LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtfttp.f
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00001 *> \brief \b DTFTTP
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DTFTTP + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfttp.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfttp.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfttp.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       DOUBLE PRECISION   AP( 0: * ), ARF( 0: * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DTFTTP copies a triangular matrix A from rectangular full packed
00038 *> format (TF) to standard packed format (TP).
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] TRANSR
00045 *> \verbatim
00046 *>          TRANSR is CHARACTER*1
00047 *>          = 'N':  ARF is in Normal format;
00048 *>          = 'T':  ARF is in Transpose format;
00049 *> \endverbatim
00050 *>
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  A is upper triangular;
00055 *>          = 'L':  A is lower triangular.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A. N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] ARF
00065 *> \verbatim
00066 *>          ARF is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
00067 *>          On entry, the upper or lower triangular matrix A stored in
00068 *>          RFP format. For a further discussion see Notes below.
00069 *> \endverbatim
00070 *>
00071 *> \param[out] AP
00072 *> \verbatim
00073 *>          AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
00074 *>          On exit, the upper or lower triangular matrix A, packed
00075 *>          columnwise in a linear array. The j-th column of A is stored
00076 *>          in the array AP as follows:
00077 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00078 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00079 *> \endverbatim
00080 *>
00081 *> \param[out] INFO
00082 *> \verbatim
00083 *>          INFO is INTEGER
00084 *>          = 0:  successful exit
00085 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00086 *> \endverbatim
00087 *
00088 *  Authors:
00089 *  ========
00090 *
00091 *> \author Univ. of Tennessee 
00092 *> \author Univ. of California Berkeley 
00093 *> \author Univ. of Colorado Denver 
00094 *> \author NAG Ltd. 
00095 *
00096 *> \date November 2011
00097 *
00098 *> \ingroup doubleOTHERcomputational
00099 *
00100 *> \par Further Details:
00101 *  =====================
00102 *>
00103 *> \verbatim
00104 *>
00105 *>  We first consider Rectangular Full Packed (RFP) Format when N is
00106 *>  even. We give an example where N = 6.
00107 *>
00108 *>      AP is Upper             AP is Lower
00109 *>
00110 *>   00 01 02 03 04 05       00
00111 *>      11 12 13 14 15       10 11
00112 *>         22 23 24 25       20 21 22
00113 *>            33 34 35       30 31 32 33
00114 *>               44 45       40 41 42 43 44
00115 *>                  55       50 51 52 53 54 55
00116 *>
00117 *>
00118 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00119 *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00120 *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00121 *>  the transpose of the first three columns of AP upper.
00122 *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00123 *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00124 *>  the transpose of the last three columns of AP lower.
00125 *>  This covers the case N even and TRANSR = 'N'.
00126 *>
00127 *>         RFP A                   RFP A
00128 *>
00129 *>        03 04 05                33 43 53
00130 *>        13 14 15                00 44 54
00131 *>        23 24 25                10 11 55
00132 *>        33 34 35                20 21 22
00133 *>        00 44 45                30 31 32
00134 *>        01 11 55                40 41 42
00135 *>        02 12 22                50 51 52
00136 *>
00137 *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00138 *>  transpose of RFP A above. One therefore gets:
00139 *>
00140 *>
00141 *>           RFP A                   RFP A
00142 *>
00143 *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00144 *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00145 *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00146 *>
00147 *>
00148 *>  We then consider Rectangular Full Packed (RFP) Format when N is
00149 *>  odd. We give an example where N = 5.
00150 *>
00151 *>     AP is Upper                 AP is Lower
00152 *>
00153 *>   00 01 02 03 04              00
00154 *>      11 12 13 14              10 11
00155 *>         22 23 24              20 21 22
00156 *>            33 34              30 31 32 33
00157 *>               44              40 41 42 43 44
00158 *>
00159 *>
00160 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00161 *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00162 *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00163 *>  the transpose of the first two columns of AP upper.
00164 *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00165 *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00166 *>  the transpose of the last two columns of AP lower.
00167 *>  This covers the case N odd and TRANSR = 'N'.
00168 *>
00169 *>         RFP A                   RFP A
00170 *>
00171 *>        02 03 04                00 33 43
00172 *>        12 13 14                10 11 44
00173 *>        22 23 24                20 21 22
00174 *>        00 33 34                30 31 32
00175 *>        01 11 44                40 41 42
00176 *>
00177 *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00178 *>  transpose of RFP A above. One therefore gets:
00179 *>
00180 *>           RFP A                   RFP A
00181 *>
00182 *>     02 12 22 00 01             00 10 20 30 40 50
00183 *>     03 13 23 33 11             33 11 21 31 41 51
00184 *>     04 14 24 34 44             43 44 22 32 42 52
00185 *> \endverbatim
00186 *>
00187 *  =====================================================================
00188       SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
00189 *
00190 *  -- LAPACK computational routine (version 3.4.0) --
00191 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00192 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00193 *     November 2011
00194 *
00195 *     .. Scalar Arguments ..
