BLAS/SRC/zher.f(3)

💅 BLAS/SRC/zher.f — the Hermitian rank-1 glow-up page ✨

Hey bestie, welcome to the zher corner of the LAPACK docs 🫶. This page lives in the BLAS/SRC/zher.f file and it's literally all about one iconic little routine. Let's get into it.

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zher (uplo, n, alpha, x, incx, a, lda) — the one and only ZHER, coming through 💅

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🌸 Function/Subroutine Documentation 🌸

🎀 subroutine zher (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*) a, integer lda)

Yep, that's her. That's ZHER. Main character energy, no cap 👑

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💖 Purpose 💖

Okay so here's what she does:

!> ZHER   performs the hermitian rank 1 operation
!>
!>    A := alpha*x*x**H + A,
!>
!> where alpha is a real scalar, x is an n element vector and A is an
!> n by n hermitian matrix.

Translation, bestie: she does a Hermitian rank-1 update. alpha is a real scalar, x is an n-element vector, and A is an n by n Hermitian matrix. Slay 🦋.

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🌈 Parameters 🌈

• UPLO — this is CHARACTER*1. On entry, UPLO tells you which triangular part of the array A is actually being referenced, like:
  • UPLO = 'U' or 'u' → only the upper triangular part of A is referenced.
  • UPLO = 'L' or 'l' → only the lower triangular part of A is referenced.
• N — this is INTEGER. On entry, N is the order of the matrix A. Important: N must be at least zero. Not optional, bestie.
• ALPHA — this is DOUBLE PRECISION. On entry, ALPHA is the scalar alpha. Simple as that 💜.
• X — this is a COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
• INCX — this is INTEGER. On entry, INCX is the increment for the elements of X. And heads up: INCX must not be zero. Like, fr fr, don't do it 🙈.
• A — this is a COMPLEX*16 array, dimension ( LDA, N ). Okay this one has a lot going on, so let me break it down:
  • Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix, and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A gets overwritten by the upper triangular part of the updated matrix ✨.
  • Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix, and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A gets overwritten by the lower triangular part of the updated matrix ✨.
  • And a lil note: the imaginary parts of the diagonal elements need not be set — they're assumed to be zero, and on exit they are set to zero. So don't stress about them, she handles it 🫶.
• LDA — this is INTEGER. On entry, LDA is the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Periodt.

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👑 Author 👑

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

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🔥 Further Details: 🔥

!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>

She's a Level 2 BLAS routine, born on 22-October-1986, and honestly that's iconic. The whole squad who wrote her: Jack Dongarra at Argonne National Lab, Jeremy Du Croz at Nag Central Office, Sven Hammarling at Nag Central Office, and Richard Hanson at Sandia National Labs 🌟.

Also, just so you know — she's defined at line 134 of file zher.f 📍.

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🧚 Author (meta edition) 🧚

Generated automatically by Doxygen for LAPACK from the source code. Very demure, very mindful.

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Okay that's the whole page, bestie! Stay hermitian, stay updated 💖

LAPACK · Version 3.12.0 · BLAS/SRC/zher.f(3) — and that's the cute lil sign-off at the bottom, mwah 💋 🎀