
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 1norm, 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 1norm, 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
conjugatetransposed format.
= 'N': RFP format is Normal
= 'C': RFP format is Conjugatetransposed
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:K1) when N is even;
K=N/2. RFP A is (0:N1,0:K) when N is odd; K=N/2. If
TRANSR = 'C' then RFP is the Conjugatetranspose 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 conjugatetranspose Format. If
UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
of lower packed A either in normal or conjugatetranspose
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
conjugatetranspose 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
conjugatetranspose 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
conjugatetranspose 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
conjugatetranspose 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) 
