BLAS/SRC/zsymm.f(3)

💖 BLAS/SRC/zsymm.f(3) — aka the LAPACK manual, bestie edition 💖

okay so this is BLAS/SRC/zsymm.f, straight out of the LAPACK manual, and it's lowkey one of the most iconic routines in the whole Level 3 BLAS lineup. sit down, grab a strawberry drink 🍓, we're doing complex symmetric matrix-matrix math and we're doing it cutely.

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✨ NAME ✨

BLAS/SRC/zsymm.f — no cap, that's literally it, that's the whole name, she's simple like that 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

💜 subroutine zsymm

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. that's her. that's the whole vibe check. 👑

🎀 Purpose:

okay so ZSYMM performs one of the 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. it's giving "scale, multiply, add, slay" and honestly? obsessed. 🔥

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💖 Parameters

• SIDE — SIDE is CHARACTER*1. on entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation, and the way she does it is:

   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 specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced, like so:

   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 specifies the number of rows of the matrix C. M must be at least zero. no negative rows bestie, that's not a thing 🙈
• N — N is INTEGER. on entry, N specifies the number of columns of the matrix C. N must be at least zero. same energy, same rule ✨
• ALPHA — ALPHA is COMPLEX*16. on entry, ALPHA specifies the scalar alpha. just a little guy. a scalar. a snack. 🍓
• A — A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is m when SIDE = 'L' or 'l' and is n otherwise. okay here's the tea 🫖:
  • 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.
• LDA — LDA is INTEGER. on entry, LDA specifies 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 the math, don't skip the math, fr fr.
• 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. she's just standing there. being a matrix. main character energy.
• LDB — LDB is INTEGER. on entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). yes bestie, m. not n. i said what i said 💅
• BETA — BETA is COMPLEX*16. on entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. free pass unlocked 🔓✨
• 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. she goes in one way and comes out ✨transformed✨
• LDC — LDC is INTEGER. on entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). last one, and she matters just as much 🫶

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👑 Author

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

the whole friend group showed up for this one, we love a collab 🌈

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🔥 Further Details:

• Level 3 Blas routine.
• ``` -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.

> not me getting emotional over a routine written on 8-February-1989 😭 legends. literal legends. no notes. 🎀

**Definition at line 188 of file `zsymm.f`.**

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# 💫 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote this part. a robot with taste. 🤖💅

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<purple>**Version 3.12.0**</purple> · <pink>Tue Nov 28 2023 12:08:41</pink> · <cyan>`BLAS/SRC/zsymm.f(3)`</cyan>

and that's the whole page bestie!! go forth, pass `SIDE`, `UPLO`, `M`, `N`, `ALPHA`, `A`, `LDA`, `B`, `LDB`, `BETA`, `C`, `LDC` in exactly that order, and slay 💖✨🦋 periodt.