TESTING/EIG/zhbt21.f(3)

💅 NAME

okay so bestie, this is TESTING/EIG/zhbt21.f — the manual page for TESTING/EIG/zhbt21.f(3) from the Library Functions Manual. It’s all about the ZHBT21 subroutine, and yes, it’s giving test-routine main character energy. 💖

✨ SYNOPSIS

🎀 Functions/Subroutines

subroutine zhbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, rwork,
    result)
    ZHBT21

• zhbt21 — the icon itself: a test subroutine with a whole lineup of parameters. Periodt. 💅

💖 Function/Subroutine Documentation

subroutine zhbt21 (character uplo, integer n, integer ka, integer ks,
     complex*16, dimension( lda, * ) a, integer lda, double precision,
     dimension( * ) d, double precision, dimension( * ) e, complex*16,
     dimension( ldu, * ) u, integer ldu, complex*16, dimension( * ) work,
     double precision, dimension( * ) rwork, double precision, dimension( 2 )
     result)

ZHBT21 🦋

🌸 Purpose

okay so ZHBT21 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 )

🦋 Parameters

• UPLO — UPLO is CHARACTER. If it’s 'U', the upper triangle of A and V gets used and the (strictly) lower triangle will not be referenced. If it’s 'L', the lower triangle of A and V gets used and the (strictly) upper triangle will not be referenced. lowkey important, bestie.
• N — N is INTEGER. The size of the matrix. If it is zero, ZHBT21 does nothing. It must be at least zero.
• KA — KA is 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 — KS is 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 — A is COMPLEX*16 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 — LDA is INTEGER. The leading dimension of A. It must be at least 1 and at least min( KA, N-1 ).
• D — D is DOUBLE PRECISION array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix S.
• E — E is DOUBLE PRECISION 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 — U is COMPLEX*16 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 — LDU is INTEGER. The leading dimension of U. LDU must be at least N and at least 1.
• WORK — WORK is COMPLEX*16 array, dimension (N**2).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESULT — RESULT is DOUBLE PRECISION 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 zhbt21.f.

💫 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

mwah 💋 LAPACK Version 3.12.0 is the source/version vibe here, and you’ve been reading the TESTING/EIG/zhbt21.f(3) page. bye bestie — go check those residuals! 🫶✨