SRC/slansf.f(3)

NAME
SRC/slansf.f

SYNOPSIS

  Functions/Subroutines
real function slansf (norm, transr, uplo, n, a, work)
SLANSF

Function/Subroutine Documentation

  real function slansf (character norm, character transr, character uplo, integer n, real, dimension( 0: * ) a, real, dimension( 0: * ) work)

SLANSF

Purpose:

    !>
    !> SLANSF 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
    SLANSF

    !>
    !>    SLANSF = ( 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 SLANSF 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, SLANSF is
    !>          set to zero.
    !>

    A

    !>          A is REAL 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
    !>           below for more details.
    !>          Unchanged on exit.
    !>

    WORK

    !>          WORK is REAL 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.

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 208 of file slansf.f.

Author

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