TESTING/EIG/ssbt21.f(3)

🌸 TESTING/EIG/ssbt21.f(3) 🌸

Hey bestie! You're looking at the TESTING/EIG/ssbt21.f(3) page from the Library Functions Manual, and honestly? This subroutine has main character energy 💖. It's giving test-suite realness, and we're gonna get into all of it.

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💅 NAME 💅

TESTING/EIG/ssbt21.f — that's the file name, periodt ✨.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine ssbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result)
    SSBT21

💖 Function/Subroutine Documentation 💖

subroutine ssbt21 (character uplo, integer n, integer ka, integer ks, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real,
    dimension( * ) work, real, dimension( 2 ) result)
    SSBT21

🎯 Purpose 🎯

Okay so SSBT21 generally checks a decomposition of the form:

A = U S U**T

where **T means transpose, A is symmetric banded, U is orthogonal, and S is diagonal (if KS=0) or symmetric tridiagonal (if KS=1) 🫶.

Specifically:

RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( 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. Pick your triangle, bestie 💅
• N — N is INTEGER. The size of the matrix. If it is zero, SSBT21 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 REAL array, dimension (LDA, N). The original (unfactored) matrix. It is assumed to be symmetric, 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 REAL array, dimension (LDU, N). The orthogonal 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 REAL array, dimension (N**2+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 145 of file ssbt21.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie 🫶 — signing off with the footer deets: LAPACK Version 3.12.0, source TESTING/EIG/ssbt21.f(3), and this page ate, no cap 💖✨.