ZHBT21(3)

🌸 NAME 🌸

okay bestie, this is the zhbt21.f(3) page from the Library Functions Manual — and the NAME section is literally the source path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zhbt21.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

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🦋 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 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 — 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.

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📝 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay bestie, that’s the whole zhbt21.f(3) vibe. This page is from LAPACK Version 3.12.0, and the footer path is /home/abui...IG/zhbt21.f(3). There’s no separate date line in this footer, so I’m not inventing one — periodt. 🫶✨