine. ✨

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🌸 SYNOPSIS

✨ Functions/Subroutines

       subroutine dlaed3 (k, n, n1, d, q, ldq, rho, dlambda, q2, indx, ctot, w,
           s, info)

DLAED3 is used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. 💖

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💖 Function/Subroutine Documentation

Here's the full signature with every type and dimension, copied exactly so we do not lose the plot, bestie:

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

🎯 Purpose:

DLAED3 finds the roots of the secular equation — the one 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. That's the whole vibe. 🌈

🌈 Parameters

• K — INTEGER. The number of terms in the rational function to be solved by DLAED4. K >= 0.
• N — INTEGER. The number of rows and columns in the Q matrix. N >= K (deflation may result in N>K).
• N1 — INTEGER. The location of the last eigenvalue in the leading submatrix. min(1,N) <= N1 <= N/2.
• D — DOUBLE PRECISION array, dimension (N). D(I) contains the updated eigenvalues for 1 <= I <= K.
• Q — 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.
• 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.
• Q2 — DOUBLE PRECISION array, dimension (LDQ2*N). The first K columns of this matrix contain the non-deflated eigenvectors for the split problem.
• INDX — 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.
• CTOT — 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.
• W — DOUBLE PRECISION array, dimension (K). The first K elements of this array contain the components of the deflation-adjusted updating vector. Destroyed on output.
• S — 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.
• 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
• Modified by Francoise Tisseur, University of Tennessee

Definition at line 175 of file dlaed3.f.

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🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, the footer sign-off is LAPACK Version 3.12.0, SRC/dlaed3.f(3) — that's the source/version tag for this page, and we are so done. 💅💖✨