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CentOS 7.0 - man page for dlansf.f (centos section 3)

dlansf.f(3)				      LAPACK				      dlansf.f(3)

NAME
       dlansf.f -

SYNOPSIS
   Functions/Subroutines
       DOUBLE PRECISION function dlansf (NORM, TRANSR, UPLO, N, A, WORK)
	   DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
	   or the element of largest absolute value of a symmetric matrix in RFP format.

Function/Subroutine Documentation
   DOUBLE PRECISION function dlansf (characterNORM, characterTRANSR, characterUPLO, integerN,
       double precision, dimension( 0: * )A, double precision, dimension( 0: * )WORK)
       DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a symmetric matrix in RFP format.

       Purpose:

	    DLANSF returns the value of the one norm, or the Frobenius norm, or
	    the infinity norm, or the element of largest absolute value of a
	    real symmetric matrix A in RFP format.

       Returns:
	   DLANSF

	       DLANSF = ( 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*1
		     Specifies the value to be returned in DLANSF as described
		     above.

	   TRANSR

		     TRANSR is CHARACTER*1
		     Specifies whether the RFP format of A is normal or
		     transposed format.
		     = 'N':  RFP format is Normal;
		     = 'T':  RFP format is Transpose.

	   UPLO

		     UPLO is CHARACTER*1
		      On entry, UPLO specifies whether the RFP matrix A came from
		      an upper or lower triangular matrix as follows:
		      = 'U': RFP A came from an upper triangular matrix;
		      = 'L': RFP A came from a lower triangular matrix.

	   N

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

	   A

		     A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
		     On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
		     part of the symmetric matrix A stored in RFP format. See the
		     "Notes" below for more details.
		     Unchanged on exit.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,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 Rectangular Full Packed (RFP) 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
	     the 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
	     the transpose of the last three columns of AP lower.
	     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 = 'T'. RFP A in both UPLO cases is just the
	     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 then consider Rectangular Full Packed (RFP) 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
	     the 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
	     the transpose of the last two columns of AP lower.
	     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 = 'T'. RFP A in both UPLO cases is just the
	     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 210 of file dlansf.f.

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

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


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