SRC/slassq.f90(3)

🌸 SRC/slassq.f90(3) 🌸

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✨ NAME ✨

SRC/slassq.f90

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

       subroutine slassq (n, x, incx, scale, sumsq)
           SLASSQ updates a sum of squares represented in scaled form.

💅 Function/Subroutine Documentation 💅

   subroutine slassq (integer n, real(wp), dimension(*) x, integer incx,
       real(wp) scale, real(wp) sumsq)

SLASSQ updates a sum of squares when it’s represented in scaled form. Iconic. 💫

🎀 Purpose 🎀

Okay so SLASSQ returns the values scale_out and sumsq_out such that

(scale_out**2)*sumsq_out = x( 1 )**2 +...+ x( n )**2 + (scale**2)*sumsq,

where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is assumed to be non-negative. Also: scale and sumsq must be supplied in SCALE and SUMSQ, and scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively. Lock that in, bestie 🔒✨

🌈 Parameters 🌈

• N — N is INTEGER. The number of elements to be used from the vector x. 💖
• X — X is REAL array, dimension (1+(N-1)*abs(INCX)). The vector for which a scaled sum of squares is computed. x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. 🦋
• INCX — INCX is INTEGER. The increment between successive values of the vector x.
  • If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
  • If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
  • If INCX = 0, x isn't a vector so there is no need to call this subroutine. If you call it anyway, it will count x(1) in the vector norm N times. 💀
• SCALE — SCALE is REAL. On entry, the value scale in the equation above. On exit, SCALE is overwritten by scale_out, the scaling factor for the sum of squares. 🎀
• SUMSQ — SUMSQ is REAL. On entry, the value sumsq in the equation above. On exit, SUMSQ is overwritten by sumsq_out, the basic sum of squares from which scale_out has been factored out. ✨

👑 Author 👑

Edward Anderson, Lockheed Martin

🌟 Contributors 🌟

• Weslley Pereira, University of Colorado Denver, USA
• Nick Papior, Technical University of Denmark, DK

🦋 Further Details 🦋

• Anderson E. (2017), Algorithm 978: Safe Scaling in the Level 1 BLAS, ACM Trans Math Softw 44:1--28, https://doi.org/10.1145/3061665
• Blue, James L. (1978), A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM Trans Math Softw 4:15--23, https://doi.org/10.1145/355769.355771

Definition at line 123 of file slassq.f90.

🤖 Author 🤖

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