CSTEIN(3)

💅 NAME

okay so this page is from the Library Functions Manual, and it’s all about CSTEIN(3) and the source file:

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

bestie, that path is a whole journey, but we’re here.

✨ SYNOPSIS

🌸 Functions/Subroutines

       subroutine CSTEIN (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork,
           ifail, info)

CSTEIN

the routine name said hi again, periodt.

🫶 Function/Subroutine Documentation

   subroutine CSTEIN (integer n, real, dimension( * ) d, real, dimension( * )
       e, integer m, real, dimension( * ) w, integer, dimension( * ) iblock,
       integer, dimension( * ) isplit, complex, dimension( ldz, * ) z, integer
       ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer,
       dimension( * ) ifail, integer info)

CSTEIN

🎯 Purpose

okay so here’s the vibe: CSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

Although the eigenvectors are real, they are stored in a complex array, which may be passed to CUNMTR or CUPMTR for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form. iconic behavior, honestly.

🌈 Parameters

• N — N is INTEGER; the order of the matrix. N >= 0. yes, zero is allowed, she’s flexible.
• D — D is REAL array, dimension (N); the n diagonal elements of the tridiagonal matrix T. main diagonal carrying the tea 💅
• E — E is REAL array, dimension (N-1); the (n-1) subdiagonal elements of the tridiagonal matrix T, stored in elements 1 to N-1. off-diagonal but never off-brand.
• M — M is INTEGER; the number of eigenvectors to be found. 0 <= M <= N. we love a bounded queen.
• W — W is REAL array, dimension (N); the first M elements of W contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. ( The output array W from SSTEBZ with ORDER = 'B' is expected here. ) that parenthetical is not optional, bestie.
• IBLOCK — IBLOCK is INTEGER array, dimension (N); the submatrix indices associated with the corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the first submatrix from the top, =2 if W(i) belongs to the second submatrix, etc. ( The output array IBLOCK from SSTEBZ is expected here. )
• ISPLIT — ISPLIT is INTEGER array, dimension (N); the splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc. ( The output array ISPLIT from SSTEBZ is expected here. )
• Z — Z is COMPLEX array, dimension (LDZ, M); the computed eigenvectors. The eigenvector associated with the eigenvalue W(i) is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations. The imaginary parts of the eigenvectors are set to zero. real eigenvectors in a complex array? it’s giving range.
• LDZ — LDZ is INTEGER; the leading dimension of the array Z. LDZ >= max(1,N). do not skimp on the leading dimension.
• WORK — WORK is REAL array, dimension (5*N). just workspace doing workspace things.
• IWORK — IWORK is INTEGER array, dimension (N). integer workspace, also just vibing.
• IFAIL — IFAIL is INTEGER array, dimension (M); on normal exit, all elements of IFAIL are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array IFAIL. failure gets receipts.
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array IFAIL.

🧚 Internal Parameters

• MAXITS — INTEGER, default = 5; the maximum number of iterations performed. tiny but mighty.
• EXTRA — INTEGER, default = 2; the number of iterations performed after norm growth criterion is satisfied, should be at least 1. at least one, bestie, don’t push it.

👑 Author

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

Definition at line 180 of file cstein.f. yes, exactly line 180, no cap.

🦋 Author

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final footer energy: this is LAPACK Version 3.12.0, source /home/abui...RC/cstein.f(3) 💖 bye bestie, go compute some eigenvectors.