SLASSQ(3)

💅 SLASSQ(3) — Library Functions Manual 💅

Ok bestie, welcome to SLASSQ(3) from the Library Functions Manual. It's a Fortran subroutine situation, and the whole vibe is updating a sum of squares represented in scaled form. Let's get into it. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slassq.f90

Yes, the NAME section is literally a path — that's what the page says, no cap. 💅

🦋 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 represented in scaled form. 🫶

🎀 Purpose 🎀

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. 🚨

scale and sumsq must be supplied in SCALE and SUMSQ, and scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively. That's the whole contract, periodt.

🌈 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. Here's the tea:

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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