SSBT21(3)

💖 SSBT21(3) 💖

okay so bestie, this is the Library Functions Manual page for SSBT21, and it’s giving “LAPACK test routine that checks a symmetric banded decomposition” energy. No cap, every little detail is below. 🫶

🌸 NAME 🌸

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ssbt21.f — that’s the file this page is documenting, 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)

and yes, the routine name is SSBT21. 💅

Purpose

Lowkey the whole point: 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.

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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okay that’s the whole vibe check, bestie 💅 — this page is LAPACK, Version 3.12.0, from the source path /home/abui...IG/ssbt21.f(3). The original footer doesn’t print a separate date, so I’m not inventing one. Mwah. 💖