ZSTT21(3)

💖 NAME 💖

okay so this is the zstt21.f(3) page from the Library Functions Manual, bestie, and the file it covers is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zstt21.f

That path is long enough to need its own group chat, but we move. 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

       subroutine ZSTT21 (n, kband, ad, ae, sd, se, u, ldu, work, rwork,
           result)
           ZSTT21

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🦋 Function/Subroutine Documentation 🦋

The whole signature, no cap:

   subroutine ZSTT21 (integer n, integer kband, double precision, dimension( *
       ) ad, double precision, dimension( * ) ae, double precision, dimension(
       * ) sd, double precision, dimension( * ) se, complex*16, dimension( ldu,
       * ) u, integer ldu, complex*16, dimension( * ) work, double precision,
       dimension( * ) rwork, double precision, dimension( 2 ) result)

ZSTT21 is literally the name. Main character subroutine energy. 👑

🎀 Purpose 🎀

So what is ZSTT21 doing? It checks a decomposition of the form

A = U S U**H

where **H means conjugate transpose, A is real symmetric tridiagonal, U is unitary, and S is real and diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed:

RESULT(1) = | A - U S U**H | / ( |A| n ulp )

RESULT(2) = | I - U U**H | / ( n ulp )

Two tests, both serving looks. 💅

🍓 Parameters 🍓

• N — N is INTEGER. The size of the matrix. If it is zero, ZSTT21 does nothing. It must be at least zero.
• KBAND — 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 — AD is DOUBLE PRECISION array, dimension (N). The diagonal of the original (unfactored) matrix A. A is assumed to be real symmetric tridiagonal.
• AE — AE is DOUBLE PRECISION array, dimension (N-1). The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
• SD — SD is DOUBLE PRECISION array, dimension (N). The diagonal of the real (symmetric tri-) diagonal matrix S.
• SE — SE is DOUBLE PRECISION array, dimension (N-1). The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc.
• U — U is COMPLEX*16 array, dimension (LDU, N). The unitary matrix in the decomposition.
• LDU — LDU is INTEGER. The leading dimension of U. LDU must be at least N.
• WORK — WORK is COMPLEX*16 array, dimension (N**2).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (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. RESULT(1) is always modified.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 131 of file zstt21.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💖 that's the whole page! Source/version sign-off: LAPACK Version 3.12.0, and the page source is /home/abui...IG/zstt21.f(3). No date on this one, just pure manual-page vibes. Bye bestie! 🫶✨