CLAED0(3)

💅 NAME

Okay so this is claed0.f(3) from the Library Functions Manual — the whole page is about that one LAPACK subroutine, and the NAME entry is literally this path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/claed0.f

That's it. That's the name. The filesystem really said "here's my whole government name" 😭💀

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✨ SYNOPSIS

Functions/Subroutines

       subroutine CLAED0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork,
           info)

CLAED0 is used by CSTEDC. It computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Periodt. 👑

🫶 Function/Subroutine Documentation

   subroutine CLAED0 (integer qsiz, integer n, real, dimension( * ) d, real,
       dimension( * ) e, complex, dimension( ldq, * ) q, integer ldq, complex,
       dimension( ldqs, * ) qstore, integer ldqs, real, dimension( * ) rwork,
       integer, dimension( * ) iwork, integer info)

Same energy as the synopsis: CLAED0 is used by CSTEDC, and it computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. 💅

🎯 Purpose

Okay so the assignment is: using the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix, plus the corresponding eigenvectors of the dense or band matrix. That's the whole vibe, and it ate. ✨

🌸 Parameters

• QSIZ — QSIZ is INTEGER. The dimension of the unitary matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. (Yes, ICOMPQ is in the building. Keep that in mind, iykyk.)
• N — N is INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
• D — D is REAL array, dimension (N). On entry, the diagonal elements of the tridiagonal matrix. On exit, the eigenvalues in ascending order. Glow-up. 🌈
• E — E is REAL array, dimension (N-1). On entry, the off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed. RIP bestie, but that's literally what the page says. 💀
• Q — Q is COMPLEX array, dimension (LDQ,N). On entry, Q must contain an QSIZ x N matrix whose columns unitarily orthonormal. It is a part of the unitary matrix that reduces the full dense Hermitian matrix to a (reducible) symmetric tridiagonal matrix.
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• IWORK — IWORK is INTEGER array. The dimension of IWORK must be at least

6 + 6*N + 5*N*lg N
( lg( N ) = smallest integer k
            such that 2^k >= N )

• RWORK — RWORK is REAL array, dimension

(1 + 3*N + 2*N*lg N + 3*N**2)
( lg( N ) = smallest integer k
            such that 2^k >= N )

• QSTORE — QSTORE is COMPLEX array, dimension (LDQS, N). Used to store parts of the eigenvector matrix when the updating matrix multiplies take place.
• LDQS — LDQS is INTEGER. The leading dimension of the array QSTORE. LDQS >= max(1,N).
• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

🧚 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 143 of file claed0.f.

🌸 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole CLAED0 moment, bestie 💖 Source/version: LAPACK Version 3.12.0. Footer path: /home/abui...RC/claed0.f(3). There's no separate date line on this page, so I'm not inventing one — mwah, go slay your tridiagonal matrix 🎀👑