BLAS/SRC/sgemmtr.f(3)

🦋 BLAS/SRC/sgemmtr.f — a page from the Library Functions Manual 💅

okay so bestie, gather round, because today we're talking about sgemmtr and honestly? she's iconic ✨

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🌸 SYNOPSIS

Functions/Subroutines

• subroutine sgemmtr (uplo, transa, transb, n, k, alpha, a, lda, b, ldb, beta, c, ldc) — SGEMMTR 👑

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🎀 Function/Subroutine Documentation

subroutine sgemmtr (character uplo, character transa, character transb, integer n, integer k, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)

SGEMMTR 🫶

💜 Purpose:

!>
!> SGEMMTR  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 n by k matrix,  op( B )  a  k by n matrix and  C an n by n matrix.
!> Thereby, the routine only accesses and updates the upper or lower
!> triangular part of the result matrix C. This behaviour can be used if
!> the resulting matrix C is known to be symmetric.
!>

so basically it's the classic C := alpha*op( A )*op( B ) + beta*C moment, except she's not doing the whole matrix — only the upper or lower triangle of C gets touched. that's the whole lewk, and it means you can use this when you already know C is symmetric 😌✨

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🍓 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the lower or the upper
!>           triangular part of C is access and updated.
!>
!>              UPLO = 'L' or 'l', the lower triangular part of C is used.
!>
!>              UPLO = 'U' or 'u', the upper triangular part of C is used.
!>

CHARACTER*1 — tells her which triangle of C she's allowed to touch and update. 'L' or 'l'? lower triangle, periodt. 'U' or 'u'? upper triangle, no cap 💅

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.
!>

CHARACTER*1 — how op( A ) shows up to the party. 'N'/'n' → op( A ) = A. 'T'/'t' → op( A ) = A**T. 'C'/'c' → op( A ) = A**T (yes, same as 'T', she said what she said) 🦋

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.
!>

CHARACTER*1 — same energy but for B. 'N'/'n' → op( B ) = B. 'T'/'t' → op( B ) = B**T. 'C'/'c' → op( B ) = B**T. twins fr fr 👯

N

!>          N is INTEGER
!>           On entry,  N specifies the number of rows and columns of
!>           the matrix C, the number of columns of op(B) and the number
!>           of rows of op(A).  N must be at least zero.
!>

INTEGER — she's doing a lot of heavy lifting: rows and columns of C, columns of op(B), rows of op(A). main character energy 👑 and N must be at least zero — negative? not today 💀

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.
!>

INTEGER — columns of op( A ), rows of op( B ). and again, K must be at least zero 🫶

ALPHA

!>          ALPHA is REAL.
!>           On entry, ALPHA specifies the scalar alpha.
!>

REAL — she's the scalar alpha, that's the whole job, and she's serving ⭐

A

!>          A is REAL array, dimension ( LDA, ka ), where ka is
!>           k  when  TRANSA = 'N' or 'n',  and is  n  otherwise.
!>           Before entry with  TRANSA = 'N' or 'n',  the leading  n 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.
!>

REAL array, dimension ( LDA, ka ) where ka is k when TRANSA = 'N' or 'n', and is n otherwise. so: with TRANSA = 'N' or 'n', the leading n 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 🙈 (yes, that's m — we're quoting her exactly, don't come for me)

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, n ), otherwise  LDA must be at
!>           least  max( 1, k ).
!>

INTEGER — first dimension of A as declared in the calling (sub) program. TRANSA = 'N' or 'n' → LDA must be at least max( 1, n ); otherwise → LDA must be at least max( 1, k ). respect the boundary bestie 🚧

B

!>          B is REAL 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.
!>

REAL array, dimension ( LDB, kb ) where kb is n when TRANSB = 'N' or 'n', and is k otherwise. TRANSB = 'N' or 'n' → the leading k by n part of B holds the matrix B; otherwise the leading n by k part holds it 🧚

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 ).
!>

INTEGER — first dimension of B as declared in the calling (sub) program. TRANSB = 'N' or 'n' → LDB must be at least max( 1, k ); otherwise → LDB must be at least max( 1, n ) 💖

BETA

!>          BETA is REAL.
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

REAL — the scalar beta. and here's the lil hack: when BETA is supplied as zero then C need not be set on input 😮‍💨 love a shortcut

C

!>          C is REAL array, dimension ( LDC, N )
!>           Before entry, the leading  n 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 upper or lower triangular part of the matrix
!>           C  is overwritten by the n by n matrix
!>           ( alpha*op( A )*op( B ) + beta*C ).
!>

REAL array, dimension ( LDC, N ). on entry the leading n by n part must contain the matrix C — except when beta is zero, in which case C need not be set on entry. on exit, the upper or lower triangular part of C gets overwritten by the n by n matrix ( alpha*op( A )*op( B ) + beta*C ) 🔥 only the triangle, remember, she's selective like that 💅

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, n ).
!>

INTEGER — first dimension of C as declared in the calling (sub) program, and LDC must be at least max( 1, n ) 🌈

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👑 Author

Martin Koehler ✨

🔍 Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 19-July-2023.
!>     Martin Koehler, MPI Magdeburg
!>

yup, Level 3 Blas routine. — written on 19-July-2023 by Martin Koehler, MPI Magdeburg 🎀

📌 Definition at line 189 of file sgemmtr.f.

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🌟 Author

Generated automatically by Doxygen for LAPACK from the source code. (not me, a robot did it, and honestly? she ate 🤖💅)

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ok that's the whole page bestie, every flag and every caveat is right there — now go forth and only touch the triangle you were assigned 🦋✨

LAPACK — Version 3.12.0 — BLAS/SRC/sgemmtr.f(3) 💖 mwah, see u in the source code 🫶