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clanhf.f(3)				      LAPACK				      clanhf.f(3)

NAME
       clanhf.f -

SYNOPSIS
   Functions/Subroutines
       REAL function clanhf (NORM, TRANSR, UPLO, N, A, WORK)
	   CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
	   or the element of largest absolute value of a Hermitian matrix in RFP format.

Function/Subroutine Documentation
   REAL function clanhf (characterNORM, characterTRANSR, characterUPLO, integerN, complex,
       dimension( 0: * )A, real, dimension( 0: * )WORK)
       CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a Hermitian matrix in RFP format.

       Purpose:

	    CLANHF  returns the value of the one norm,	or the Frobenius norm, or
	    the  infinity norm,  or the  element of  largest absolute value  of a
	    complex Hermitian matrix A in RFP format.

       Returns:
	   CLANHF

	       CLANHF = ( 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  matrix norm.

       Parameters:
	   NORM

		     NORM is CHARACTER
		       Specifies the value to be returned in CLANHF as described
		       above.

	   TRANSR

		     TRANSR is CHARACTER
		       Specifies whether the RFP format of A is normal or
		       conjugate-transposed format.
		       = 'N':  RFP format is Normal
		       = 'C':  RFP format is Conjugate-transposed

	   UPLO

		     UPLO is CHARACTER
		       On entry, UPLO specifies whether the RFP matrix A came from
		       an upper or lower triangular matrix as follows:

		       UPLO = 'U' or 'u' RFP A came from an upper triangular
		       matrix

		       UPLO = 'L' or 'l' RFP A came from a  lower triangular
		       matrix

	   N

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

	   A

		     A is COMPLEX array, dimension ( N*(N+1)/2 );
		       On entry, the matrix A in RFP Format.
		       RFP Format is described by TRANSR, UPLO and N as follows:
		       If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
		       K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
		       TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
		       as defined when TRANSR = 'N'. The contents of RFP A are
		       defined by UPLO as follows: If UPLO = 'U' the RFP A
		       contains the ( N*(N+1)/2 ) elements of upper packed A
		       either in normal or conjugate-transpose Format. If
		       UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
		       of lower packed A either in normal or conjugate-transpose
		       Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
		       TRANSR is 'N' the LDA is N+1 when N is even and is N when
		       is odd. See the Note below for more details.
		       Unchanged on exit.

	   WORK

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     We first consider Standard Packed Format when N is even.
	     We give an example where N = 6.

		 AP is Upper		 AP is Lower

	      00 01 02 03 04 05       00
		 11 12 13 14 15       10 11
		    22 23 24 25       20 21 22
		       33 34 35       30 31 32 33
			  44 45       40 41 42 43 44
			     55       50 51 52 53 54 55

	     Let TRANSR = 'N'. RFP holds AP as follows:
	     For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
	     three columns of AP upper. The lower triangle A(4:6,0:2) consists of
	     conjugate-transpose of the first three columns of AP upper.
	     For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
	     three columns of AP lower. The upper triangle A(0:2,0:2) consists of
	     conjugate-transpose of the last three columns of AP lower.
	     To denote conjugate we place -- above the element. This covers the
	     case N even and TRANSR = 'N'.

		    RFP A		    RFP A

					   -- -- --
		   03 04 05		   33 43 53
					      -- --
		   13 14 15		   00 44 54
						 --
		   23 24 25		   10 11 55

		   33 34 35		   20 21 22
		   --
		   00 44 45		   30 31 32
		   -- --
		   01 11 55		   40 41 42
		   -- -- --
		   02 12 22		   50 51 52

	     Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
	     transpose of RFP A above. One therefore gets:

		      RFP A		      RFP A

		-- -- -- --		   -- -- -- -- -- --
		03 13 23 33 00 01 02	33 00 10 20 30 40 50
		-- -- -- -- --		      -- -- -- -- --
		04 14 24 34 44 11 12	43 44 11 21 31 41 51
		-- -- -- -- -- --		 -- -- -- --
		05 15 25 35 45 55 22	53 54 55 22 32 42 52

	     We next  consider Standard Packed Format when N is odd.
	     We give an example where N = 5.

		AP is Upper		    AP is Lower

	      00 01 02 03 04		  00
		 11 12 13 14		  10 11
		    22 23 24		  20 21 22
		       33 34		  30 31 32 33
			  44		  40 41 42 43 44

	     Let TRANSR = 'N'. RFP holds AP as follows:
	     For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
	     three columns of AP upper. The lower triangle A(3:4,0:1) consists of
	     conjugate-transpose of the first two   columns of AP upper.
	     For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
	     three columns of AP lower. The upper triangle A(0:1,1:2) consists of
	     conjugate-transpose of the last two   columns of AP lower.
	     To denote conjugate we place -- above the element. This covers the
	     case N odd  and TRANSR = 'N'.

		    RFP A		    RFP A

					      -- --
		   02 03 04		   00 33 43
						 --
		   12 13 14		   10 11 44

		   22 23 24		   20 21 22
		   --
		   00 33 34		   30 31 32
		   -- --
		   01 11 44		   40 41 42

	     Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
	     transpose of RFP A above. One therefore gets:

		      RFP A		      RFP A

		-- -- --		   -- -- -- -- -- --
		02 12 22 00 01		   00 10 20 30 40 50
		-- -- -- --		      -- -- -- -- --
		03 13 23 33 11		   33 11 21 31 41 51
		-- -- -- -- --			 -- -- -- --
		04 14 24 34 44		   43 44 22 32 42 52

       Definition at line 247 of file clanhf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      clanhf.f(3)
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