TESTING/EIG/dsbt21.f(3)

🎀 NAME 🎀

TESTING/EIG/dsbt21.f

Hey bestie 💖 welcome to the TESTING/EIG/dsbt21.f page from the Library Functions Manual — yes, the manual name is folded in right here, and we're about to make this Fortran testing routine make sense. No cap.

✨ SYNOPSIS ✨

🧁 Functions/Subroutines 🧁

• subroutine dsbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result) — DSBT21

🧚 Function/Subroutine Documentation 🧚

subroutine dsbt21 (character uplo, integer n, integer ka, integer ks, double
     precision, dimension( lda, * ) a, integer lda, double precision,
     dimension( * ) d, double precision, dimension( * ) e, double precision,
     dimension( ldu, * ) u, integer ldu, double precision, dimension( * )
     work, double precision, dimension( 2 ) result)

DSBT21

💅 Purpose 💅

Okay so DSBT21 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). Obsessed with a clean factorization check, honestly.

Specifically, it computes:

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

Literally the two glow-up checks: one for the factorization and one for orthogonality. ✨

🌸 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, DSBT21 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 DOUBLE PRECISION 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 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N**2+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 145 of file dsbt21.f. 📌

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bye bestie 🫶💋 — this whole thing is from LAPACK Version 3.12.0, and it's the TESTING/EIG/dsbt21.f(3) page. Slay, stay orthogonal, and don't let your factorization overflow. 💅✨