SRC/claed0.f(3)

Okay bestie, you opened SRC/claed0.f(3) — page name, right there — and it’s living in the Library Functions Manual 💅✨

💖 NAME 💖

SRC/claed0.f

Just the file name, clean and simple 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine claed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork,
    info)

• CLAED0 — used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Iconic divide-and-conquer behavior, no cap 🔥

🫶 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)

CLAED0 is used by CSTEDC. It computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. That’s the whole vibe: divide, conquer, eigenvalues, eigenvectors, slay 💅

🎀 Purpose 🎀

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 and corresponding eigenvectors of the dense or band matrix. Periodt. ✨

🌸 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. This is the “how big is the unitary matrix” parameter, bestie 🎀
• N — N is INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0. Zero is allowed, so don’t panic 🌸
• 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: diagonal entries become sorted eigenvalues 👑
• 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 to E, it did its job 💀
• 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. Unitary and orthonormal, truly main character energy 🦋
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N). Leading dimension check, no cap 💅
• 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). That’s the integer workspace math, write it down bestie 🍓
• 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). Big real workspace energy, respect it 🌈
• QSTORE — QSTORE is COMPLEX array, dimension (LDQS, N). Used to store parts of the eigenvector matrix when the updating matrix multiplies take place. It’s holding the eigenvector-matrix pieces during the update, iykyk 🧚
• LDQS — LDQS is INTEGER. The leading dimension of the array QSTORE. LDQS >= max(1,N). Another leading-dimension vibe check 💜
• INFO — INFO is INTEGER.
  • = 0: successful exit. We love a clean win ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value. Rude, but at least it tells you which argument 🙈
  • > 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). That’s the “algorithm said nah” case 😭

👑 Author 👑

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

Definition at line 143 of file claed0.f. 🫶

👑 Author 👑

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