LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stftri.f
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00001 *> \brief \b STFTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download STFTRI + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stftri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stftri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE STFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO, DIAG
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               A( 0: * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> STFTRI computes the inverse of a triangular matrix A stored in RFP
00038 *> format.
00039 *>
00040 *> This is a Level 3 BLAS version of the algorithm.
00041 *> \endverbatim
00042 *
00043 *  Arguments:
00044 *  ==========
00045 *
00046 *> \param[in] TRANSR
00047 *> \verbatim
00048 *>          TRANSR is CHARACTER*1
00049 *>          = 'N':  The Normal TRANSR of RFP A is stored;
00050 *>          = 'T':  The Transpose TRANSR of RFP A is stored.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] UPLO
00054 *> \verbatim
00055 *>          UPLO is CHARACTER*1
00056 *>          = 'U':  A is upper triangular;
00057 *>          = 'L':  A is lower triangular.
00058 *> \endverbatim
00059 *>
00060 *> \param[in] DIAG
00061 *> \verbatim
00062 *>          DIAG is CHARACTER*1
00063 *>          = 'N':  A is non-unit triangular;
00064 *>          = 'U':  A is unit triangular.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] N
00068 *> \verbatim
00069 *>          N is INTEGER
00070 *>          The order of the matrix A.  N >= 0.
00071 *> \endverbatim
00072 *>
00073 *> \param[in,out] A
00074 *> \verbatim
00075 *>          A is REAL array, dimension (NT);
00076 *>          NT=N*(N+1)/2. On entry, the triangular factor of a Hermitian
00077 *>          Positive Definite matrix A in RFP format. RFP format is
00078 *>          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
00079 *>          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
00080 *>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
00081 *>          the transpose of RFP A as defined when
00082 *>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
00083 *>          follows: If UPLO = 'U' the RFP A contains the nt elements of
00084 *>          upper packed A; If UPLO = 'L' the RFP A contains the nt
00085 *>          elements of lower packed A. The LDA of RFP A is (N+1)/2 when
00086 *>          TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
00087 *>          even and N is odd. See the Note below for more details.
00088 *>
00089 *>          On exit, the (triangular) inverse of the original matrix, in
00090 *>          the same storage format.
00091 *> \endverbatim
00092 *>
00093 *> \param[out] INFO
00094 *> \verbatim
00095 *>          INFO is INTEGER
00096 *>          = 0: successful exit
00097 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00098 *>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
00099 *>               matrix is singular and its inverse can not be computed.
00100 *> \endverbatim
00101 *
00102 *  Authors:
00103 *  ========
00104 *
00105 *> \author Univ. of Tennessee 
00106 *> \author Univ. of California Berkeley 
00107 *> \author Univ. of Colorado Denver 
00108 *> \author NAG Ltd. 
00109 *
00110 *> \date November 2011
00111 *
00112 *> \ingroup realOTHERcomputational
00113 *
00114 *> \par Further Details:
00115 *  =====================
00116 *>
00117 *> \verbatim
00118 *>
00119 *>  We first consider Rectangular Full Packed (RFP) Format when N is
00120 *>  even. We give an example where N = 6.
00121 *>
00122 *>      AP is Upper             AP is Lower
00123 *>
00124 *>   00 01 02 03 04 05       00
00125 *>      11 12 13 14 15       10 11
00126 *>         22 23 24 25       20 21 22
00127 *>            33 34 35       30 31 32 33
00128 *>               44 45       40 41 42 43 44
00129 *>                  55       50 51 52 53 54 55
00130 *>
00131 *>
00132 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00133 *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00134 *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00135 *>  the transpose of the first three columns of AP upper.
00136 *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00137 *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00138 *>  the transpose of the last three columns of AP lower.
00139 *>  This covers the case N even and TRANSR = 'N'.
00140 *>
00141 *>         RFP A                   RFP A
00142 *>
00143 *>        03 04 05                33 43 53
00144 *>        13 14 15                00 44 54
00145 *>        23 24 25                10 11 55
00146 *>        33 34 35                20 21 22
00147 *>        00 44 45                30 31 32
00148 *>        01 11 55                40 41 42
00149 *>        02 12 22                50 51 52
00150 *>
00151 *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00152 *>  transpose of RFP A above. One therefore gets:
00153 *>
00154 *>
00155 *>           RFP A                   RFP A
00156 *>
00157 *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00158 *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00159 *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00160 *>
00161 *>
00162 *>  We then consider Rectangular Full Packed (RFP) Format when N is
00163 *>  odd. We give an example where N = 5.
00164 *>
00165 *>     AP is Upper                 AP is Lower
00166 *>
00167 *>   00 01 02 03 04              00
00168 *>      11 12 13 14              10 11
00169 *>         22 23 24              20 21 22
00170 *>            33 34              30 31 32 33
00171 *>               44              40 41 42 43 44
00172 *>
00173 *>
00174 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00175 *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00176 *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00177 *>  the transpose of the first two columns of AP upper.
