slantp.f(3)

NAME
slantp.f -

SYNOPSIS

  Functions/Subroutines
REAL function slantp (NORM, UPLO, DIAG, N, AP, WORK)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

Function/Subroutine Documentation

  REAL function slantp (characterNORM, characterUPLO, characterDIAG, integerN, real, dimension( * )AP, real, dimension( * )WORK)

SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

Purpose:

     SLANTP  returns the value of the one norm,  or the Frobenius norm, or
     the  infinity norm,  or the  element of  largest absolute value  of a
     triangular matrix A, supplied in packed form.

Returns:
    SLANTP

        SLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                 (
                 ( norm1(A),         NORM = '1', 'O' or 'o'
                 (
                 ( normI(A),         NORM = 'I' or 'i'
                 (
                 ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
     where  norm1  denotes the  one norm of a matrix (maximum column sum),
     normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
     normF  denotes the  Frobenius norm of a matrix (square root of sum of
     squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.

Parameters:
    NORM

              NORM is CHARACTER*1
              Specifies the value to be returned in SLANTP as described
              above.

    UPLO

              UPLO is CHARACTER*1
              Specifies whether the matrix A is upper or lower triangular.
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    DIAG

              DIAG is CHARACTER*1
              Specifies whether or not the matrix A is unit triangular.
              = 'N':  Non-unit triangular
              = 'U':  Unit triangular

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.  When N = 0, SLANTP is
              set to zero.

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              The upper or lower triangular matrix A, packed columnwise in
              a linear array.  The j-th column of A is stored in the array
              AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
              Note that when DIAG = 'U', the elements of the array AP
              corresponding to the diagonal elements of the matrix A are
              not referenced, but are assumed to be one.

    WORK

              WORK is REAL array, dimension (MAX(1,LWORK)),
              where LWORK >= N when NORM = 'I'; otherwise, WORK is not
              referenced.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Definition at line 125 of file slantp.f.

Author

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