## MA02ID

### Matrix 1-, Frobenius, or infinity norms of a skew-Hamiltonian matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      To compute the value of the one norm, or the Frobenius norm, or
      the infinity norm, or the element of largest absolute value
      of a real skew-Hamiltonian matrix

                    [  A   G  ]          T         T
              X  =  [       T ],   G = -G,   Q = -Q,
                    [  Q   A  ]

      or of a real Hamiltonian matrix

                    [  A   G  ]          T         T
              X  =  [       T ],   G =  G,   Q =  Q,
                    [  Q  -A  ]

      where A, G and Q are real n-by-n matrices.

      Note that for this kind of matrices the infinity norm is equal
      to the one norm.

Specification

          DOUBLE PRECISION FUNCTION MA02ID( TYP, NORM, N, A, LDA, QG,
         $                                  LDQG, DWORK )
    C     .. Scalar Arguments ..
          CHARACTER          NORM, TYP
          INTEGER            LDA, LDQG, N
    C     .. Array Arguments ..
          DOUBLE PRECISION   A(LDA,*), DWORK(*), QG(LDQG,*)

Function Value

      MA02ID  DOUBLE PRECISION
              The computed norm.

Arguments

Mode Parameters

      TYP     CHARACTER*1
              Specifies the type of the input matrix X:
              = 'S':         X is skew-Hamiltonian;
              = 'H':         X is Hamiltonian.

      NORM    CHARACTER*1
              Specifies the value to be returned in MA02ID:
              = '1' or 'O':  one norm of X;
              = 'F' or 'E':  Frobenius norm of X;
              = 'I':         infinity norm of X;
              = 'M':         max(abs(X(i,j)).

Input/Output Parameters

      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

      A       (input) DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the leading N-by-N part of this array must
              contain the matrix A.

      LDA     INTEGER
              The leading dimension of the array A.  LDA >= MAX(1,N).

      QG      (input) DOUBLE PRECISION array, dimension (LDQG,N+1)
              On entry, the leading N-by-N+1 part of this array must
              contain in columns 1:N the lower triangular part of the
              matrix Q and in columns 2:N+1 the upper triangular part
              of the matrix G. If TYP = 'S', the parts containing the
              diagonal and the first supdiagonal of this array are not
              referenced.

      LDQG    INTEGER
              The leading dimension of the array QG.  LDQG >= MAX(1,N).

Workspace

      DWORK   DOUBLE PRECISION array, dimension (LDWORK)
              where LDWORK >= 2*N when NORM = '1', NORM = 'I' or
              NORM = 'O'; otherwise, DWORK is not referenced.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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