TESTING/EIG/sstt22.f(3)

🌸 NAME 🌸

okay bestie, this is the manual page for TESTING/EIG/sstt22.f — Library Functions Manual, section 3, and the main character is literally the routine SSTT22. 💅

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine sstt22 (n, m, kband, ad, ae, sd, se, u, ldu, work, ldwork, result)
           SSTT22

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💅 Function/Subroutine Documentation 💅

here’s the full signature, exactly as the page gives it, no edits:

subroutine sstt22 (integer n, integer m, integer kband, real, dimension( * ) ad, real, dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldwork, * ) work, integer ldwork, real, dimension( 2 ) result)

SSTT22 — that’s the routine, periodt. ✨

🎀 Purpose 🎀

the source comment is giving exact math energy, so here it is verbatim:

!> SSTT22  checks a set of M eigenvalues and eigenvectors,
!>
!>     A U = U S
!>
!> where A is symmetric tridiagonal, the columns of U are orthogonal,
!> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
!> Two tests are performed:
!>
!>    RESULT(1) = | U' A U - S | / ( |A| m ulp )
!>
!>    RESULT(2) = | I - U'U | / ( m ulp )
!>

so yeah: M eigenpairs, two tests, very demure, very mindful. 🦋

🌸 Parameters 🌸

• N is INTEGER — the size of the matrix. If it is zero, SSTT22 does nothing. It must be at least zero. 📏
• M is INTEGER — the number of eigenpairs to check. If it is zero, SSTT22 does nothing. It must be at least zero. 🔢
• KBAND is INTEGER — the bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and SE is not referenced. If one, then S is symmetric tri-diagonal. 🎚️
• AD is REAL array, dimension (N) — the diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. 🧵
• AE is REAL array, dimension (N) — the off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc. 🪡
• SD is REAL array, dimension (N) — the diagonal of the (symmetric tri-) diagonal matrix S. 💫
• SE is REAL array, dimension (N) — the off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is ignored, SE(2) is the (1,2) and (2,1) element, etc. 🫶
• U is REAL array, dimension (LDU, N) — the orthogonal matrix in the decomposition. 👑
• LDU is INTEGER — the leading dimension of U. LDU must be at least N. 📐
• WORK is REAL array, dimension (LDWORK, M+1). 🧺
• LDWORK is INTEGER — the leading dimension of WORK. LDWORK must be at least max(1,M). 📏
• 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 137 of file sstt22.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋✨ footer check: LAPACK Version 3.12.0 and TESTING/EIG/sstt22.f(3) — that’s the source/version sign-off, bestie. bye 🫶🌈