CHBT21(3)

💖 CHBT21(3) — Library Functions Manual 💖

okay bestie, this is the CHBT21 page, and it’s giving very specific LAPACK test-routine energy. 💅

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🌸 NAME 🌸

This page’s NAME is literally this file path, no more, no less:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/chbt21.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CHBT21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, rwork,
    result)

CHBT21

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🦋 Function/Subroutine Documentation 🦋

subroutine CHBT21 (character uplo, integer n, integer ka, integer ks,
    complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d,
    real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu,
    complex, dimension( * ) work, real, dimension( * ) rwork, real,
    dimension( 2 ) result)

CHBT21

🎀 Purpose 🎀

So, CHBT21 generally checks a decomposition of the form:

A = U S U**H

where **H means conjugate transpose, A is hermitian banded, U is unitary, and S is diagonal (if KS=0) or symmetric tridiagonal (if KS=1).

Specifically:

RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
RESULT(2) = | I - U U**H | / ( n ulp )

Not me being obsessed with two whole RESULT values, but here we are. 💖

💜 Parameters 💜

• UPLO — CHARACTER. If UPLO='U', the upper triangle of A and V will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced.
• N — INTEGER. The size of the matrix. If it is zero, CHBT21 does nothing. It must be at least zero.
• KA — INTEGER. The bandwidth of the matrix A. It must be at least zero. If it is larger than N-1, then max( 0, N-1 ) will be used.
• KS — INTEGER. The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal.
• A — COMPLEX array, dimension (LDA, N). The original (unfactored) matrix. It is assumed to be hermitian, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced.
• LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least min( KA, N-1 ).
• D — REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix S.
• E — REAL array, dimension (N-1). The off-diagonal of the (symmetric tri-) diagonal matrix S. E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and (3,2) element, etc. Not referenced if KS=0.
• U — COMPLEX array, dimension (LDU, N). The unitary matrix in the decomposition, expressed as a dense matrix (i.e., not as a product of Householder transformations, Givens transformations, etc.).
• LDU — INTEGER. The leading dimension of U. LDU must be at least N and at least 1.
• WORK — COMPLEX array, dimension (N**2).
• RWORK — REAL array, dimension (N).
• RESULT — REAL array, dimension (2). The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow.

👑 Author 👑

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

Definition at line 150 of file chbt21.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Cute little sign-off, bestie: this page says source/version LAPACK Version 3.12.0, and the footer path is /home/abui...IG/chbt21.f(3). Slay, and may your RESULT values stay tiny. 💖✨