00178 *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00179 *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00180 *>  the transpose of the last two columns of AP lower.
00181 *>  This covers the case N odd and TRANSR = 'N'.
00182 *>
00183 *>         RFP A                   RFP A
00184 *>
00185 *>        02 03 04                00 33 43
00186 *>        12 13 14                10 11 44
00187 *>        22 23 24                20 21 22
00188 *>        00 33 34                30 31 32
00189 *>        01 11 44                40 41 42
00190 *>
00191 *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
00192 *>  transpose of RFP A above. One therefore gets:
00193 *>
00194 *>           RFP A                   RFP A
00195 *>
00196 *>     02 12 22 00 01             00 10 20 30 40 50
00197 *>     03 13 23 33 11             33 11 21 31 41 51
00198 *>     04 14 24 34 44             43 44 22 32 42 52
00199 *> \endverbatim
00200 *>
00201 *  =====================================================================
00202       SUBROUTINE STFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
00203 *
00204 *  -- LAPACK computational routine (version 3.4.0) --
00205 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00206 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00207 *     November 2011
00208 *
00209 *     .. Scalar Arguments ..
00210       CHARACTER          TRANSR, UPLO, DIAG
00211       INTEGER            INFO, N
00212 *     ..
00213 *     .. Array Arguments ..
00214       REAL               A( 0: * )
00215 *     ..
00216 *
00217 *  =====================================================================
00218 *
00219 *     .. Parameters ..
00220       REAL               ONE
00221       PARAMETER          ( ONE = 1.0E+0 )
00222 *     ..
00223 *     .. Local Scalars ..
00224       LOGICAL            LOWER, NISODD, NORMALTRANSR
00225       INTEGER            N1, N2, K
00226 *     ..
00227 *     .. External Functions ..
00228       LOGICAL            LSAME
00229       EXTERNAL           LSAME
00230 *     ..
00231 *     .. External Subroutines ..
00232       EXTERNAL           XERBLA, STRMM, STRTRI
00233 *     ..
00234 *     .. Intrinsic Functions ..
00235       INTRINSIC          MOD
00236 *     ..
00237 *     .. Executable Statements ..
00238 *
00239 *     Test the input parameters.
00240 *
00241       INFO = 0
00242       NORMALTRANSR = LSAME( TRANSR, 'N' )
00243       LOWER = LSAME( UPLO, 'L' )
00244       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
00245          INFO = -1
00246       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00247          INFO = -2
00248       ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
00249      $         THEN
00250          INFO = -3
00251       ELSE IF( N.LT.0 ) THEN
00252          INFO = -4
00253       END IF
00254       IF( INFO.NE.0 ) THEN
00255          CALL XERBLA( 'STFTRI', -INFO )
00256          RETURN
00257       END IF
00258 *
00259 *     Quick return if possible
00260 *
00261       IF( N.EQ.0 )
00262      $   RETURN
00263 *
00264 *     If N is odd, set NISODD = .TRUE.
00265 *     If N is even, set K = N/2 and NISODD = .FALSE.
