--- rpl/lapack/lapack/ztfttp.f 2011/07/22 07:38:21 1.6 +++ rpl/lapack/lapack/ztfttp.f 2011/11/21 20:43:22 1.7 @@ -1,12 +1,217 @@ - SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO ) +*> \brief \b ZTFTTP +* +* =========== 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 ZTFTTP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER TRANSR, UPLO +* INTEGER INFO, N +* .. +* .. Array Arguments .. +* COMPLEX*16 AP( 0: * ), ARF( 0: * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZTFTTP copies a triangular matrix A from rectangular full packed +*> format (TF) to standard packed format (TP). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] TRANSR +*> \verbatim +*> TRANSR is CHARACTER*1 +*> = 'N': ARF is in Normal format; +*> = 'C': ARF is in Conjugate-transpose format; +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': A is upper triangular; +*> = 'L': A is lower triangular. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] ARF +*> \verbatim +*> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), +*> On entry, the upper or lower triangular matrix A stored in +*> RFP format. For a further discussion see Notes below. +*> \endverbatim +*> +*> \param[out] AP +*> \verbatim +*> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ), +*> On exit, the upper or lower triangular matrix A, packed +*> columnwise in a linear array. The j-th column of A is stored +*> in the array AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> We first consider Standard Packed 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 +*> conjugate-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 +*> conjugate-transpose of the last three columns of AP lower. +*> To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- +*> 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 next consider Standard Packed 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 +*> conjugate-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 +*> conjugate-transpose of the last two columns of AP lower. +*> To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- +*> 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 ZTFTTP( TRANSR, UPLO, N, ARF, AP, 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 @@ -16,146 +221,6 @@ COMPLEX*16 AP( 0: * ), ARF( 0: * ) * .. * -* Purpose -* ======= -* -* ZTFTTP copies a triangular matrix A from rectangular full packed -* format (TF) to standard packed format (TP). -* -* Arguments -* ========= -* -* TRANSR (input) CHARACTER*1 -* = 'N': ARF is in Normal format; -* = 'C': ARF is in Conjugate-transpose format; -* -* UPLO (input) CHARACTER*1 -* = 'U': A is upper triangular; -* = 'L': A is lower triangular. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* ARF (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ), -* On entry, the upper or lower triangular matrix A stored in -* RFP format. For a further discussion see Notes below. -* -* AP (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ), -* On exit, the upper or lower triangular matrix A, packed -* columnwise in a linear array. The j-th column of A is stored -* in the array AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* -* Further Details -* =============== -* -* We first consider Standard Packed 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 -* conjugate-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 -* conjugate-transpose of the last three columns of AP lower. -* To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- -* 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 next consider Standard Packed 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 -* conjugate-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 -* conjugate-transpose of the last two columns of AP lower. -* To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- -* 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 ..