00196       CHARACTER          TRANSR, UPLO
00197       INTEGER            INFO, N
00198 *     ..
00199 *     .. Array Arguments ..
00200       DOUBLE PRECISION   AP( 0: * ), ARF( 0: * )
00201 *     ..
00202 *
00203 *  =====================================================================
00204 *
00205 *     .. Parameters ..
00206 *     ..
00207 *     .. Local Scalars ..
00208       LOGICAL            LOWER, NISODD, NORMALTRANSR
00209       INTEGER            N1, N2, K, NT
00210       INTEGER            I, J, IJ
00211       INTEGER            IJP, JP, LDA, JS
00212 *     ..
00213 *     .. External Functions ..
00214       LOGICAL            LSAME
00215       EXTERNAL           LSAME
00216 *     ..
00217 *     .. External Subroutines ..
00218       EXTERNAL           XERBLA
00219 *     ..
00220 *     .. Executable Statements ..
00221 *
00222 *     Test the input parameters.
00223 *
00224       INFO = 0
00225       NORMALTRANSR = LSAME( TRANSR, 'N' )
00226       LOWER = LSAME( UPLO, 'L' )
00227       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
00228          INFO = -1
00229       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00230          INFO = -2
00231       ELSE IF( N.LT.0 ) THEN
00232          INFO = -3
00233       END IF
00234       IF( INFO.NE.0 ) THEN
00235          CALL XERBLA( 'DTFTTP', -INFO )
00236          RETURN
00237       END IF
00238 *
00239 *     Quick return if possible
00240 *
00241       IF( N.EQ.0 )
00242      $   RETURN
00243 *
00244       IF( N.EQ.1 ) THEN
00245          IF( NORMALTRANSR ) THEN
00246             AP( 0 ) = ARF( 0 )
00247          ELSE
00248             AP( 0 ) = ARF( 0 )
00249          END IF
00250          RETURN
00251       END IF
00252 *
00253 *     Size of array ARF(0:NT-1)
00254 *
00255       NT = N*( N+1 ) / 2
00256 *
00257 *     Set N1 and N2 depending on LOWER
00258 *
00259       IF( LOWER ) THEN
00260          N2 = N / 2
00261          N1 = N - N2
00262       ELSE
00263          N1 = N / 2
00264          N2 = N - N1
00265       END IF
00266 *
00267 *     If N is odd, set NISODD = .TRUE.
00268 *     If N is even, set K = N/2 and NISODD = .FALSE.
00269 *
00270 *     set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
00271 *     where noe = 0 if n is even, noe = 1 if n is odd
00272 *
00273       IF( MOD( N, 2 ).EQ.0 ) THEN
00274          K = N / 2
00275          NISODD = .FALSE.
00276          LDA = N + 1
00277       ELSE
00278          NISODD = .TRUE.
00279          LDA = N
00280       END IF
00281 *
00282 *     ARF^C has lda rows and n+1-noe cols
00283 *
00284       IF( .NOT.NORMALTRANSR )
00285      $   LDA = ( N+1 ) / 2
00286 *
00287 *     start execution: there are eight cases
00288 *
00289       IF( NISODD ) THEN
00290 *
00291 *        N is odd
00292 *
00293          IF( NORMALTRANSR ) THEN
00294 *
00295 *           N is odd and TRANSR = 'N'
00296 *
00297             IF( LOWER ) THEN
00298 *
00299 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00300 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00301 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
00302 *
00303                IJP = 0
00304                JP = 0
00305                DO J = 0, N2
00306                   DO I = J, N - 1
00307                      IJ = I + JP
00308                      AP( IJP ) = ARF( IJ )
00309                      IJP = IJP + 1
00310                   END DO
00311                   JP = JP + LDA
00312                END DO
00313                DO I = 0, N2 - 1
00314                   DO J = 1 + I, N2
00315                      IJ = I + J*LDA
00316                      AP( IJP ) = ARF( IJ )
00317                      IJP = IJP + 1
00318                   END DO
00319                END DO
00320 *
00321             ELSE
00322 *
00323 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00324 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00325 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00326 *
00327                IJP = 0
00328                DO J = 0, N1 - 1
00329                   IJ = N2 + J
00330                   DO I = 0, J
00331                      AP( IJP ) = ARF( IJ )
00332                      IJP = IJP + 1
00333                      IJ = IJ + LDA
00334                   END DO
00335                END DO
00336                JS = 0
00337                DO J = N1, N - 1
00338                   IJ = JS
00339                   DO IJ = JS, JS + J
00340                      AP( IJP ) = ARF( IJ )
00341                      IJP = IJP + 1
00342                   END DO
00343                   JS = JS + LDA
00344                END DO
00345 *
00346             END IF
00347 *
00348          ELSE
00349 *
00350 *           N is odd and TRANSR = 'T'
00351 *
00352             IF( LOWER ) THEN
00353 *
00354 *              SRPA for LOWER, TRANSPOSE and N is odd
00355 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
00356 *              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
00357 *
00358                IJP = 0
00359                DO I = 0, N2
00360                   DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
00361                      AP( IJP ) = ARF( IJ )
