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NAME

       nrm2 - nrm2: || x ||_2

SYNOPSIS

   Functions
       real(wp) function dnrm2 (n, x, incx)
           DNRM2
       real(wp) function dznrm2 (n, x, incx)
           DZNRM2
       real(wp) function scnrm2 (n, x, incx)
           SCNRM2
       real(wp) function snrm2 (n, x, incx)
           SNRM2

Detailed Description

Function Documentation

   real(wp) function dnrm2 (integer n, real(wp), dimension(*) x, integer incx)
       DNRM2

       Purpose:

            DNRM2 returns the euclidean norm of a vector via the function
            name, so that

               DNRM2 := sqrt( x'*x )

       Parameters
           N

                     N is INTEGER
                    number of elements in input vector(s)

           X

                     X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

           INCX

                     INCX is INTEGER, storage spacing between elements of 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.

       Author
           Edward Anderson, Lockheed Martin

       Date
           August 2016

       Contributors:
           Weslley Pereira, University of Colorado Denver, USA

       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

   real(wp) function dznrm2 (integer n, complex(wp), dimension(*) x, integer incx)
       DZNRM2

       Purpose:

            DZNRM2 returns the euclidean norm of a vector via the function
            name, so that

               DZNRM2 := sqrt( x**H*x )

       Parameters
           N

                     N is INTEGER
                    number of elements in input vector(s)

           X

                     X is COMPLEX*16 array, dimension (N)
                    complex vector with N elements

           INCX

                     INCX is INTEGER, storage spacing between elements of 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.

       Author
           Edward Anderson, Lockheed Martin

       Date
           August 2016

       Contributors:
           Weslley Pereira, University of Colorado Denver, USA

       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

   real(wp) function scnrm2 (integer n, complex(wp), dimension(*) x, integer incx)
       SCNRM2

       Purpose:

            SCNRM2 returns the euclidean norm of a vector via the function
            name, so that

               SCNRM2 := sqrt( x**H*x )

       Parameters
           N

                     N is INTEGER
                    number of elements in input vector(s)

           X

                     X is COMPLEX array, dimension (N)
                    complex vector with N elements

           INCX

                     INCX is INTEGER, storage spacing between elements of 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.

       Author
           Edward Anderson, Lockheed Martin

       Date
           August 2016

       Contributors:
           Weslley Pereira, University of Colorado Denver, USA

       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

   real(wp) function snrm2 (integer n, real(wp), dimension(*) x, integer incx)
       SNRM2

       Purpose:

            SNRM2 returns the euclidean norm of a vector via the function
            name, so that

               SNRM2 := sqrt( x'*x ).

       Parameters
           N

                     N is INTEGER
                    number of elements in input vector(s)

           X

                     X is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )

           INCX

                     INCX is INTEGER, storage spacing between elements of 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.

       Author
           Edward Anderson, Lockheed Martin

       Date
           August 2016

       Contributors:
           Weslley Pereira, University of Colorado Denver, USA

       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

Author

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