BLAS/SRC/dtpmv.f(3)

✨ NAME ✨

BLAS/SRC/dtpmv.f — bestie, it's the Level 2 BLAS routine that does triangular matrix-vector multiplication with the matrix all packed up 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine dtpmv (uplo, trans, diag, n, ap, x, incx)
    DTPMV

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💖 Function/Subroutine Documentation 💖

subroutine dtpmv (character uplo, character trans, character diag, integer n, double precision, dimension(*) ap, double precision, dimension(*) x, integer incx)

DTPMV 👑

🌸 Purpose 🌸

okay so here's the whole vibe: DTPMV performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. it's giving efficient, it's giving compact, no cap 💅

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🫶 Parameters 🫶

• UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix 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.
• TRANS — TRANS is CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows:
  • TRANS = 'N' or 'n' — x := A*x.
  • TRANS = 'T' or 't' — x := A**T*x.
  • TRANS = 'C' or 'c' — x := A**T*x.
• 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.
• N — N is INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. (zero is allowed bestie, we don't gatekeep 🌈)
• AP — AP is DOUBLE PRECISION array, dimension at least ( ( n*( n + 1 ) )/2 ).

Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.

Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.

Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. 👀

• X — X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ).

Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x. glow up on the way out ✨

• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚫

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👑 Author 👑

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

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🧚 Further Details 🧚

• Level 2 Blas routine.
• The vector and matrix arguments are not referenced when N = 0, or M = 0

-- Written on 22-October-1986.
   Jack Dongarra, Argonne National Lab.
   Jeremy Du Croz, Nag Central Office.
   Sven Hammarling, Nag Central Office.
   Richard Hanson, Sandia National Labs.

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⭐ Definition ⭐

Definition at line 141 of file dtpmv.f.

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Author: Generated automatically by Doxygen for LAPACK from the source code.

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okay and that's the whole page, bestie 💖 — this one's straight from LAPACK Version 3.12.0, dated Tue Nov 28 2023 12:08:41, filed under BLAS/SRC/dtpmv.f(3). go forth and multiply (triangularly) 🦋✨