BLAS/SRC/zgemm.f(3)

💖 BLAS/SRC/zgemm.f — the LAPACK manual, but make it make sense 💖

okay bestie, welcome to the page for BLAS/SRC/zgemm.f(3), straight out of the LAPACK docs. this is the glow-up edition. same facts, way better vibes. let's get into it 🫶

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✨ NAME ✨

BLAS/SRC/zgemm.f — that's the file, that's the whole name, she's simple like that 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

here's the actual call signature, copy it exactly bestie, no typos, no cap:

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

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🦋 Function/Subroutine Documentation 🦋

the actual subroutine, full glow-up:

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 👑

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🎀 Purpose 🎀

okay so ZGEMM does one of the matrix-matrix operations:

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

and op( X ) is one of these three icons:

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

alpha and beta are scalars, and A, B and C are matrices — where op( A ) is an m by k matrix, op( B ) is a k by n matrix, and C is an m by n matrix. the shape math is doing its thing, trust ✨

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💜 Parameters 💜

TRANSA

• TRANSA is CHARACTER*1.
• on entry, TRANSA says which form of op( A ) we're using in the multiplication, and the options are:
  • TRANSA = 'N' or 'n', then op( A ) = A.
  • TRANSA = 'T' or 't', then op( A ) = A**T.
  • TRANSA = 'C' or 'c', then op( A ) = A**H.

TRANSB

• TRANSB is CHARACTER*1.
• on entry, TRANSB says which form of op( B ) we're using in the multiplication, options are:
  • TRANSB = 'N' or 'n', then op( B ) = B.
  • TRANSB = 'T' or 't', then op( B ) = B**T.
  • TRANSB = 'C' or 'c', then 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. no negative row counts, we don't do that here 🙈

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 💫

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.

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. free pass on the input, we love a low-effort entry ✨

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 gets rewritten, that's the whole point 💅

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 ).

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👑 Author 👑

the legends behind this:

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

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🔥 Further Details 🔥

level 3 Blas routine. yep, she's a level 3 icon, top tier, no notes 🏆

-- 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.

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definition at line 186 of file zgemm.f. (iykyk 📍)

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Author (the meta one)

generated automatically by Doxygen for LAPACK from the source code. the docs wrote themselves, basically 🤖✨

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aaaand that's the whole page bestie, you ate it, you understood it, periodt 💖

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this was LAPACK Version 3.12.0, dated Tue Nov 28 2023 12:08:41, from BLAS/SRC/zgemm.f(3) — thanks for reading, love u, bye 🎀🦋