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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/clanhf.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/clanhf.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/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 (character norm, character transr, character uplo, integer n, 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.

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 245 of file clanhf.f.

Author

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