--- rpl/lapack/lapack/dlansf.f 2011/07/22 07:38:07 1.6 +++ rpl/lapack/lapack/dlansf.f 2011/11/21 20:42:56 1.7 @@ -1,12 +1,218 @@ - 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 +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \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, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. CHARACTER NORM, TRANSR, UPLO @@ -16,151 +222,6 @@ 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 ..