SRC/zsteqr.f(3)

💖 SRC/zsteqr.f(3) — Library Functions Manual 💖

okay bestie, welcome to the ZSTEQR page. This is the LAPACK glow-up where tridiagonal matrices get their eigenvalues and eigenvectors served fresh. ✨

🌸 NAME 🌸

SRC/zsteqr.f — the home of ZSTEQR, your routine for symmetric tridiagonal eigenvalue realness. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zsteqr (compz, n, d, e, z, ldz, work, info) — ZSTEQR

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

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🫶 Function/Subroutine Documentation 🫶

💅 subroutine zsteqr (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)

ZSTEQR

       subroutine zsteqr (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)

🔥 Purpose

okay so here's the main character energy: ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. 🦋

The eigenvectors of a full or band complex Hermitian matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form. no cap, that's the whole vibe. 💫

🍓 Parameters

• COMPZ — COMPZ is CHARACTER*1
  • = 'N': Compute eigenvalues only.
  • = 'V': Compute eigenvalues and eigenvectors of the original Hermitian matrix. On entry, Z must contain the unitary matrix used to reduce the original matrix to tridiagonal form.
  • = 'I': Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.
• N — N is INTEGER
  • The order of the matrix. N >= 0. 📏
• D — D is DOUBLE PRECISION array, dimension (N)
  • On entry, the diagonal elements of the tridiagonal matrix.
  • On exit, if INFO = 0, the eigenvalues in ascending order. 👑
• E — 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. 💀 (not dramatic, just facts)
• Z — Z is COMPLEX*16 array, dimension (LDZ, N)
  • On entry, if COMPZ = 'V', then Z contains the unitary matrix used in the reduction to tridiagonal form.
  • On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
  • If COMPZ = 'N', then Z is not referenced. 🙈
• LDZ — LDZ is INTEGER
  • The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N). 🎯
• WORK — WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
  • If COMPZ = 'N', then WORK is not referenced. 🫶
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is unitarily similar to the original matrix. 😭

👑 Author

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

Definition at line 131 of file zsteqr.f. 📌

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🧚

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sign-off bestie style: brought to you by LAPACK Version 3.12.0, page SRC/zsteqr.f(3). slay, go compute those eigenvalues responsibly. 💖✨