00362                      IJP = IJP + 1
00363                   END DO
00364                END DO
00365                JS = 1
00366                DO J = 0, N2 - 1
00367                   DO IJ = JS, JS + N2 - J - 1
00368                      AP( IJP ) = ARF( IJ )
00369                      IJP = IJP + 1
00370                   END DO
00371                   JS = JS + LDA + 1
00372                END DO
00373 *
00374             ELSE
00375 *
00376 *              SRPA for UPPER, TRANSPOSE and N is odd
00377 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
00378 *              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
00379 *
00380                IJP = 0
00381                JS = N2*LDA
00382                DO J = 0, N1 - 1
00383                   DO IJ = JS, JS + J
00384                      AP( IJP ) = ARF( IJ )
00385                      IJP = IJP + 1
00386                   END DO
00387                   JS = JS + LDA
00388                END DO
00389                DO I = 0, N1
00390                   DO IJ = I, I + ( N1+I )*LDA, LDA
00391                      AP( IJP ) = ARF( IJ )
00392                      IJP = IJP + 1
00393                   END DO
00394                END DO
00395 *
00396             END IF
00397 *
00398          END IF
00399 *
00400       ELSE
00401 *
00402 *        N is even
00403 *
00404          IF( NORMALTRANSR ) THEN
00405 *
00406 *           N is even and TRANSR = 'N'
00407 *
00408             IF( LOWER ) THEN
00409 *
00410 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00411 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00412 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00413 *
00414                IJP = 0
00415                JP = 0
00416                DO J = 0, K - 1
00417                   DO I = J, N - 1
00418                      IJ = 1 + I + JP
00419                      AP( IJP ) = ARF( IJ )
00420                      IJP = IJP + 1
00421                   END DO
00422                   JP = JP + LDA
00423                END DO
00424                DO I = 0, K - 1
00425                   DO J = I, K - 1
00426                      IJ = I + J*LDA
00427                      AP( IJP ) = ARF( IJ )
00428                      IJP = IJP + 1
00429                   END DO
00430                END DO
00431 *
00432             ELSE
00433 *
00434 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00435 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00436 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00437 *
00438                IJP = 0
00439                DO J = 0, K - 1
00440                   IJ = K + 1 + J
00441                   DO I = 0, J
00442                      AP( IJP ) = ARF( IJ )
00443                      IJP = IJP + 1
00444                      IJ = IJ + LDA
00445                   END DO
00446                END DO
00447                JS = 0
00448                DO J = K, N - 1
00449                   IJ = JS
00450                   DO IJ = JS, JS + J
00451                      AP( IJP ) = ARF( IJ )
00452                      IJP = IJP + 1
00453                   END DO
00454                   JS = JS + LDA
00455                END DO
00456 *
00457             END IF
00458 *
00459          ELSE
00460 *
00461 *           N is even and TRANSR = 'T'
00462 *
00463             IF( LOWER ) THEN
00464 *
00465 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00466 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00467 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00468 *
00469                IJP = 0
00470                DO I = 0, K - 1
00471                   DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
00472                      AP( IJP ) = ARF( IJ )
00473                      IJP = IJP + 1
00474                   END DO
00475                END DO
00476                JS = 0
00477                DO J = 0, K - 1
00478                   DO IJ = JS, JS + K - J - 1
00479                      AP( IJP ) = ARF( IJ )
00480                      IJP = IJP + 1
00481                   END DO
00482                   JS = JS + LDA + 1
00483                END DO
00484 *
00485             ELSE
00486 *
00487 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00488 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00489 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00490 *
00491                IJP = 0
00492                JS = ( K+1 )*LDA
00493                DO J = 0, K - 1
00494                   DO IJ = JS, JS + J
00495                      AP( IJP ) = ARF( IJ )
00496                      IJP = IJP + 1
00497                   END DO
00498                   JS = JS + LDA
00499                END DO
00500                DO I = 0, K - 1
00501                   DO IJ = I, I + ( K+I )*LDA, LDA
00502                      AP( IJP ) = ARF( IJ )
00503                      IJP = IJP + 1
00504                   END DO
00505                END DO
00506 *
00507             END IF
00508 *
00509          END IF
00510 *
00511       END IF
00512 *
00513       RETURN
00514 *
00515 *     End of DTFTTP
00516 *
00517       END
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