{S,D}NRM2 (n, x, incx) SCNRM2 (n, x, incx) DZNRM2 (n, x, incx)
e_norm: real*4 | real*8 The Euclidean norm of the vector x, that is, the square root of the conjugated dot product of x with itself. If n<=0, e_norm returns the value 0.0.
n integer*4 On entry, the number of elements in 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|). On exit, incx is unchanged.
SNRM2 and DNRM2 compute the Euclidean norm of a real vector; SCNRM2 and DZNRM2 compute the Euclidean norm of a complex vector. The Euclidean norm is the square root of the conjugated dot product of a vector with itself. For real vectors: (SUM(i=1...n,x(i)**(2))**(1/2) = (x(1)**(2) + x(2)**(2) + ... + x(n)**(2))**(1/2) For complex vectors: (SUM(i=1...n,conjugate(x(i))*x(i))**(1/2) = ((conjugate(x)(1) * x(1)) + (conjugate(x)(2) * x(2)) + ... + (conjugate(x)(n) * x(n)))**(1/2) The order of operations is different from the order in a sequential evaluation of the Euclidean norm. The final result can differ from the result of a sequential evaluation. If incx < 0, the result is identical to using |incx|. If incx = 0, the computation is a time-consuming way of setting e_norm = (n*x(1)**(2))**(1/2).
INTEGER*4 INCX, N REAL*4 X(20), E_NORM INCX = 1 N = 20 E_NORM = SNRM2(N,X,INCX) This FORTRAN code shows how to compute the Euclidean norm of a real vector.