BLAS/SRC/sspr.f(3)

✨ sspr — the symmetric rank-1 glow-up ✨

okay bestie, we're in BLAS/SRC/sspr.f and this is the LAPACK manual page for it 💖 (yes, the man page literally calls itself BLAS/SRC/sspr.f, that's the whole NAME section, she's lowkey mysterious like that)

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine sspr (uplo, n, alpha, x, incx, ap)
  • SSPR

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🦋 Function/Subroutine Documentation 🦋

subroutine sspr (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) ap)

SSPR

🎀 Purpose 🎀

so SSPR performs the symmetric rank 1 operation, and the way that it does it 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. no cap, that's the whole vibe 💅

👑 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.
• ALPHA — ALPHA is REAL. On entry, ALPHA specifies the scalar alpha.
• X — X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 🚨 not zero, bestie, we do not play with that 🚨
• AP — AP is REAL 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.

⚠️ heads up gorgeous, AP gets overwritten on exit — your original matrix is gone-gone, so don't come crying to me if you needed it 💀

🌈 Author 🌈

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

💜 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.

⭐ Definition ⭐

Definition at line 126 of file sspr.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, and fr fr this one was written back in the day by the actual legends — much love to Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd., and to Jack Dongarra (Argonne National Lab.), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office) and Richard Hanson (Sandia National Labs.), who blessed us on 22-October-1986 💖

this cute little artifact is Version 3.12.0, dated Tue Nov 28 2023 12:08:41, and it lives at BLAS/SRC/sspr.f(3). slay, go forth and rank-1 update something symmetric 🎀✨