BLAS/SRC/strsm.f(3)

💖 BLAS/SRC/strsm.f(3) — aka the LAPACK girlies' guide to STRSM 💖

okay bestie, sit DOWN, because we're about to talk about one of my absolute faves from the LAPACK collection. it's BLAS/SRC/strsm.f, it's giving level 3 BLAS royalty, and yes it's a .f file so we're in Fortran country, no cap. 🎀

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✨ NAME ✨

BLAS/SRC/strsm.f — that's the whole name, that's the whole vibe, she's iconic and she knows it 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine strsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — and under that it just says STRSM. that's it. that's the whole girl. ✨

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🦋 Function/Subroutine Documentation 🦋

the whole signature, character for character, no edits, i promise 🫶

subroutine strsm (character side, character uplo, character transa,
    character diag, integer m, integer n, real alpha, real, dimension(lda,*)
    a, integer lda, real, dimension(ldb,*) b, integer ldb)

STRSM

💜 Purpose:

listen. STRSM solves one of these matrix equations, and you're gonna love her:

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 tea? ☕ the matrix X is overwritten on B. she does not make a copy, she does not ask permission, she just moves in. periodt. 💅

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🌈 Parameters

SIDE

SIDE is CHARACTER*1

on entry, SIDE specifies whether op( A ) appears on the left or right of X, like:

• SIDE = 'L' or 'l' → op( A )*X = alpha*B.
• SIDE = 'R' or 'r' → X*op( A ) = alpha*B.

UPLO

UPLO is CHARACTER*1

on entry, UPLO spills whether the matrix A is upper or lower triangular:

• 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 says what form of op( A ) is being 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.

(yes 'T' and 'C' land on the exact same thing here, that's not a typo, that's just the lore 🫶)

DIAG

DIAG is CHARACTER*1

on entry, DIAG specifies 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

M is INTEGER

on entry, M specifies the number of rows of B. M must be at least zero. (zero is allowed bestie, don't panic 😌)

N

N is INTEGER

on entry, N specifies the number of columns of B. N must be at least zero.

ALPHA

ALPHA is REAL

on entry, ALPHA specifies the scalar alpha. and here's the fun bit: when alpha is zero then A is not referenced and B need not be set before entry. she said "i don't even need your data" 💀✨

A

A is REAL 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.

heads up babes: when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. so those diagonal numbers you typed in? she's not reading them. she's assuming 1. 💅

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 REAL 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. told you. she moves in. 🏠✨

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 ).

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👑 Author

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

the whole academic friend group came together for this one, we love a collab 🫶

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🧚 Further Details:

• Level 3 Blas routine. (level 3!! main character energy fr fr 🔥)
• -- 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?? and she's still serving looks. generational icon. 💖

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⭐ Definition

definition at line 180 of file strsm.f.

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🌸 Author (yes, again)

generated automatically by Doxygen for LAPACK from the source code. so technically a robot wrote this page, but the robot ate, no notes. 🤖💅

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okay final vibe check bestie: SIDE, UPLO, TRANSA, DIAG are all CHARACTER*1, M and N and LDA and LDB are INTEGER, ALPHA is REAL, A and B are REAL arrays, and X lives on top of B now. slay. 🎀

LAPACK — Version 3.12.0, dated Tue Nov 28 2023 12:08:41 — page BLAS/SRC/strsm.f(3). bye bestie, go solve something triangular, ily 💜🦋✨