ZGEMM(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZGEMM — the BLAS routine that does complex matrix-matrix math and SERVES 👑

okay bestie, so this page is from the LAPACK library functions manual (the file lives at /home/abui...SRC/zgemm.f(3) if you're nosy like me 🎀). It's the docs for ZGEMM, and honestly? She's a legend. Let's get into it 💖

✨ NAME ✨

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

that's the whole vibe check — that's the file. lowercase, .f, Fortran, iconic 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZGEMM (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta,
    c, ldc)

ZGEMM

like… that's her. that's the whole signature. slay ✨

🦋 Function/Subroutine Documentation 🦋

subroutine ZGEMM (character transa, character transb, integer m, integer n,
    integer k, 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)

ZGEMM

🎀 Purpose 🎀

bestie. listen. ZGEMM performs one of the matrix-matrix operations

C := alpha*op( A )*op( B ) + beta*C,

where op( X ) is one of

op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,

and like — alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. the dimensions line UP, the math lines UP, everything is correct. periodt 🔥

💜 Parameters 💜

  • TRANSA — TRANSA is CHARACTER*1. on entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication, like this:
    • TRANSA = 'N' or 'n', op( A ) = A.
    • TRANSA = 'T' or 't', op( A ) = A**T.
    • TRANSA = 'C' or 'c', op( A ) = A**H.
  • TRANSB — TRANSB is CHARACTER*1. on entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication, as follows:
    • TRANSB = 'N' or 'n', op( B ) = B.
    • TRANSB = 'T' or 't', op( B ) = B**T.
    • TRANSB = 'C' or 'c', op( B ) = B**H.
  • M — M is INTEGER. on entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero. (zero is allowed, she's not gonna judge 🫶)
  • N — N is INTEGER. on entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.
  • K — K is INTEGER. on entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K must be at least zero.
  • ALPHA — ALPHA is COMPLEX*16. on entry, ALPHA specifies the scalar alpha. the main character scalar, honestly ✨
  • A — A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is k when TRANSA = 'N' or 'n', and is m otherwise. before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. iykyk 💅
  • LDA — LDA is INTEGER. on entry, LDA specifies the first dimension of A as declared in the calling (sub) program. when TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
  • B — B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B.
  • LDB — LDB is INTEGER. on entry, LDB specifies the first dimension of B as declared in the calling (sub) program. when TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
  • 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. (yes really, she said you can skip it 🙈)
  • 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 matrix ( alpha*op( A )*op( B ) + beta*C ). she goes IN and she replaces the whole thing, no cap 😭🔥
  • 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 ).

👑 Author 👑

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

the whole squad, the founding mothers and fathers of your linear algebra 🫶

🌈 Further Details: 🌈

  • Level 3 Blas routine. (level 3! she's not a vector, she's not a matrix-vector, she's the full matrix-matrix experience 💅)
  • -- 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.

like… 1989. they were doing this before most of us were born and it still hits. respect the elders 🎀

⭐ Definition ⭐

Definition at line 186 of file zgemm.f.

🍓 Author 🍓

(pulling up in a whole second author section, because sure)

Generated automatically by Doxygen for LAPACK from the source code. the doc generator said "I got this" and honestly it did 💖

real talk though bestie: LDA, LDB and LDC have minimum requirements — LDA at least max( 1, m ) or max( 1, k ) depending on TRANSA; LDB at least max( 1, k ) or max( 1, n ) depending on TRANSB; LDC at least max( 1, m ). and M, N, K must all be at least zero. don't come for me if you skip those, the routine will not be nice about it 😭

so yeah, that's ZGEMM. ❤️ this was LAPACK, Version 3.12.0, and the page itself was /home/abui...SRC/zgemm.f(3) — go forth and multiply your complex matrices, bestie. mwah 💋✨

📦 where this page comes from