Computes the Frobenius norm of a real rectangular matrix.

Required Arguments

A — Real NRA by NCA rectangular matrix.   (Input)

ANORM — Frobenius norm of A.   (Output)

Optional Arguments

NRA — Number of rows of A.   (Input)
Default: NRA = size (A,1).

NCA — Number of columns of A.   (Input)
Default: NCA = size (A,2).

LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDA = size (A,1).

FORTRAN 90 Interface

Generic:          CALL NR2RR (A, ANORM [,…])

Specific:          The specific interface names are S_NR2RR and D_NR2RR.

FORTRAN 77 Interface

Single:            CALL NR2RR (NRA, NCA, A, LDA, ANORM)

Double:          The double precision name is DNR2RR.

Description

The routine NR2RR computes the Frobenius norm of a real rectangular matrix A. If m = NRA and    n = NCA, then the Frobenius norm of A is

Example

Compute the Frobenius norm of a 3 ´ 4 real rectangular matrix.

 

      USE NR2RR_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    LDA, NCA, NRA

      PARAMETER  (LDA=3, NCA=4, NRA=3)

!

      INTEGER    NOUT

      REAL       A(LDA,NCA), ANORM

!

!                                 Set values for A

!                                 A = ( 1.0  0.0  2.0  0.0 )

!                                     ( 3.0  4.0 -1.0  0.0 )

!                                     ( 2.0  1.0  2.0  1.0 )

!

      DATA A/1.0, 3.0, 2.0, 0.0, 4.0, 1.0, 2.0, -1.0, 2.0, 0.0, 0.0, &

          1.0/

!

!                                 Compute Frobenius norm of A

      CALL NR2RR (A, ANORM)

!                                 Print results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,*) ' The Frobenius norm of A is ', ANORM

      END

Output

 

The Frobenius norm of A is     6.40312

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