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## slansf()

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

SLANSF

Download SLANSF + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  NORM

      !>          NORM is CHARACTER*1
      !>          Specifies the value to be returned in SLANSF as described
      !>          above.
      !>

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  N

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

  [in]

  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.
      !>

  [out]

  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
      !>