LAPACK 3.3.1
Linear Algebra PACKage

ctpttf.f

Go to the documentation of this file.
00001       SUBROUTINE CTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.3.1)                                    --
00004 *
00005 *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
00006 *  -- April 2011                                                      --
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       COMPLEX            AP( 0: * ), ARF( 0: * )
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  CTPTTF copies a triangular matrix A from standard packed format (TP)
00023 *  to rectangular full packed format (TF).
00024 *
00025 *  Arguments
00026 *  =========
00027 *
00028 *  TRANSR   (input) CHARACTER*1
00029 *          = 'N':  ARF in Normal format is wanted;
00030 *          = 'C':  ARF in Conjugate-transpose format is wanted.
00031 *
00032 *  UPLO    (input) CHARACTER*1
00033 *          = 'U':  A is upper triangular;
00034 *          = 'L':  A is lower triangular.
00035 *
00036 *  N       (input) INTEGER
00037 *          The order of the matrix A.  N >= 0.
00038 *
00039 *  AP      (input) COMPLEX array, dimension ( N*(N+1)/2 ),
00040 *          On entry, the upper or lower triangular matrix A, packed
00041 *          columnwise in a linear array. The j-th column of A is stored
00042 *          in the array AP as follows:
00043 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00044 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00045 *
00046 *  ARF     (output) COMPLEX array, dimension ( N*(N+1)/2 ),
00047 *          On exit, the upper or lower triangular matrix A stored in
00048 *          RFP format. For a further discussion see Notes below.
00049 *
00050 *  INFO    (output) INTEGER
00051 *          = 0:  successful exit
00052 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00053 *
00054 *  Further Details
00055 *  ===============
00056 *
00057 *  We first consider Standard Packed Format when N is even.
00058 *  We give an example where N = 6.
00059 *
00060 *      AP is Upper             AP is Lower
00061 *
00062 *   00 01 02 03 04 05       00
00063 *      11 12 13 14 15       10 11
00064 *         22 23 24 25       20 21 22
00065 *            33 34 35       30 31 32 33
00066 *               44 45       40 41 42 43 44
00067 *                  55       50 51 52 53 54 55
00068 *
00069 *
00070 *  Let TRANSR = 'N'. RFP holds AP as follows:
00071 *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00072 *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00073 *  conjugate-transpose of the first three columns of AP upper.
00074 *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00075 *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00076 *  conjugate-transpose of the last three columns of AP lower.
00077 *  To denote conjugate we place -- above the element. This covers the
00078 *  case N even and TRANSR = 'N'.
00079 *
00080 *         RFP A                   RFP A
00081 *
00082 *                                -- -- --
00083 *        03 04 05                33 43 53
00084 *                                   -- --
00085 *        13 14 15                00 44 54
00086 *                                      --
00087 *        23 24 25                10 11 55
00088 *
00089 *        33 34 35                20 21 22
00090 *        --
00091 *        00 44 45                30 31 32
00092 *        -- --
00093 *        01 11 55                40 41 42
00094 *        -- -- --
00095 *        02 12 22                50 51 52
00096 *
00097 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00098 *  transpose of RFP A above. One therefore gets:
00099 *
00100 *
00101 *           RFP A                   RFP A
00102 *
00103 *     -- -- -- --                -- -- -- -- -- --
00104 *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00105 *     -- -- -- -- --                -- -- -- -- --
00106 *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00107 *     -- -- -- -- -- --                -- -- -- --
00108 *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00109 *
00110 *
00111 *  We next  consider Standard Packed Format when N is odd.
00112 *  We give an example where N = 5.
00113 *
00114 *     AP is Upper                 AP is Lower
00115 *
00116 *   00 01 02 03 04              00
00117 *      11 12 13 14              10 11
00118 *         22 23 24              20 21 22
00119 *            33 34              30 31 32 33
00120 *               44              40 41 42 43 44
00121 *
00122 *
00123 *  Let TRANSR = 'N'. RFP holds AP as follows:
00124 *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00125 *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00126 *  conjugate-transpose of the first two   columns of AP upper.
00127 *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00128 *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00129 *  conjugate-transpose of the last two   columns of AP lower.
00130 *  To denote conjugate we place -- above the element. This covers the
00131 *  case N odd  and TRANSR = 'N'.
00132 *
00133 *         RFP A                   RFP A
00134 *
00135 *                                   -- --
00136 *        02 03 04                00 33 43
00137 *                                      --
00138 *        12 13 14                10 11 44
00139 *
00140 *        22 23 24                20 21 22
00141 *        --
00142 *        00 33 34                30 31 32
00143 *        -- --
00144 *        01 11 44                40 41 42
00145 *
00146 *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00147 *  transpose of RFP A above. One therefore gets:
00148 *
00149 *
00150 *           RFP A                   RFP A
00151 *
00152 *     -- -- --                   -- -- -- -- -- --
00153 *     02 12 22 00 01             00 10 20 30 40 50
00154 *     -- -- -- --                   -- -- -- -- --
00155 *     03 13 23 33 11             33 11 21 31 41 51
00156 *     -- -- -- -- --                   -- -- -- --
00157 *     04 14 24 34 44             43 44 22 32 42 52
00158 *
00159 *  =====================================================================
00160 *
00161 *     .. Parameters ..
