ZSYMM(3)

💖 ZSYMM(3) 💖

okay so bestie, welcome to the manual page for zsymm.f(3) — straight outta the LAPACK Library Functions Manual, and yes the whole vibe is "BLAS Level 3 but make it glam." 🦋

The file lives at this absolutely unhinged path, and I'm quoting it exactly because I would never do you dirty like that:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/zsymm.f

(the header up top also shows /home/abui...SRC/zsymm.f(3) — same file, truncated path, no cap 🙈)

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZSYMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

ZSYMM — that's the whole description, it's giving "I let my code speak for me." 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine ZSYMM (character side, character uplo, integer m, integer n,
    complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
    complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta,
    complex*16, dimension(ldc,*) c, integer ldc)

ZSYMM ⭐

🌸 Purpose 🌸

okay so here's the whole personality of ZSYMM — it performs one of these two matrix-matrix operations:

C := alpha*A*B + beta*C,

or

C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices. that's it. that's the whole function. iconic behavior honestly 👑

💜 Parameters 💜

• SIDE — SIDE is CHARACTER*1. On entry, SIDE tells us whether the symmetric matrix A shows up on the left or the right in the operation, like this:

SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

• UPLO — UPLO is CHARACTER*1. On entry, UPLO says whether we're referencing the upper or lower triangular part of the symmetric matrix A, bestie:

UPLO = 'U' or 'u'   Only the upper triangular part of the
                    symmetric matrix is to be referenced.

UPLO = 'L' or 'l'   Only the lower triangular part of the
                    symmetric matrix is to be referenced.

• M — M is INTEGER. On entry, M is the number of rows of the matrix C. M must be at least zero. (>= 0 or we don't talk 💀)
• N — N is INTEGER. On entry, N is the number of columns of the matrix C. N must be at least zero. same energy, different axis 🧚
• ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha. that's the whole job. main character scalar energy.
• A — A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. okay this one's a whole paragraph so buckle up bestie:
  • Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix, and the strictly lower triangular part of A is not referenced. And when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix, and the strictly upper triangular part of A is not referenced. 🫶
  • Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix, and the strictly lower triangular part of A is not referenced. And when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix, and the strictly upper triangular part of A is not referenced.

yes it's long. yes every word matters. the untouched triangle is literally just vibing in memory untouched, we do not read it, we do not perceive it 🙈

• LDA — LDA is INTEGER. On entry, LDA is the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ). do not skimp on this one, the leading dimension is not a suggestion 🔥
• B — B is COMPLEX*16 array, dimension ( LDB, N ). Before entry, the leading m by n part of the array B must contain the matrix B. that's it, that's the whole assignment 💖
• LDB — LDB is INTEGER. On entry, LDB is the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). minimum effort, maximum max( 1, m ).
• BETA — BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. ⚠️ and here's the slay: when BETA is supplied as zero then C need not be set on input. free real estate, no setup required 🎀
• C — C is COMPLEX*16 array, dimension ( LDC, N ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. it goes in one thing and comes out another, that's just the cycle of life 💫
• LDC — LDC is INTEGER. On entry, LDC is the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). same rule, third time, we love consistency 🌈

👑 Author 👑

the credits, because someone has to take responsibility for all this linear algebra:

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

🦋 Further Details 🦋

• Level 3 Blas routine. (capital-B Blas, I don't make the rules, I just report them ✨)
• -- Written on 8-February-1989. and the lineup is legendary:
  • Jack Dongarra, Argonne National Laboratory.
  • Iain Duff, AERE Harwell.
  • Jeremy Du Croz, Numerical Algorithms Group Ltd.
  • Sven Hammarling, Numerical Algorithms Group Ltd.

1989 and still running the group chat, we stan a long-lived icon 💅

📍 Definition 📍

Definition at line 188 of file zsymm.f.

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💀 Author 💀

(lowercase author, this time it's the meta one)

Generated automatically by Doxygen for LAPACK from the source code. not me being a whole auto-generated document and still serving looks 😭

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ngl bestie, if you got this far: the strictly-untouched triangle of A is not your business, LDA/LDB/LDC are max( 1, m ) (or max( 1, n ) for LDA when SIDE = 'R'), and BETA = 0 means C doesn't have to have its life together on entry. that's the tea. now go multiply some symmetric matrices 🫶💖

LAPACK — Version 3.12.0 · from /home/abui...SRC/zsymm.f(3) · bye bestie, ily, go slay those matrices 🎀✨