LAPACK 3.3.0

dtfttp.f

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00001       SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.3.0)                                    --
00004 *
00005 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
00006 *     November 2010
00007 *
00008 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00009 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00010 *
00011 *     ..
00012 *     .. Scalar Arguments ..
00013       CHARACTER          TRANSR, UPLO
00014       INTEGER            INFO, N
00015 *     ..
00016 *     .. Array Arguments ..
00017       DOUBLE PRECISION   AP( 0: * ), ARF( 0: * )
00018 *     ..
00019 *
00020 *  Purpose
00021 *  =======
00022 *
00023 *  DTFTTP copies a triangular matrix A from rectangular full packed
00024 *  format (TF) to standard packed format (TP).
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  TRANSR  (input) CHARACTER*1
00030 *          = 'N':  ARF is in Normal format;
00031 *          = 'T':  ARF is in Transpose format;
00032 *
00033 *  UPLO    (input) CHARACTER*1
00034 *          = 'U':  A is upper triangular;
00035 *          = 'L':  A is lower triangular.
00036 *
00037 *  N       (input) INTEGER
00038 *          The order of the matrix A. N >= 0.
00039 *
00040 *  ARF     (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
00041 *          On entry, the upper or lower triangular matrix A stored in
00042 *          RFP format. For a further discussion see Notes below.
00043 *
00044 *  AP      (output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
00045 *          On exit, the upper or lower triangular matrix A, packed
00046 *          columnwise in a linear array. The j-th column of A is stored
00047 *          in the array AP as follows:
00048 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00049 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00050 *
00051 *  INFO    (output) INTEGER
00052 *          = 0:  successful exit
00053 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00054 *
00055 *  Further Details
00056 *  ===============
00057 *
00058 *  We first consider Rectangular Full Packed (RFP) Format when N is
00059 *  even. We give an example where N = 6.
00060 *
00061 *      AP is Upper             AP is Lower
00062 *
00063 *   00 01 02 03 04 05       00
00064 *      11 12 13 14 15       10 11
00065 *         22 23 24 25       20 21 22
00066 *            33 34 35       30 31 32 33
00067 *               44 45       40 41 42 43 44
00068 *                  55       50 51 52 53 54 55
00069 *
00070 *
00071 *  Let TRANSR = 'N'. RFP holds AP as follows:
00072 *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00073 *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00074 *  the transpose of the first three columns of AP upper.
00075 *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00076 *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00077 *  the transpose of the last three columns of AP lower.
00078 *  This covers the case N even and TRANSR = 'N'.
00079 *
00080 *         RFP A                   RFP A
00081 *
00082 *        03 04 05                33 43 53
00083 *        13 14 15                00 44 54
00084 *        23 24 25                10 11 55
00085 *        33 34 35                20 21 22
00086 *        00 44 45                30 31 32
00087 *        01 11 55                40 41 42
00088 *        02 12 22                50 51 52
00089 *
00090 *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00091 *  transpose of RFP A above. One therefore gets:
00092 *
00093 *
00094 *           RFP A                   RFP A
00095 *
00096 *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00097 *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00098 *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00099 *
00100 *
00101 *  We then consider Rectangular Full Packed (RFP) Format when N is
00102 *  odd. We give an example where N = 5.
00103 *
00104 *     AP is Upper                 AP is Lower
00105 *
00106 *   00 01 02 03 04              00
00107 *      11 12 13 14              10 11
00108 *         22 23 24              20 21 22
00109 *            33 34              30 31 32 33
00110 *               44              40 41 42 43 44
00111 *
00112 *
00113 *  Let TRANSR = 'N'. RFP holds AP as follows:
00114 *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00115 *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00116 *  the transpose of the first two columns of AP upper.
00117 *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00118 *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00119 *  the transpose of the last two columns of AP lower.
00120 *  This covers the case N odd and TRANSR = 'N'.
00121 *
00122 *         RFP A                   RFP A
00123 *
00124 *        02 03 04                00 33 43
00125 *        12 13 14                10 11 44
00126 *        22 23 24                20 21 22
00127 *        00 33 34                30 31 32
00128 *        01 11 44                40 41 42
00129 *
00130 *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00131 *  transpose of RFP A above. One therefore gets:
00132 *
00133 *           RFP A                   RFP A
00134 *
00135 *     02 12 22 00 01             00 10 20 30 40 50
00136 *     03 13 23 33 11             33 11 21 31 41 51
00137 *     04 14 24 34 44             43 44 22 32 42 52
00138 *
00139 *  =====================================================================
00140 *
00141 *     .. Parameters ..
