ZPTEQR(3)

💖 NAME

okay bestie, welcome to the zpteqr.f(3) page from the LAPACK / Library Functions Manual. The actual source file is right here:

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

This is all about the ZPTEQR routine. periodt. ✨

🌈 SYNOPSIS

Functions/Subroutines

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

ZPTEQR

🦋 Function/Subroutine Documentation

   subroutine ZPTEQR (character compz, integer n, double precision, dimension(
       * ) d, double precision, dimension( * ) e, complex*16, dimension( ldz, *
       ) z, integer ldz, double precision, dimension( * ) work, integer info)
       ZPTEQR

💅 Purpose

okay so, ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix. It does this by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidiagonal factor. no cap. 🫶

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. bestie, that's the whole flex. 💅

The eigenvectors of a full or band positive definite Hermitian matrix can also be found if ZHETRD, ZHPTRD, or ZHBTRD 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.) 👑

✨ Parameters

here's the whole cast, no skips:

• COMPZ — is CHARACTER*1. The values are:
  • = '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 — is INTEGER. The order of the matrix. N >= 0.
• D — is DOUBLE PRECISION array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix. On normal exit, D contains the eigenvalues, in descending order.
• E — is DOUBLE PRECISION array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. 💀
• Z — is COMPLEX*16 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 — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if COMPZ = 'V' or 'I', LDZ >= max(1,N).
• WORK — is DOUBLE PRECISION array, dimension (4*N).
• 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

Definition at line 144 of file zpteqr.f.

🌟 Author

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and that's the whole page, bestie! the footer energy is LAPACK, Version 3.12.0, source path /home/abui...RC/zpteqr.f(3) — slay. 🫶💖