BLAS/SRC/dgemm.f(3)

✨ BLAS/SRC/dgemm.f ✨

okay bestie, sit down, hydrate, because we're about to talk about DGEMM — the actual main character of BLAS. it's the Level 3 BLAS routine that does matrix-matrix multiplication, and honestly? she ate. 💅

This page lives at BLAS/SRC/dgemm.f and it's the Fortran source we're documenting here. no cap. 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

DGEMM 🫶

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💖 Function/Subroutine Documentation 💖

subroutine dgemm

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

DGEMM 👑

Purpose:

okay so here's the whole vibe. DGEMM 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,

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. periodt. ✨

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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**T.
• 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**T.
• 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.
• 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
• A — A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. (yes bestie, free real estate 🎀)
• C — C is DOUBLE PRECISION 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 ).
• 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.

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Further Details:

Level 3 Blas routine.

the lore, for the historians in the chat 🧚:

-- 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.

Definition at line 186 of file dgemm.f. 🔥

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Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just vibes and parsing 😭)

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aaaand that's the whole page, bestie. this was Version 3.12.0, dated Tue Nov 28 2023 12:08:41, from BLAS/SRC/dgemm.f(3). go forth and multiply your matrices. alpha*op( A )*op( B ) + beta*C and slay. 👑💖🌈