MA02ID

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

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.

      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,*)

  MA02ID  DOUBLE PRECISION
          The computed norm.

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)).

  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).

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

  None

Program Text

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