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