00162 *     ..
00163 *     .. Local Scalars ..
00164       LOGICAL            LOWER, NISODD, NORMALTRANSR
00165       INTEGER            N1, N2, K, NT
00166       INTEGER            I, J, IJ
00167       INTEGER            IJP, JP, LDA, JS
00168 *     ..
00169 *     .. External Functions ..
00170       LOGICAL            LSAME
00171       EXTERNAL           LSAME
00172 *     ..
00173 *     .. External Subroutines ..
00174       EXTERNAL           XERBLA
00175 *     ..
00176 *     .. Intrinsic Functions ..
00177       INTRINSIC          CONJG, MOD
00178 *     ..
00179 *     .. Executable Statements ..
00180 *
00181 *     Test the input parameters.
00182 *
00183       INFO = 0
00184       NORMALTRANSR = LSAME( TRANSR, 'N' )
00185       LOWER = LSAME( UPLO, 'L' )
00186       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00187          INFO = -1
00188       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00189          INFO = -2
00190       ELSE IF( N.LT.0 ) THEN
00191          INFO = -3
00192       END IF
00193       IF( INFO.NE.0 ) THEN
00194          CALL XERBLA( 'CTPTTF', -INFO )
00195          RETURN
00196       END IF
00197 *
00198 *     Quick return if possible
00199 *
00200       IF( N.EQ.0 )
00201      $   RETURN
00202 *
00203       IF( N.EQ.1 ) THEN
00204          IF( NORMALTRANSR ) THEN
00205             ARF( 0 ) = AP( 0 )
00206          ELSE
00207             ARF( 0 ) = CONJG( AP( 0 ) )
00208          END IF
00209          RETURN
00210       END IF
00211 *
00212 *     Size of array ARF(0:NT-1)
00213 *
00214       NT = N*( N+1 ) / 2
00215 *
00216 *     Set N1 and N2 depending on LOWER
00217 *
00218       IF( LOWER ) THEN
00219          N2 = N / 2
00220          N1 = N - N2
00221       ELSE
00222          N1 = N / 2
00223          N2 = N - N1
00224       END IF
00225 *
00226 *     If N is odd, set NISODD = .TRUE.
00227 *     If N is even, set K = N/2 and NISODD = .FALSE.
00228 *
00229 *     set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
00230 *     where noe = 0 if n is even, noe = 1 if n is odd
00231 *
00232       IF( MOD( N, 2 ).EQ.0 ) THEN
00233          K = N / 2
00234          NISODD = .FALSE.
00235          LDA = N + 1
00236       ELSE
00237          NISODD = .TRUE.
00238          LDA = N
00239       END IF
00240 *
00241 *     ARF^C has lda rows and n+1-noe cols
00242 *
00243       IF( .NOT.NORMALTRANSR )
00244      $   LDA = ( N+1 ) / 2
00245 *
00246 *     start execution: there are eight cases
00247 *
00248       IF( NISODD ) THEN
00249 *
00250 *        N is odd
00251 *
00252          IF( NORMALTRANSR ) THEN
00253 *
00254 *           N is odd and TRANSR = 'N'
00255 *
00256             IF( LOWER ) THEN
00257 *
00258 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00259 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00260 *             T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
00261 *
00262                IJP = 0
00263                JP = 0
00264                DO J = 0, N2
00265                   DO I = J, N - 1
00266                      IJ = I + JP
00267                      ARF( IJ ) = AP( IJP )
00268                      IJP = IJP + 1
00269                   END DO
00270                   JP = JP + LDA
00271                END DO
00272                DO I = 0, N2 - 1
00273                   DO J = 1 + I, N2
00274                      IJ = I + J*LDA
00275                      ARF( IJ ) = CONJG( AP( IJP ) )
00276                      IJP = IJP + 1
00277                   END DO
00278                END DO
00279 *
00280             ELSE
00281 *
00282 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00283 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00284 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00285 *
00286                IJP = 0
00287                DO J = 0, N1 - 1
00288                   IJ = N2 + J
00289                   DO I = 0, J
00290                      ARF( IJ ) = CONJG( AP( IJP ) )
00291                      IJP = IJP + 1
00292                      IJ = IJ + LDA
00293                   END DO
00294                END DO
00295                JS = 0
00296                DO J = N1, N - 1
00297                   IJ = JS
00298                   DO IJ = JS, JS + J
00299                      ARF( IJ ) = AP( IJP )
00300                      IJP = IJP + 1
00301                   END DO
00302                   JS = JS + LDA
00303                END DO
00304 *
00305             END IF
00306 *
00307          ELSE
00308 *
00309 *           N is odd and TRANSR = 'C'
00310 *
00311             IF( LOWER ) THEN
00312 *
00313 *              SRPA for LOWER, TRANSPOSE and N is odd
00314 *              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
00315 *              T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
00316 *
00317                IJP = 0
00318                DO I = 0, N2
00319                   DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
00320                      ARF( IJ ) = CONJG( AP( IJP ) )
00321                      IJP = IJP + 1
00322                   END DO
00323                END DO
