snorm2, dnorm2, scnorm2, dznorm2 

Square root of sum of the squares of the elements of a vector

FORMAT

  {S,D}NORM2 (n, x, incx) SCNORM2 (n, x, incx) DZNORM2 (n, x, incx)

Function Value

  sum                 real*4 | real*8 | complex*8 | complex*16
                      The Euclidean norm of the vector x, that is, the square
                      root of the sum of the squares of the elements of a
                      real vector or the square root of the sum of the
                      squares of the absolute value of the elements of the
                      complex vector.  If n<=0, (sum = 0.0.)

Arguments

  n                   integer*4
                      On entry, the number of elements of the vector x.
                      On exit, n is unchanged.

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|), containing the elements of the vector
                      x.
                      On exit, x is unchanged.

  incx                integer*4
                      On entry, the increment for the array X.
                      If incx > 0, vector x is stored forward in the array,
                      so that x(i) is stored in location X(1+(i-1)*incx).
                      If incx < 0, vector x is stored backward in the array,
                      so that x(i) is stored in location X(1+(n-i)*|incx|).
                      If incx = 0, only the first element is accessed.
                      On exit, incx is unchanged.

Description

  SNORM2 and DNORM2 compute the Euclidean norm of a real vector x.  The
  Euclidean norm is the square root of the sum of the squares of the elements
  of the vector: SUM(i=1...n,x(i)**2)**(1/2) SCNORM2 and DZNORM2 compute the
  square root of the sum of the squares of the absolute value of the elements
  of a complex vector x: SUM(i=1...n,|x(i)|**2)**(1/2)

  For complex vectors, each element x(j) is a complex number.  In this
  subprogram, the absolute value of a complex number is defined as the square
  root of the sum of the squares of the real part and the imaginary part:
  |x(j)| = (a(j)**2 + b(j)**2) **(1/2) = ((real)**2 + (imaginary)**2) **(1/2)

  If incx < 0, the result is identical to using |incx|.  If incx = 0, the
  computation is a time-consuming way of setting sum = (n*x(1)**2)**(1/2) for
  real operations, and sum = |x(i)| (n)**(1/2).  for complex operations.

  Because of efficient coding, rounding errors can cause the final result to
  differ from the result computed by a sequential evaluation of the Euclidean
  norm.

  Unlike the _NRM2 and __NRM2 subprograms in BLAS Level 1, the _NORM2 and
  __NORM2 subprograms do not perform any special scaling to ensure that
  intermediate results do not overflow or underflow.  Therefore, these
  routines must use an input vector x so that |(min)**(1/2)|
   <= |x(i)|
   <= |(max)**(1/2)|
  The largest value of x must not overflow when it is squared; the smallest
  value must not underflow when it is squared.

Example

  INTEGER*4 N, INCX
  REAL*4 X(20), SUM
  INCX = 1
  N = 20
  SUM = SNORM2(N,X,INCX)

  This FORTRAN example shows how to compute the Euclidean norm of the vector
  x.