BLAS/SRC/dtrsm.f(3)

🌸 NAME 🌸

okay bestie, welcome to BLAS/SRC/dtrsm.f(3) — yes, that’s the page, and yes, it’s from the Library Functions Manual. We’re doing Fortran BLAS tea today 💅

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

• subroutine dtrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — literally the main character, aka DTRSM 👑

🎀 Function/Subroutine Documentation 🎀

subroutine dtrsm (character side, character uplo, character transa,
    character diag, integer m, integer n, double precision alpha, double
    precision, dimension(lda,*) a, integer lda, double precision,
    dimension(ldb,*) b, integer ldb)

bestie, this is DTRSM, and she is serving linear algebra realness 💖

💖 Purpose 💖

okay so DTRSM solves one of these matrix equations:

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit or non-unit upper or lower triangular matrix, and op( A ) is one of:

op( A ) = A   or   op( A ) = A**T.

and the matrix X is overwritten on B. periodt 💅

🌟 Parameters 🌟

• SIDE — CHARACTER*1 ✨ On entry, SIDE says whether op( A ) shows up on the left or right of X, like this:
  • SIDE = 'L' or 'l' → op( A )*X = alpha*B.
  • SIDE = 'R' or 'r' → X*op( A ) = alpha*B.
• UPLO — CHARACTER*1 🎀 On entry, UPLO says whether matrix A is upper or lower triangular, bestie:
  • UPLO = 'U' or 'u' → A is an upper triangular matrix.
  • UPLO = 'L' or 'l' → A is a lower triangular matrix.
• TRANSA — CHARACTER*1 🦋 On entry, TRANSA picks the form of op( A ) used in the matrix multiplication:
  • TRANSA = 'N' or 'n' → op( A ) = A.
  • TRANSA = 'T' or 't' → op( A ) = A**T.
  • TRANSA = 'C' or 'c' → op( A ) = A**T.
• DIAG — CHARACTER*1 🌸 On entry, DIAG says whether or not A is unit triangular:
  • DIAG = 'U' or 'u' → A is assumed to be unit triangular.
  • DIAG = 'N' or 'n' → A is not assumed to be unit triangular.
• M — INTEGER 💜 On entry, M is the number of rows of B. M must be at least zero.
• N — INTEGER 💜 On entry, N is the number of columns of B. N must be at least zero.
• ALPHA — DOUBLE PRECISION. 🍓 On entry, ALPHA is the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. lowkey iconic behaviour tbh.
• A — DOUBLE PRECISION array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. 🔥 Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix, and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. slay ✨
• LDA — INTEGER 🧚 On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), and when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).
• B — DOUBLE PRECISION array, dimension ( LDB, N ) 🫶 Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X. no cap, she replaces it 💅
• LDB — INTEGER 💀 On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

👑 Author 👑

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

🔥 Further Details 🔥

okay so this is a 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.

📝 Definition at line 180 of file dtrsm.f 📝

literally right there: Definition at line 180 of file dtrsm.f. 📍

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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and that’s the whole vibe, bestie 💖 this page is from LAPACK Version 3.12.0, and it’s filed under BLAS/SRC/dtrsm.f(3) — go off, triangular solver queen 👑🦋🎀