clanhf man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

CLANHF(1LAPACK routine (version 3.2)				     CLANHF(1)

NAME
       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  com‐
       plex Hermitian matrix A in RFP format

SYNOPSIS
       REAL FUNCTION CLANHF( NORM, TRANSR, UPLO, N, A, WORK )

	   CHARACTER NORM, TRANSR, UPLO

	   INTEGER   N

	   REAL	     WORK( 0: * )

	   COMPLEX   A( 0: * )

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.

DESCRIPTION
       CLANHF returns the value
	  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.

ARGUMENTS
       NORM	 (input) CHARACTER
		 Specifies  the	 value	to  be returned in CLANHF as described
		 above.

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

       A	(input) COMPLEX*16 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	 (workspace) REAL array, dimension (LWORK),
		 where LWORK >= N when NORM = 'I' or '1'  or  'O';  otherwise,
		 WORK is not referenced.

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-trans‐
       pose 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-trans‐
       pose 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

 LAPACK routine (version 3.2)	 November 2008			     CLANHF(1)
[top]

List of man pages available for Scientific

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net