SRC/cstein.f(3)

💅 cstein.f: Library Functions Manual, but make it cute 💅

Bestie, welcome to SRC/cstein.f, the manual page for the CSTEIN subroutine. This is where real symmetric tridiagonal tea gets served. 💖

🌟 NAME 🌟

SRC/cstein.f

That's it, that's the name. The actual function is CSTEIN, and she's iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

That's the whole callable, bestie. Slay. 💖

🦋 Function/Subroutine Documentation 🦋

Here's the full signature in all its glory:

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 CSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. Periodt. 💅

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5). Not me forgetting that detail, bestie. 😭

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. Yes, real vibes in a complex array — that's the whole point. 💖

🧾 Parameters 🧾

• N — N is INTEGER. The order of the matrix. N >= 0.
• D — D is REAL array, dimension (N). The n diagonal elements of the tridiagonal matrix T.
• 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.
• M — M is INTEGER. The number of eigenvectors to be found. 0 <= M <= N.
• 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.)
• 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.
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= max(1,N).
• WORK — WORK is REAL array, dimension (5*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• 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.
• INFO — INFO is INTEGER. The exit-status tea:

= 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.
• EXTRA — INTEGER, default = 2. The number of iterations performed after norm growth criterion is satisfied, should be at least 1.

🫶 Author 🫶

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

Definition at line 180 of file cstein.f.

🫶 Author (Doxygen edition) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Footer flex: LAPACK Version 3.12.0, SRC/cstein.f(3) — source/version energy only, no date printed, bestie. Mwah, byeee 💋💖✨