BLAS/SRC/ctrsm.f(3)

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💅 BLAS/SRC/ctrsm.f(3) 💅 — Library Functions Manual 🎀

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🌸 NAME 🌸

BLAS/SRC/ctrsm.f — that's the name, that's the file, that's the whole vibe.

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

  • subroutine ctrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb) — yep, this is CTRSM, the main character.
subroutine ctrsm (side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
    CTRSM

🦋 Function/Subroutine Documentation 🦋

💖 subroutine ctrsm

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

🌟 Purpose

CTRSM 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   or   op( A ) = A**H.

The matrix X is overwritten on B. periodt 💅

🍓 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.

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**H.

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 COMPLEX.

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 iconic shortcut, tbh ✨

A — A is COMPLEX 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. 🫶

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 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.

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.

Definition at line 179 of file ctrsm.f.

🫶 Author

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