SRC/slassq.f90(3)

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 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.

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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