00266 *
00267       IF( MOD( N, 2 ).EQ.0 ) THEN
00268          K = N / 2
00269          NISODD = .FALSE.
00270       ELSE
00271          NISODD = .TRUE.
00272       END IF
00273 *
00274 *     Set N1 and N2 depending on LOWER
00275 *
00276       IF( LOWER ) THEN
00277          N2 = N / 2
00278          N1 = N - N2
00279       ELSE
00280          N1 = N / 2
00281          N2 = N - N1
00282       END IF
00283 *
00284 *
00285 *     start execution: there are eight cases
00286 *
00287       IF( NISODD ) THEN
00288 *
00289 *        N is odd
00290 *
00291          IF( NORMALTRANSR ) THEN
00292 *
00293 *           N is odd and TRANSR = 'N'
00294 *
00295             IF( LOWER ) THEN
00296 *
00297 *             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
00298 *             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
00299 *             T1 -> a(0), T2 -> a(n), S -> a(n1)
00300 *
00301                CALL STRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
00302                IF( INFO.GT.0 )
00303      $            RETURN
00304                CALL STRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
00305      $                     N, A( N1 ), N )
00306                CALL STRTRI( 'U', DIAG, N2, A( N ), N, INFO )
00307                IF( INFO.GT.0 )
00308      $            INFO = INFO + N1
00309                IF( INFO.GT.0 )
00310      $            RETURN
00311                CALL STRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
00312      $                     A( N1 ), N )
00313 *
00314             ELSE
00315 *
00316 *             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
00317 *             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
00318 *             T1 -> a(n2), T2 -> a(n1), S -> a(0)
00319 *
00320                CALL STRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
00321                IF( INFO.GT.0 )
00322      $            RETURN
00323                CALL STRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
00324      $                     N, A( 0 ), N )
00325                CALL STRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
00326                IF( INFO.GT.0 )
00327      $            INFO = INFO + N1
00328                IF( INFO.GT.0 )
00329      $            RETURN
00330                CALL STRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
00331      $                     N, A( 0 ), N )
00332 *
00333             END IF
00334 *
00335          ELSE
00336 *
00337 *           N is odd and TRANSR = 'T'
00338 *
00339             IF( LOWER ) THEN
00340 *
00341 *              SRPA for LOWER, TRANSPOSE and N is odd
00342 *              T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
00343 *
00344                CALL STRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
00345                IF( INFO.GT.0 )
00346      $            RETURN
00347                CALL STRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
00348      $                     N1, A( N1*N1 ), N1 )
00349                CALL STRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
00350                IF( INFO.GT.0 )
00351      $            INFO = INFO + N1
00352                IF( INFO.GT.0 )
00353      $            RETURN
00354                CALL STRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
00355      $                     N1, A( N1*N1 ), N1 )
00356 *
00357             ELSE
00358 *
00359 *              SRPA for UPPER, TRANSPOSE and N is odd
00360 *              T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
00361 *
00362                CALL STRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
00363                IF( INFO.GT.0 )
00364      $            RETURN
00365                CALL STRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
00366      $                     A( N2*N2 ), N2, A( 0 ), N2 )
00367                CALL STRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
00368                IF( INFO.GT.0 )
00369      $            INFO = INFO + N1
00370                IF( INFO.GT.0 )
00371      $            RETURN
00372                CALL STRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
00373      $                     A( N1*N2 ), N2, A( 0 ), N2 )
00374             END IF
00375 *
00376          END IF
00377 *
00378       ELSE
00379 *
00380 *        N is even
00381 *
00382          IF( NORMALTRANSR ) THEN
00383 *
00384 *           N is even and TRANSR = 'N'
00385 *
00386             IF( LOWER ) THEN
00387 *
00388 *              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
00389 *              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
00390 *              T1 -> a(1), T2 -> a(0), S -> a(k+1)
00391 *
00392                CALL STRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
00393                IF( INFO.GT.0 )
00394      $            RETURN
00395                CALL STRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
00396      $                     N+1, A( K+1 ), N+1 )
00397                CALL STRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
00398                IF( INFO.GT.0 )
00399      $            INFO = INFO + K
00400                IF( INFO.GT.0 )
00401      $            RETURN
00402                CALL STRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
00403      $                     A( K+1 ), N+1 )
00404 *
00405             ELSE
00406 *
00407 *              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
00408 *              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
00409 *              T1 -> a(k+1), T2 -> a(k), S -> a(0)
00410 *
00411                CALL STRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
00412                IF( INFO.GT.0 )
00413      $            RETURN
00414                CALL STRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
00415      $                     N+1, A( 0 ), N+1 )
00416                CALL STRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
00417                IF( INFO.GT.0 )
00418      $            INFO = INFO + K
00419                IF( INFO.GT.0 )
00420      $            RETURN
00421                CALL STRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
00422      $                     A( 0 ), N+1 )
00423             END IF
00424          ELSE
00425 *
00426 *           N is even and TRANSR = 'T'
00427 *
00428             IF( LOWER ) THEN
00429 *
00430 *              SRPA for LOWER, TRANSPOSE and N is even (see paper)
00431 *              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
00432 *              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
00433 *
00434                CALL STRTRI( 'U', DIAG, K, A( K ), K, INFO )
00435                IF( INFO.GT.0 )
00436      $            RETURN
00437                CALL STRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
00438      $                     A( K*( K+1 ) ), K )
00439                CALL STRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
00440                IF( INFO.GT.0 )
00441      $            INFO = INFO + K
00442                IF( INFO.GT.0 )
00443      $            RETURN
00444                CALL STRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
00445      $                     A( K*( K+1 ) ), K )
00446             ELSE
00447 *
00448 *              SRPA for UPPER, TRANSPOSE and N is even (see paper)
00449 *              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
00450 *              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
00451 *
00452                CALL STRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
00453                IF( INFO.GT.0 )
00454      $            RETURN
00455                CALL STRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
00456      $                     A( K*( K+1 ) ), K, A( 0 ), K )
00457                CALL STRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
00458                IF( INFO.GT.0 )
00459      $            INFO = INFO + K
00460                IF( INFO.GT.0 )
00461      $            RETURN
00462                CALL STRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
00463      $                     A( 0 ), K )
00464             END IF
00465          END IF
00466       END IF
00467 *
00468       RETURN
00469 *
00470 *     End of STFTRI
00471 *
00472       END
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