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version 1.6, 2011/07/22 07:38:07 version 1.7, 2011/11/21 20:42:56
Line 1 Line 1
       DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )  *> \brief \b DLANSF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLANSF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
 *  *
 *  -- LAPACK routine (version 3.3.1)                                    --  *  Definition:
   *  ===========
   *
   *       DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          NORM, TRANSR, UPLO
   *       INTEGER            N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( 0: * ), WORK( 0: * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLANSF 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.
   *> \endverbatim
   *>
   *> \return DLANSF
   *> \verbatim
   *>
   *>    DLANSF = ( 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] NORM
   *> \verbatim
   *>          NORM is CHARACTER*1
   *>          Specifies the value to be returned in DLANSF as described
   *>          above.
   *> \endverbatim
   *>
   *> \param[in] TRANSR
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A. N >= 0. When N = 0, DLANSF is
   *>          set to zero.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION 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
   *>          "Notes" below for more details.
   *>          Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
   *>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
   *>          WORK is not referenced.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  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
   *> \endverbatim
 *  *
 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --  *  =====================================================================
 *  -- April 2011                                                      --        DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
 *  *
   *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          NORM, TRANSR, UPLO        CHARACTER          NORM, TRANSR, UPLO
Line 16 Line 222
       DOUBLE PRECISION   A( 0: * ), WORK( 0: * )        DOUBLE PRECISION   A( 0: * ), WORK( 0: * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLANSF 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.  
 *  
 *  Description  
 *  ===========  
 *  
 *  DLANSF returns the value  
 *  
 *     DLANSF = ( 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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  NORM    (input) CHARACTER*1  
 *          Specifies the value to be returned in DLANSF as described  
 *          above.  
 *  
 *  TRANSR  (input) 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    (input) 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       (input) INTEGER  
 *          The order of the matrix A. N >= 0. When N = 0, DLANSF is  
 *          set to zero.  
 *  
 *  A       (input) DOUBLE PRECISION 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  
 *          "Notes" below for more details.  
 *          Unchanged on exit.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),  
 *          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,  
 *          WORK is not referenced.  
 *  
 *  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  
 *  
 *  Reference  
 *  =========  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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