00142 *     ..
00143 *     .. Local Scalars ..
00144       LOGICAL            LOWER, NISODD, NORMALTRANSR
00145       INTEGER            N1, N2, K, NT
00146       INTEGER            I, J, IJ
00147       INTEGER            IJP, JP, LDA, JS
00148 *     ..
00149 *     .. External Functions ..
00150       LOGICAL            LSAME
00151       EXTERNAL           LSAME
00152 *     ..
00153 *     .. External Subroutines ..
00154       EXTERNAL           XERBLA
00155 *     ..
00156 *     .. Executable Statements ..
00157 *
00158 *     Test the input parameters.
00159 *
00160       INFO = 0
00161       NORMALTRANSR = LSAME( TRANSR, 'N' )
00162       LOWER = LSAME( UPLO, 'L' )
00163       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
00164          INFO = -1
00165       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00166          INFO = -2
00167       ELSE IF( N.LT.0 ) THEN
00168          INFO = -3
00169       END IF
00170       IF( INFO.NE.0 ) THEN
00171          CALL XERBLA( 'DTFTTP', -INFO )
00172          RETURN
00173       END IF
00174 *
00175 *     Quick return if possible
00176 *
00177       IF( N.EQ.0 )
00178      +   RETURN
00179 *
00180       IF( N.EQ.1 ) THEN
00181          IF( NORMALTRANSR ) THEN
00182             AP( 0 ) = ARF( 0 )
00183          ELSE
00184             AP( 0 ) = ARF( 0 )
00185          END IF
00186          RETURN
00187       END IF
00188 *
00189 *     Size of array ARF(0:NT-1)
00190 *
00191       NT = N*( N+1 ) / 2
00192 *
00193 *     Set N1 and N2 depending on LOWER
00194 *
00195       IF( LOWER ) THEN
00196          N2 = N / 2
00197          N1 = N - N2
00198       ELSE
00199          N1 = N / 2
00200          N2 = N - N1
00201       END IF
00202 *
00203 *     If N is odd, set NISODD = .TRUE.
00204 *     If N is even, set K = N/2 and NISODD = .FALSE.
00205 *
00206 *     set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
00207 *     where noe = 0 if n is even, noe = 1 if n is odd
00208 *
00209       IF( MOD( N, 2 ).EQ.0 ) THEN
00210          K = N / 2
00211          NISODD = .FALSE.
00212          LDA = N + 1
00213       ELSE
00214          NISODD = .TRUE.
00215          LDA = N
00216       END IF
00217 *
00218 *     ARF^C has lda rows and n+1-noe cols
00219 *
00220       IF( .NOT.NORMALTRANSR )
00221      +   LDA = ( N+1 ) / 2
00222 *
00223 *     start execution: there are eight cases
00224 *
00225       IF( NISODD ) THEN
00226 *
00227 *        N is odd
00228 *
00229          IF( NORMALTRANSR ) THEN
00230 *
00231 *           N is odd and TRANSR = 'N'
00232 *
00233             IF( LOWER ) THEN
00234 *
00235 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00236 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00237 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
00238 *
00239                IJP = 0
00240                JP = 0
00241                DO J = 0, N2
00242                   DO I = J, N - 1
00243                      IJ = I + JP
00244                      AP( IJP ) = ARF( IJ )
00245                      IJP = IJP + 1
00246                   END DO
00247                   JP = JP + LDA
00248                END DO
00249                DO I = 0, N2 - 1
00250                   DO J = 1 + I, N2
00251                      IJ = I + J*LDA
00252                      AP( IJP ) = ARF( IJ )
00253                      IJP = IJP + 1
00254                   END DO
00255                END DO
00256 *
00257             ELSE
00258 *
00259 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00260 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00261 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00262 *
00263                IJP = 0
00264                DO J = 0, N1 - 1
00265                   IJ = N2 + J
00266                   DO I = 0, J
00267                      AP( IJP ) = ARF( IJ )
00268                      IJP = IJP + 1
00269                      IJ = IJ + LDA
00270                   END DO
00271                END DO
00272                JS = 0
00273                DO J = N1, N - 1
00274                   IJ = JS
00275                   DO IJ = JS, JS + J
00276                      AP( IJP ) = ARF( IJ )
00277                      IJP = IJP + 1
00278                   END DO
00279                   JS = JS + LDA
00280                END DO
00281 *
00282             END IF
00283 *
00284          ELSE
00285 *
00286 *           N is odd and TRANSR = 'T'
00287 *
00288             IF( LOWER ) THEN
00289 *
00290 *              SRPA for LOWER, TRANSPOSE and N is odd
00291 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
00292 *              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
00293 *
00294                IJP = 0
00295                DO I = 0, N2
00296                   DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
00297                      AP( IJP ) = ARF( IJ )
00298                      IJP = IJP + 1
00299                   END DO
00300                END DO
00301                JS = 1
00302                DO J = 0, N2 - 1
