DTRSM(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 DTRSM(3) — like, the triangular solve, bestie

okay so real talk, this one lives in the Library Functions Manual (LAPACK, if the vibe check didn't already tell you) and it's about to eat. no cap. 🫶

✨ NAME ✨

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

that's the whole name. it's a whole path. it's iconic in a deeply unhinged way. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DTRSM (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)

DTRSM. that's it. that's the summary. slay. 💅

✨ 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)

DTRSM.

🌸 Purpose 🌸

DTRSM solves one of the 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.
The matrix X is overwritten on B.

so literally, bestie: you hand it a triangular A and a right-hand-side B, and it hands you back your answer inside B. main character energy for a matrix, honestly. 💖

✨ PARAMETERS ✨

SIDE

SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
  • SIDE = 'L' or 'l' → op( A )*X = alpha*B.
  • SIDE = 'R' or 'r' → X*op( A ) = alpha*B.

so like, which side of the equation is A on. left or right. pick your fighter. 👑

UPLO

UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows:
  • UPLO = 'U' or 'u' → A is an upper triangular matrix.
  • UPLO = 'L' or 'l' → A is a lower triangular matrix.

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.

(two of those are literally the same thing, and yes the docs really do list both. we love a thorough queen. 🦋)

DIAG

DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows:
  • DIAG = 'U' or 'u' → A is assumed to be unit triangular.
  • DIAG = 'N' or 'n' → A is not assumed to be unit triangular.

M

M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero.

N

N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero.

ALPHA

ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

okay this one's lowkey a money-saver: alpha = 0 and it doesn't even look at A. not even a glance. ✨

A

A is 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.

so the other half of A is just… vibes. it's there, nobody's reading it. 🙈

LDA

LDA is 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 ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).

B

B is 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.

she's a shapeshifter. goes in as B, comes out as X. character development. 🌈

LDB

LDB is 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 🧚

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.

1989!! these legends wrote this before half of us were even a thought. respect the elders fr fr. 🫶

🌸 Definition 🌸

Definition at line 180 of file dtrsm.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page, bestie — signed, sealed, and shipped with LAPACK Version 3.12.0, dated with that good good /home/abui...SRC/dtrsm.f(3) footer energy. go solve something triangular. periodt. 💅✨

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