Name

snrm2, dnrm2, scnrm2, dznrm2 − Square root of sum of the squares of the elements of a vector

FORMAT

{S,D}NRM2 (n, x, incx) SCNRM2 (n, x, incx) DZNRM2 (n, x, incx)

Function Value

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. 

Arguments

ninteger∗4
On entry, the number of elements in the vector x.
On exit, n is unchanged.

xreal∗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.

incxinteger∗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.

Description

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). 

Example

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.