SRC/zstedc.f(3)

🦋 SRC/zstedc.f

Okay bestie, this page is from the Library Functions Manual — it’s SRC/zstedc.f(3), and it’s giving full LAPACK main-character energy. No cap. ✨

🌸 NAME

SRC/zstedc.f

✨ SYNOPSIS

🎀 Functions/Subroutines

subroutine zstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork,
    iwork, liwork, info)

ZSTEDC 💅

💖 Function/Subroutine Documentation

subroutine zstedc (character compz, integer n, double precision, dimension(
    * ) d, double precision, dimension( * ) e, complex*16, dimension( ldz, *
    ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double
    precision, dimension( * ) rwork, integer lrwork, integer, dimension( * )
    iwork, integer liwork, integer info)

ZSTEDC 👑

🦋 Purpose

Okay so ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer 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. Slay. 🔥

🎀 Parameters

COMPZ

• COMPZ is CHARACTER*1 — here’s the vibe check:
  • = 'N': Compute eigenvalues only. 💅
  • = 'I': Compute eigenvectors of tridiagonal matrix also. ✨
  • = 'V': Compute eigenvectors of original Hermitian matrix also. On entry, Z contains the unitary matrix used to reduce the original matrix to tridiagonal form. 👑

N

• N is INTEGER — the dimension of the symmetric tridiagonal 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 subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. 💀

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. If eigenvectors are desired, then LDZ >= max(1,N). 🎀

WORK

• WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) — on exit, if INFO = 0, WORK(1) returns the optimal LWORK. ⭐

LWORK

• LWORK is INTEGER — the dimension of the array WORK.
  • If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
  • If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
  • Note that for COMPZ = 'V', then if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be 1.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 😭

RWORK

• RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) — on exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 💖

LRWORK

• LRWORK is INTEGER — the dimension of the array RWORK.
  • If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
  • If COMPZ = 'V' and N > 1, LRWORK must be at least:

1 + 3*N + 2*N*lg N + 4*N**2 ,
where lg( N ) = smallest integer k such
that 2**k >= N.

• If COMPZ = 'I' and N > 1, LRWORK must be at least 1 + 4*N + 2*N**2.
• Note that for COMPZ = 'I' or 'V', then if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)).
• If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 🙈

IWORK

• IWORK is INTEGER array, dimension (MAX(1,LIWORK)) — on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 🍓

LIWORK

• LIWORK is INTEGER — the dimension of the array IWORK.
  • If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
  • If COMPZ = 'V' or N > 1, LIWORK must be at least 6 + 6*N + 5*N*lg N.
  • If COMPZ = 'I' or N > 1, LIWORK must be at least 3 + 5*N .
  • Note that for COMPZ = 'I' or 'V', then if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.
  • If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. 💀

INFO

• INFO is INTEGER — the exit-status tea:
  • = 0: successful exit. 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. 😭
  • > 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). 💀

🫶 Author

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

🍓 Contributors:

• Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 204 of file zstedc.f. 🎀

🧚 Author

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

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And that’s the whole page, bestie. Source/version sign-off: LAPACK Version 3.12.0, page SRC/zstedc.f(3). The footer doesn’t hand us a date, so I’m not inventing one — just keeping it 100 with the version. 💅🫶