BLAS/SRC/cgemm.f(3)

💖 BLAS/SRC/cgemm.f 💖

okay bestie, gather round, because this is the file BLAS/SRC/cgemm.f and it is literally the moment complex matrix multiplication became the main character. no cap. 🦋

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✨ NAME ✨

BLAS/SRC/cgemm.f — the glow-up page for CGEMM, the Level 3 BLAS routine that does complex matrix-matrix multiply. she's iconic, she's foundational, she's been carrying linear algebra on her back since 1989. 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine cgemm (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc) — the whole vibe in one line
• CGEMM — the name, the legend, the brand 🎀

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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. yeah. that's her. 🫶

💜 Purpose:

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. it's giving linear algebra royalty, honestly. 🌈

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🌟 Parameters

• TRANSA

TRANSA is CHARACTER*1. on entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:

• 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 judgy. 💀

• 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. on entry, ALPHA specifies the scalar alpha. the moment of scaling, the drama of it all. ✨

• 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 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 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. on entry, BETA specifies the scalar beta. when BETA is supplied as zero then C need not be set on input. free pass, bestie, no setup required. 🙈

• 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 gets replaced, and honestly? she ate. 🔥

• 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

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

the whole squad showed up for this one. 💖

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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.

like... 1989. they were doing complex matrix multiplication before it was cool. legends only. 👑

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Definition at line 186 of file cgemm.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote this part, and it slayed.)

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and that's the whole page, bestie — every flag, every dimension, every max( 1, ... ), untouched. facts preserved, vibes immaculate. 🎀

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/cgemm.f(3) 💅✨