CPTEQR(3)

💖 CPTEQR(3) — cpteqr.f 💖

okay so this is the Library Functions Manual page for CPTEQR(3), aka the cpteqr.f page. We're gonna make it make sense, bestie. 🫶

✨ NAME ✨

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

🌈 SYNOPSIS 🌈

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

This is the full signature, copied exactly, periodt:

   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 ✨

okay bestie, CPTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix. How? First it factors the matrix using SPTTRF, then it calls CBDSQR to compute the singular values of the bidiagonal factor. Slay. 💅

This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. That means 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.) This caveat is important, iykyk. 🫶

Parameters 🧚

COMPZ

COMPZ is CHARACTER*1, and here are the options:

• = '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. So if you needed E, she's gone 💀.

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).

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.

Author 🫶

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

Definition at line 144 of file cpteqr.f.

Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Signed off with LAPACK Version 3.12.0 and the footer path /home/abui...RC/cpteqr.f(3) — go be iconic with your eigenvalues 💅✨