SRC/cpteqr.f(3)

✨ SRC/cpteqr.f ✨

okay bestie, gather round, because this one is the literal blueprint for cpteqr — a Fortran subroutine living in the LAPACK library functions manual and honestly? she's iconic. 💅

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🌸 NAME 🌸

SRC/cpteqr.f

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine cpteqr (compz, n, d, e, z, ldz, work, info) — CPTEQR

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👑 Function/Subroutine Documentation 👑

subroutine cpteqr (character compz, integer n, real, dimension( * ) d, real,
    dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, real,
    dimension( * ) work, integer info)

CPTEQR

💖 Purpose 💖

!> !> CPTEQR computes all eigenvalues and, optionally, eigenvectors of a !> symmetric positive definite tridiagonal matrix by first factoring the !> matrix using SPTTRF and then calling CBDSQR to compute the singular !> values of the bidiagonal factor. !> !> This routine computes the eigenvalues of the positive definite !> tridiagonal matrix to high relative accuracy. This means that if the !> eigenvalues range over many orders of magnitude in size, then the !> small eigenvalues and corresponding eigenvectors will be computed !> more accurately than, for example, with the standard QR method. !> !> The eigenvectors of a full or band positive definite Hermitian matrix !> can also be found if CHETRD, CHPTRD, or CHBTRD has been used to !> reduce this matrix to tridiagonal form. (The reduction to !> tridiagonal form, however, may preclude the possibility of obtaining !> high relative accuracy in the small eigenvalues of the original !> matrix, if these eigenvalues range over many orders of magnitude.) !>

like, she factors with SPTTRF, then hands the bidiagonal factor over to CBDSQR to get those singular values — and the tiny eigenvalues stay accurate instead of getting absolutely lost in the sauce 😭✨

🎀 Parameters 🎀

COMPZ

!> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only. !> = 'V': Compute eigenvectors of original Hermitian !> matrix also. Array Z contains the unitary matrix !> used to reduce the original matrix to tridiagonal !> form. !> = 'I': Compute eigenvectors of tridiagonal matrix also. !>

N

!> N is INTEGER !> The order of the matrix. N >= 0. !>

D

!> D is REAL array, dimension (N) !> On entry, the n diagonal elements of the tridiagonal matrix. !> On normal exit, D contains the eigenvalues, in descending !> order. !>

E

!> E is REAL array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix. !> On exit, E has been destroyed. !>

bestie, E does not survive the function. she's gone. destroyed. no cap 💀

Z

!> Z is COMPLEX array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', the unitary matrix used in the !> reduction to tridiagonal form. !> On exit, if COMPZ = 'V', the orthonormal eigenvectors of the !> original Hermitian matrix; !> if COMPZ = 'I', the orthonormal eigenvectors of the !> tridiagonal matrix. !> If INFO > 0 on exit, Z contains the eigenvectors associated !> with only the stored eigenvalues. !> If COMPZ = 'N', then Z is not referenced. !>

LDZ

!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> COMPZ = 'V' or 'I', LDZ >= max(1,N). !>

WORK

!> WORK is REAL array, dimension (4*N) !>

four times N, she's got room to work okay 🫶

INFO

!> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if INFO = i, and i is: !> <= N the Cholesky factorization of the matrix could !> not be performed because the leading principal !> minor of order i was not positive. !> > N the SVD algorithm failed to converge; !> if INFO = N+i, i off-diagonal elements of the !> bidiagonal factor did not converge to zero. !>

⚠️ quick vibe check: INFO < 0 means a bad argument got passed in, and INFO > 0 is the "something went sideways" zone — either the Cholesky factorization couldn't happen (<= N) or the SVD didn't converge (> N). read it carefully, iykyk 👀

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🧚 Author 🧚

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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⭐ Definition ⭐

Definition at line 144 of file cpteqr.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie, and she ATE 💅 no crumbs. this came straight from LAPACK, Version 3.12.0, for SRC/cpteqr.f(3) — stan the tridiagonal queen 👑✨🎀