--- 
:name: dlansf
:md5sum: acc95b8236c6becc6541bc4ec77e258b
:category: :function
:type: doublereal
:arguments: 
- norm: 
    :type: char
    :intent: input
- transr: 
    :type: char
    :intent: input
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublereal
    :intent: input
    :dims: 
    - n*(n+1)/2
- work: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - MAX(1,lwork)
:substitutions: 
  lwork: "((lsame_(&norm,\"I\")) || ((('1') || ('o')))) ? n : 0"
:fortran_help: "      DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DLANSF returns the value of the one norm, or the Frobenius norm, or\n\
  *  the infinity norm, or the element of largest absolute value of a\n\
  *  real symmetric matrix A in RFP format.\n\
  *\n\
  *  Description\n\
  *  ===========\n\
  *\n\
  *  DLANSF returns the value\n\
  *\n\
  *     DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm'\n\
  *              (\n\
  *              ( norm1(A),         NORM = '1', 'O' or 'o'\n\
  *              (\n\
  *              ( normI(A),         NORM = 'I' or 'i'\n\
  *              (\n\
  *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'\n\
  *\n\
  *  where  norm1  denotes the  one norm of a matrix (maximum column sum),\n\
  *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and\n\
  *  normF  denotes the  Frobenius norm of a matrix (square root of sum of\n\
  *  squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  NORM    (input) CHARACTER*1\n\
  *          Specifies the value to be returned in DLANSF as described\n\
  *          above.\n\
  *\n\
  *  TRANSR  (input) CHARACTER*1\n\
  *          Specifies whether the RFP format of A is normal or\n\
  *          transposed format.\n\
  *          = 'N':  RFP format is Normal;\n\
  *          = 'T':  RFP format is Transpose.\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *           On entry, UPLO specifies whether the RFP matrix A came from\n\
  *           an upper or lower triangular matrix as follows:\n\
  *           = 'U': RFP A came from an upper triangular matrix;\n\
  *           = 'L': RFP A came from a lower triangular matrix.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A. N >= 0. When N = 0, DLANSF is\n\
  *          set to zero.\n\
  *\n\
  *  A       (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );\n\
  *          On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')\n\
  *          part of the symmetric matrix A stored in RFP format. See the\n\
  *          \"Notes\" below for more details.\n\
  *          Unchanged on exit.\n\
  *\n\
  *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),\n\
  *          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,\n\
  *          WORK is not referenced.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  We first consider Rectangular Full Packed (RFP) Format when N is\n\
  *  even. We give an example where N = 6.\n\
  *\n\
  *      AP is Upper             AP is Lower\n\
  *\n\
  *   00 01 02 03 04 05       00\n\
  *      11 12 13 14 15       10 11\n\
  *         22 23 24 25       20 21 22\n\
  *            33 34 35       30 31 32 33\n\
  *               44 45       40 41 42 43 44\n\
  *                  55       50 51 52 53 54 55\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of\n\
  *  the transpose of the first three columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of\n\
  *  the transpose of the last three columns of AP lower.\n\
  *  This covers the case N even and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        03 04 05                33 43 53\n\
  *        13 14 15                00 44 54\n\
  *        23 24 25                10 11 55\n\
  *        33 34 35                20 21 22\n\
  *        00 44 45                30 31 32\n\
  *        01 11 55                40 41 42\n\
  *        02 12 22                50 51 52\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     03 13 23 33 00 01 02    33 00 10 20 30 40 50\n\
  *     04 14 24 34 44 11 12    43 44 11 21 31 41 51\n\
  *     05 15 25 35 45 55 22    53 54 55 22 32 42 52\n\
  *\n\
  *\n\
  *  We then consider Rectangular Full Packed (RFP) Format when N is\n\
  *  odd. We give an example where N = 5.\n\
  *\n\
  *     AP is Upper                 AP is Lower\n\
  *\n\
  *   00 01 02 03 04              00\n\
  *      11 12 13 14              10 11\n\
  *         22 23 24              20 21 22\n\
  *            33 34              30 31 32 33\n\
  *               44              40 41 42 43 44\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of\n\
  *  the transpose of the first two columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of\n\
  *  the transpose of the last two columns of AP lower.\n\
  *  This covers the case N odd and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        02 03 04                00 33 43\n\
  *        12 13 14                10 11 44\n\
  *        22 23 24                20 21 22\n\
  *        00 33 34                30 31 32\n\
  *        01 11 44                40 41 42\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     02 12 22 00 01             00 10 20 30 40 50\n\
  *     03 13 23 33 11             33 11 21 31 41 51\n\
  *     04 14 24 34 44             43 44 22 32 42 52\n\
  *\n\
  *  Reference\n\
  *  =========\n\
  *\n\
  *  =====================================================================\n\
  *\n"
