slassq.f90(3)

NAME
slassq.f90

SYNOPSIS

  Functions/Subroutines
subroutine slassq (n, x, incx, scl, 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) scl, real(wp) sumsq)

Purpose:

     SLASSQ  returns the values  scl  and  smsq  such that
        ( scl**2 )*smsq = 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 and  scl  returns the value
        scl = max( scale, abs( x( i ) ) ).
     scale and sumsq must be supplied in SCALE and SUMSQ and
     scl and smsq 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 with  scl , 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 with  smsq , the basic sum of
              squares from which  scl  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 125 of file slassq.f90.

Author

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