00324                JS = 1
00325                DO J = 0, N2 - 1
00326                   DO IJ = JS, JS + N2 - J - 1
00327                      ARF( IJ ) = AP( IJP )
00328                      IJP = IJP + 1
00329                   END DO
00330                   JS = JS + LDA + 1
00331                END DO
00332 *
00333             ELSE
00334 *
00335 *              SRPA for UPPER, TRANSPOSE and N is odd
00336 *              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
00337 *              T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
00338 *
00339                IJP = 0
00340                JS = N2*LDA
00341                DO J = 0, N1 - 1
00342                   DO IJ = JS, JS + J
00343                      ARF( IJ ) = AP( IJP )
00344                      IJP = IJP + 1
00345                   END DO
00346                   JS = JS + LDA
00347                END DO
00348                DO I = 0, N1
00349                   DO IJ = I, I + ( N1+I )*LDA, LDA
00350                      ARF( IJ ) = CONJG( AP( IJP ) )
00351                      IJP = IJP + 1
00352                   END DO
00353                END DO
00354 *
00355             END IF
00356 *
00357          END IF
00358 *
00359       ELSE
00360 *
00361 *        N is even
00362 *
00363          IF( NORMALTRANSR ) THEN
00364 *
00365 *           N is even and TRANSR = 'N'
00366 *
00367             IF( LOWER ) THEN
00368 *
00369 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00370 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00371 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00372 *
00373                IJP = 0
00374                JP = 0
00375                DO J = 0, K - 1
00376                   DO I = J, N - 1
00377                      IJ = 1 + I + JP
00378                      ARF( IJ ) = AP( IJP )
00379                      IJP = IJP + 1
00380                   END DO
00381                   JP = JP + LDA
00382                END DO
00383                DO I = 0, K - 1
00384                   DO J = I, K - 1
00385                      IJ = I + J*LDA
00386                      ARF( IJ ) = CONJG( AP( IJP ) )
00387                      IJP = IJP + 1
00388                   END DO
00389                END DO
00390 *
00391             ELSE
00392 *
00393 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00394 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00395 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00396 *
00397                IJP = 0
00398                DO J = 0, K - 1
00399                   IJ = K + 1 + J
00400                   DO I = 0, J
00401                      ARF( IJ ) = CONJG( AP( IJP ) )
00402                      IJP = IJP + 1
00403                      IJ = IJ + LDA
00404                   END DO
00405                END DO
00406                JS = 0
00407                DO J = K, N - 1
00408                   IJ = JS
00409                   DO IJ = JS, JS + J
00410                      ARF( IJ ) = AP( IJP )
00411                      IJP = IJP + 1
00412                   END DO
00413                   JS = JS + LDA
00414                END DO
00415 *
00416             END IF
00417 *
00418          ELSE
00419 *
00420 *           N is even and TRANSR = 'C'
00421 *
00422             IF( LOWER ) THEN
00423 *
00424 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00425 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00426 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00427 *
00428                IJP = 0
00429                DO I = 0, K - 1
00430                   DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
00431                      ARF( IJ ) = CONJG( AP( IJP ) )
00432                      IJP = IJP + 1
00433                   END DO
00434                END DO
00435                JS = 0
00436                DO J = 0, K - 1
00437                   DO IJ = JS, JS + K - J - 1
00438                      ARF( IJ ) = AP( IJP )
00439                      IJP = IJP + 1
00440                   END DO
00441                   JS = JS + LDA + 1
00442                END DO
00443 *
00444             ELSE
00445 *
00446 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00447 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00448 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00449 *
00450                IJP = 0
00451                JS = ( K+1 )*LDA
00452                DO J = 0, K - 1
00453                   DO IJ = JS, JS + J
00454                      ARF( IJ ) = AP( IJP )
00455                      IJP = IJP + 1
00456                   END DO
00457                   JS = JS + LDA
00458                END DO
00459                DO I = 0, K - 1
00460                   DO IJ = I, I + ( K+I )*LDA, LDA
00461                      ARF( IJ ) = CONJG( AP( IJP ) )
00462                      IJP = IJP + 1
00463                   END DO
00464                END DO
00465 *
00466             END IF
00467 *
00468          END IF
00469 *
00470       END IF
00471 *
00472       RETURN
00473 *
00474 *     End of CTPTTF
00475 *
00476       END
 All Files Functions