00303                   DO IJ = JS, JS + N2 - J - 1
00304                      AP( IJP ) = ARF( IJ )
00305                      IJP = IJP + 1
00306                   END DO
00307                   JS = JS + LDA + 1
00308                END DO
00309 *
00310             ELSE
00311 *
00312 *              SRPA for UPPER, TRANSPOSE and N is odd
00313 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
00314 *              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
00315 *
00316                IJP = 0
00317                JS = N2*LDA
00318                DO J = 0, N1 - 1
00319                   DO IJ = JS, JS + J
00320                      AP( IJP ) = ARF( IJ )
00321                      IJP = IJP + 1
00322                   END DO
00323                   JS = JS + LDA
00324                END DO
00325                DO I = 0, N1
00326                   DO IJ = I, I + ( N1+I )*LDA, LDA
00327                      AP( IJP ) = ARF( IJ )
00328                      IJP = IJP + 1
00329                   END DO
00330                END DO
00331 *
00332             END IF
00333 *
00334          END IF
00335 *
00336       ELSE
00337 *
00338 *        N is even
00339 *
00340          IF( NORMALTRANSR ) THEN
00341 *
00342 *           N is even and TRANSR = 'N'
00343 *
00344             IF( LOWER ) THEN
00345 *
00346 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00347 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00348 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00349 *
00350                IJP = 0
00351                JP = 0
00352                DO J = 0, K - 1
00353                   DO I = J, N - 1
00354                      IJ = 1 + I + JP
00355                      AP( IJP ) = ARF( IJ )
00356                      IJP = IJP + 1
00357                   END DO
00358                   JP = JP + LDA
00359                END DO
00360                DO I = 0, K - 1
00361                   DO J = I, K - 1
00362                      IJ = I + J*LDA
00363                      AP( IJP ) = ARF( IJ )
00364                      IJP = IJP + 1
00365                   END DO
00366                END DO
00367 *
00368             ELSE
00369 *
00370 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00371 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00372 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00373 *
00374                IJP = 0
00375                DO J = 0, K - 1
00376                   IJ = K + 1 + J
00377                   DO I = 0, J
00378                      AP( IJP ) = ARF( IJ )
00379                      IJP = IJP + 1
00380                      IJ = IJ + LDA
00381                   END DO
00382                END DO
00383                JS = 0
00384                DO J = K, N - 1
00385                   IJ = JS
00386                   DO IJ = JS, JS + J
00387                      AP( IJP ) = ARF( IJ )
00388                      IJP = IJP + 1
00389                   END DO
00390                   JS = JS + LDA
00391                END DO
00392 *
00393             END IF
00394 *
00395          ELSE
00396 *
00397 *           N is even and TRANSR = 'T'
00398 *
00399             IF( LOWER ) THEN
00400 *
00401 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00402 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00403 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00404 *
00405                IJP = 0
00406                DO I = 0, K - 1
00407                   DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
00408                      AP( IJP ) = ARF( IJ )
00409                      IJP = IJP + 1
00410                   END DO
00411                END DO
00412                JS = 0
00413                DO J = 0, K - 1
00414                   DO IJ = JS, JS + K - J - 1
00415                      AP( IJP ) = ARF( IJ )
00416                      IJP = IJP + 1
00417                   END DO
00418                   JS = JS + LDA + 1
00419                END DO
00420 *
00421             ELSE
00422 *
00423 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00424 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00425 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00426 *
00427                IJP = 0
00428                JS = ( K+1 )*LDA
00429                DO J = 0, K - 1
00430                   DO IJ = JS, JS + J
00431                      AP( IJP ) = ARF( IJ )
00432                      IJP = IJP + 1
00433                   END DO
00434                   JS = JS + LDA
00435                END DO
00436                DO I = 0, K - 1
00437                   DO IJ = I, I + ( K+I )*LDA, LDA
00438                      AP( IJP ) = ARF( IJ )
00439                      IJP = IJP + 1
00440                   END DO
00441                END DO
00442 *
00443             END IF
00444 *
00445          END IF
00446 *
00447       END IF
00448 *
00449       RETURN
00450 *
00451 *     End of DTFTTP
00452 *
00453       END
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