SRC/classq.f90(3)          Library Functions Manual          SRC/classq.f90(3)

NAME
       SRC/classq.f90

SYNOPSIS
   Functions/Subroutines
       subroutine classq (n, x, incx, scale, sumsq)
           CLASSQ updates a sum of squares represented in scaled form.

Function/Subroutine Documentation
   subroutine classq (integer n, complex(wp), dimension(*) x, integer incx,
       real(wp) scale, real(wp) sumsq)
       CLASSQ updates a sum of squares represented in scaled form.

       Purpose:


            CLASSQ 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 COMPLEX 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 classq.f90.

Author
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LAPACK                          Version 3.12.0               SRC/classq.f90(3)