TESTING/EIG/chbt21.f(3)

okay so bestie, welcome to the Library Functions Manual page for TESTING/EIG/chbt21.f — it's giving “let's check a hermitian banded decomposition” and honestly the math is lowkey iconic. 💅✨

🌸 NAME 🌸

TESTING/EIG/chbt21.f — the CHBT21 page, no cap. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       subroutine chbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, rwork,
           result)
           CHBT21

and here's the whole typed-out signature, exactly as the page serves it:

   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

🎀 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 💖

the Purpose block is literally:

           !>
           !> 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 )
           !>

🧚 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, CHBT21 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 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 REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix S.
• E — E is 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 — U is 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 — LDU is INTEGER. The leading dimension of U. LDU must be at least N and at least 1.
• WORK — WORK is COMPLEX array, dimension (N**2).
• RWORK — RWORK is REAL array, dimension (N).
• RESULT — RESULT is 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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