CGEMM(3)

🎀 CGEMM (cgemm.f) — Library Functions Manual 🎀

Okay bestie, so this page lives in the Library Functions Manual, and the file it's documenting is literally right here:

/home/abu...SRC/cgemm.f(3)

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✨ NAME ✨

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

That's the whole name section, no cap. It's just the path. The BLAS girlies keep it simple 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines 🦋

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

CGEMM — that's her, that's the function 💖

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👑 Function/Subroutine Documentation 👑

subroutine CGEMM (character transa, character transb, integer m, integer n,
    integer k, complex alpha, complex, dimension(lda,*) a, integer lda,
    complex, dimension(ldb,*) b, integer ldb, complex beta, complex,
    dimension(ldc,*) c, integer ldc)

CGEMM, again, iconic behavior ✨

💜 Purpose

Look at this, she literally told us herself:

!>
!> CGEMM  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,
!>
!> 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.
!>

So basically: matrix-matrix multiply, complex edition, with a little scalar seasoning (alpha, beta) and a transposition option on each side. Main character energy for real 🫶

🌈 Parameters

Okay this is the part you actually need, so pay attention bestie 👀

• TRANSA — TRANSA is CHARACTER*1

On entry, TRANSA tells you what form of op( A ) to use in the multiply. Here's the menu:

!>              TRANSA = 'N' or 'n',  op( A ) = A.
!>
!>              TRANSA = 'T' or 't',  op( A ) = A**T.
!>
!>              TRANSA = 'C' or 'c',  op( A ) = A**H.
!>

So 'N'/'n' = no touch, 'T'/'t' = transpose, 'C'/'c' = conjugate transpose. Slay 🔥

• TRANSB — TRANSB is CHARACTER*1

On entry, TRANSB specifies the form of op( B ) in the multiply:

!>              TRANSB = 'N' or 'n',  op( B ) = B.
!>
!>              TRANSB = 'T' or 't',  op( B ) = B**T.
!>
!>              TRANSB = 'C' or 'c',  op( B ) = B**H.
!>

Same deal, applied to B. Both sides get their own vibe check 💅

• M — M is INTEGER

On entry, M is how many rows op( A ) has, and how many rows C has. M must be at least zero. Not negative, bestie, zero is the floor 🙈

• N — N is INTEGER

On entry, N is the number of columns of op( B ) and also the number of columns of C. N must be at least zero.

• K — K is INTEGER

On entry, K is the number of columns of op( A ) and the number of rows of op( B ). K must be at least zero.

• ALPHA — ALPHA is COMPLEX

On entry, ALPHA is the scalar alpha. That's it, that's the whole description. A whole scalar. She's just a girl 🎀

• A — A is COMPLEX 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 is 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 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 is 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

On entry, BETA is the scalar beta. And here's the cute part: when BETA is supplied as zero, then C need not be set on input. Free real estate ✨

• C — C is COMPLEX 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 ate and left no crumbs 💀

• 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 ).

🌟 Author

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

Four whole institutions, we stan a collaborative queen 👑

🦋 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.
!>

Level 3 Blas routine. Written on 8-February-1989 by Jack Dongarra (Argonne National Laboratory), Iain Duff (AERE Harwell), Jeremy Du Croz (Numerical Algorithms Group Ltd.), and Sven Hammarling (Numerical Algorithms Group Ltd.). Vintage icon behavior, honestly 🌸

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📍 Definition at line 186 of file cgemm.f.

That's where she's defined, bestie, line 186, no cap.

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. The robots did the typing, we just did the reading 🧚

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Heads up: this is all straight from the LAPACK Version 3.12.0 docs, page /home/abui...SRC/cgemm.f(3), so if anything's off it's the auto-generator's fault, not mine 💖

okay bye, go multiply some complex matrices, ily 🫶💜