TESTING/EIG/zstt21.f(3)

💖 TESTING/EIG/zstt21.f(3) 💖

okay bestie, welcome to the Library Functions Manual entry for TESTING/EIG/zstt21.f — it’s giving LAPACK testing-subroutine energy, and we are gonna get through every single flag, formula, and footnote together. no cap. 💅

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✨ NAME ✨

TESTING/EIG/zstt21.f

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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 🌸

here’s the full signature, bestie — exact characters, no edits:

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

🎀 Purpose 🎀

ZSTT21 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 )

slay, that’s the whole purpose. 🫶

🍓 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.

okay bestie, yes — that really says KBSND=0 in the original. we’re keeping it exactly as it appears. 💀

🧚 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.

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👑 Author 👑

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

Definition at line 131 of file zstt21.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 bestie, that’s the whole page — source/version: LAPACK, Version 3.12.0, for TESTING/EIG/zstt21.f(3), and the footer date slot is lowkey empty, so no date to spill. 🫶