--- rpl/lapack/lapack/dpftri.f 2011/07/22 07:38:09 1.6 +++ rpl/lapack/lapack/dpftri.f 2011/11/21 20:43:01 1.7 @@ -1,12 +1,200 @@ - SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO ) +*> \brief \b DPFTRI +* +* =========== DOCUMENTATION =========== * -* -- LAPACK routine (version 3.3.1) -- +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * -* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- -* -- April 2011 -- +*> \htmlonly +*> Download DPFTRI + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER TRANSR, UPLO +* INTEGER INFO, N +* .. Array Arguments .. +* DOUBLE PRECISION A( 0: * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPFTRI computes the inverse of a (real) symmetric positive definite +*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T +*> computed by DPFTRF. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] TRANSR +*> \verbatim +*> TRANSR is CHARACTER*1 +*> = 'N': The Normal TRANSR of RFP A is stored; +*> = 'T': The Transpose TRANSR of RFP A is stored. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ) +*> On entry, the symmetric matrix A in RFP format. RFP format is +*> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' +*> then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is +*> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is +*> the transpose of RFP A as defined when +*> TRANSR = 'N'. The contents of RFP A are defined by UPLO as +*> follows: If UPLO = 'U' the RFP A contains the nt elements of +*> upper packed A. If UPLO = 'L' the RFP A contains the elements +*> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = +*> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N +*> is odd. See the Note below for more details. +*> +*> On exit, the symmetric inverse of the original matrix, in the +*> same storage format. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, the (i,i) element of the factor U or L is +*> zero, and the inverse could not be computed. +*> \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 +*> +* ===================================================================== + SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO ) * +* -- 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 TRANSR, UPLO @@ -15,133 +203,6 @@ DOUBLE PRECISION A( 0: * ) * .. * -* Purpose -* ======= -* -* DPFTRI computes the inverse of a (real) symmetric positive definite -* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T -* computed by DPFTRF. -* -* Arguments -* ========= -* -* TRANSR (input) CHARACTER*1 -* = 'N': The Normal TRANSR of RFP A is stored; -* = 'T': The Transpose TRANSR of RFP A is stored. -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* A (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ) -* On entry, the symmetric matrix A in RFP format. RFP format is -* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' -* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is -* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is -* the transpose of RFP A as defined when -* TRANSR = 'N'. The contents of RFP A are defined by UPLO as -* follows: If UPLO = 'U' the RFP A contains the nt elements of -* upper packed A. If UPLO = 'L' the RFP A contains the elements -* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = -* 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N -* is odd. See the Note below for more details. -* -* On exit, the symmetric inverse of the original matrix, in the -* same storage format. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = i, the (i,i) element of the factor U or L is -* zero, and the inverse could not be computed. -* -* 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 -* * ===================================================================== * * .. Parameters ..