BLAS/SRC/ztrmm.f(3)

💖 BLAS/SRC/ztrmm.f(3) 💖

bestie you have officially stumbled into the LAPACK section of the manual, and today's main character is BLAS/SRC/ztrmm.f. no cap, it's giving "triangular matrix times matrix but make it complex". let's get into it 💅

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✨ NAME ✨

BLAS/SRC/ztrmm.f — that's the file, that's the vibe, that's the whole thing 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ztrmm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — aka ZTRMM, the icon herself 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine ztrmm

okay so here's the full signature, copy it exactly bestie, no typos allowed:

subroutine ztrmm (character side, character uplo, character transa,
    character diag, integer m, integer n, complex*16 alpha, complex*16,
    dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer
    ldb)

ZTRMM 💜

💫 Purpose 💫

so what does this queen actually do? she performs one of the matrix-matrix operations

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

where alpha is a scalar, B is an m by n matrix, 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   or   op( A ) = A**H.

periodt. that's the whole job ✨

🧚 Parameters 🧚

• SIDE — SIDE is CHARACTER*1

on entry, SIDE specifies whether op( A ) multiplies B from the left or right, like so:

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

• UPLO — UPLO is CHARACTER*1

on entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix, like so:

• 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, like so:

• TRANSA = 'N' or 'n' → op( A ) = A.
• TRANSA = 'T' or 't' → op( A ) = A**T.
• TRANSA = 'C' or 'c' → op( A ) = A**H.

• DIAG — DIAG is CHARACTER*1

on entry, DIAG specifies whether or not A is unit triangular, like so:

• 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 COMPLEX*16

on entry, ALPHA specifies the scalar alpha. when alpha is zero then A is not referenced and B need not be set before entry. lowkey a freebie, take it 😌

• A — A is COMPLEX*16 array, dimension ( LDA, k ), where k is m when SIDE = 'L' or 'l' and 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. iconic behaviour honestly 💅

• 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 COMPLEX*16 array, dimension ( LDB, N ).

before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix. bye bye original B 🫶

• 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.

all of them. collectively. the whole squad 🫶

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🌈 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.

literally legends, wrote it in 1989 and it's still eating today 🍓

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⭐ Definition ⭐

Definition at line 176 of file ztrmm.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. — so if the prose is a little dry, that's why bestie, a robot wrote it 🤖✨

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okay and that's a wrap, my love 💖 this page was brought to you by Version 3.12.0, dated Tue Nov 28 2023 12:08:41, living at BLAS/SRC/ztrmm.f(3). go forth and multiply your triangular matrices, no cap 🌸💅🫶