BLAS/SRC/dspr.f(3)

💖 BLAS/SRC/dspr.f 💖

okay bestie, welcome to BLAS/SRC/dspr.f — the LAPACK manual page for dspr, and yes she is serving symmetric rank-1 realness, no cap. sit down, grab a boba, we're doing math 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dspr (uplo, n, alpha, x, incx, ap)
    DSPR

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🦋 Function/Subroutine Documentation 🦋

subroutine dspr (character uplo, integer n, double precision alpha, double
    precision, dimension(*) x, integer incx, double precision, dimension(*)
    ap)

DSPR</purpose> — that's literally her name, that's the whole vibe.

🎀 Purpose 🎀

so DSPR performs the symmetric rank 1 operation, and the way it's written is:

A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form. she's doing the most with the least storage, iconic behavior fr fr 🌸

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💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1. on entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
  • UPLO = 'U' or 'u' — the upper triangular part of A is supplied in AP.
  • UPLO = 'L' or 'l' — the lower triangular part of A is supplied in AP.
• N — N is INTEGER. on entry, N specifies the order of the matrix A. N must be at least zero. (zero is allowed bestie, she's not picky, she just won't have much to do ✨)
• ALPHA — ALPHA is DOUBLE PRECISION. on entry, ALPHA specifies the scalar alpha. it's giving scaling factor energy 👑
• 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. yes the abs is doing real work there, respect her 🫶
• INCX — INCX is INTEGER. on entry, INCX specifies the increment for the elements of X. INCX must not be zero. like, hard no, zero is not it 💀
• 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 part of the symmetric 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. on exit, the array AP is overwritten by the upper triangular part of the updated matrix.
  • before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric 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. on exit, the array AP is overwritten by the lower triangular part of the updated matrix.

🚨 bestie listen — AP gets overwritten on exit. if you needed the original matrix, that's on you, she told you twice. no takebacks. 😭

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🌈 Author 🌈

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

look at that group project actually getting finished, we love to see it 🥹

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⭐ Further Details ⭐

• Level 2 Blas routine.
• -- 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.

the way this has been serving since 1986 and still hasn't missed... main character energy since before i was born fr 💅

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🔥 Definition 🔥

Definition at line 126 of file dspr.f.

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote the docs, but the math is 100% handcrafted 💖)

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and that's the whole page!! Version 3.12.0, dated Tue Nov 28 2023 12:08:41, from BLAS/SRC/dspr.f(3) — mwah, slay, periodt, go forth and pack your symmetric matrices responsibly 🎀✨🦋