LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cpftrs.f
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00001 *> \brief \b CPFTRS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CPFTRS + 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/cpftrs.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          TRANSR, UPLO
00025 *       INTEGER            INFO, LDB, N, NRHS
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            A( 0: * ), B( LDB, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CPFTRS solves a system of linear equations A*X = B with a Hermitian
00038 *> positive definite matrix A using the Cholesky factorization
00039 *> A = U**H*U or A = L*L**H computed by CPFTRF.
00040 *> \endverbatim
00041 *
00042 *  Arguments:
00043 *  ==========
00044 *
00045 *> \param[in] TRANSR
00046 *> \verbatim
00047 *>          TRANSR is CHARACTER*1
00048 *>          = 'N':  The Normal TRANSR of RFP A is stored;
00049 *>          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
00050 *> \endverbatim
00051 *>
00052 *> \param[in] UPLO
00053 *> \verbatim
00054 *>          UPLO is CHARACTER*1
00055 *>          = 'U':  Upper triangle of RFP A is stored;
00056 *>          = 'L':  Lower triangle of RFP A is stored.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] N
00060 *> \verbatim
00061 *>          N is INTEGER
00062 *>          The order of the matrix A.  N >= 0.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] NRHS
00066 *> \verbatim
00067 *>          NRHS is INTEGER
00068 *>          The number of right hand sides, i.e., the number of columns
00069 *>          of the matrix B.  NRHS >= 0.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] A
00073 *> \verbatim
00074 *>          A is COMPLEX array, dimension ( N*(N+1)/2 );
00075 *>          The triangular factor U or L from the Cholesky factorization
00076 *>          of RFP A = U**H*U or RFP A = L*L**H, as computed by CPFTRF.
00077 *>          See note below for more details about RFP A.
00078 *> \endverbatim
00079 *>
00080 *> \param[in,out] B
00081 *> \verbatim
00082 *>          B is COMPLEX array, dimension (LDB,NRHS)
00083 *>          On entry, the right hand side matrix B.
00084 *>          On exit, the solution matrix X.
00085 *> \endverbatim
00086 *>
00087 *> \param[in] LDB
00088 *> \verbatim
00089 *>          LDB is INTEGER
00090 *>          The leading dimension of the array B.  LDB >= max(1,N).
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 *> \endverbatim
00099 *
00100 *  Authors:
00101 *  ========
00102 *
00103 *> \author Univ. of Tennessee 
00104 *> \author Univ. of California Berkeley 
00105 *> \author Univ. of Colorado Denver 
00106 *> \author NAG Ltd. 
00107 *
00108 *> \date November 2011
00109 *
00110 *> \ingroup complexOTHERcomputational
00111 *
00112 *> \par Further Details:
00113 *  =====================
00114 *>
00115 *> \verbatim
00116 *>
00117 *>  We first consider Standard Packed Format when N is even.
00118 *>  We give an example where N = 6.
00119 *>
00120 *>      AP is Upper             AP is Lower
00121 *>
00122 *>   00 01 02 03 04 05       00
00123 *>      11 12 13 14 15       10 11
00124 *>         22 23 24 25       20 21 22
00125 *>            33 34 35       30 31 32 33
00126 *>               44 45       40 41 42 43 44
00127 *>                  55       50 51 52 53 54 55
00128 *>
00129 *>
00130 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00131 *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
00132 *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
00133 *>  conjugate-transpose of the first three columns of AP upper.
00134 *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
00135 *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
00136 *>  conjugate-transpose of the last three columns of AP lower.
00137 *>  To denote conjugate we place -- above the element. This covers the
00138 *>  case N even and TRANSR = 'N'.
00139 *>
00140 *>         RFP A                   RFP A
00141 *>
00142 *>                                -- -- --
00143 *>        03 04 05                33 43 53
00144 *>                                   -- --
00145 *>        13 14 15                00 44 54
00146 *>                                      --
00147 *>        23 24 25                10 11 55
00148 *>
00149 *>        33 34 35                20 21 22
00150 *>        --
00151 *>        00 44 45                30 31 32
00152 *>        -- --
00153 *>        01 11 55                40 41 42
00154 *>        -- -- --
00155 *>        02 12 22                50 51 52
00156 *>
00157 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00158 *>  transpose of RFP A above. One therefore gets:
00159 *>
00160 *>
00161 *>           RFP A                   RFP A
00162 *>
00163 *>     -- -- -- --                -- -- -- -- -- --
00164 *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
00165 *>     -- -- -- -- --                -- -- -- -- --
00166 *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
00167 *>     -- -- -- -- -- --                -- -- -- --
00168 *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
00169 *>
00170 *>
00171 *>  We next  consider Standard Packed Format when N is odd.
00172 *>  We give an example where N = 5.
00173 *>
00174 *>     AP is Upper                 AP is Lower
00175 *>
00176 *>   00 01 02 03 04              00
00177 *>      11 12 13 14              10 11
00178 *>         22 23 24              20 21 22
00179 *>            33 34              30 31 32 33
00180 *>               44              40 41 42 43 44
00181 *>
00182 *>
00183 *>  Let TRANSR = 'N'. RFP holds AP as follows:
00184 *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
00185 *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
00186 *>  conjugate-transpose of the first two   columns of AP upper.
00187 *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
00188 *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
00189 *>  conjugate-transpose of the last two   columns of AP lower.
00190 *>  To denote conjugate we place -- above the element. This covers the
00191 *>  case N odd  and TRANSR = 'N'.
00192 *>
00193 *>         RFP A                   RFP A
00194 *>
00195 *>                                   -- --
00196 *>        02 03 04                00 33 43
00197 *>                                      --
00198 *>        12 13 14                10 11 44
00199 *>
00200 *>        22 23 24                20 21 22
00201 *>        --
00202 *>        00 33 34                30 31 32
00203 *>        -- --
00204 *>        01 11 44                40 41 42
00205 *>
00206 *>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
00207 *>  transpose of RFP A above. One therefore gets:
00208 *>
00209 *>
00210 *>           RFP A                   RFP A
00211 *>
00212 *>     -- -- --                   -- -- -- -- -- --
00213 *>     02 12 22 00 01             00 10 20 30 40 50
00214 *>     -- -- -- --                   -- -- -- -- --
00215 *>     03 13 23 33 11             33 11 21 31 41 51
00216 *>     -- -- -- -- --                   -- -- -- --
00217 *>     04 14 24 34 44             43 44 22 32 42 52
00218 *> \endverbatim
00219 *>
00220 *  =====================================================================
00221       SUBROUTINE CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
00222 *
00223 *  -- LAPACK computational routine (version 3.4.0) --
00224 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00225 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00226 *     November 2011
00227 *
00228 *     .. Scalar Arguments ..
00229       CHARACTER          TRANSR, UPLO
00230       INTEGER            INFO, LDB, N, NRHS
00231 *     ..
00232 *     .. Array Arguments ..
00233       COMPLEX            A( 0: * ), B( LDB, * )
00234 *     ..
00235 *
00236 *  =====================================================================
00237 *
00238 *     .. Parameters ..
00239       COMPLEX            CONE
00240       PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
00241 *     ..
00242 *     .. Local Scalars ..
00243       LOGICAL            LOWER, NORMALTRANSR
00244 *     ..
00245 *     .. External Functions ..
00246       LOGICAL            LSAME
00247       EXTERNAL           LSAME
00248 *     ..
00249 *     .. External Subroutines ..
00250       EXTERNAL           XERBLA, CTFSM
00251 *     ..
00252 *     .. Intrinsic Functions ..
00253       INTRINSIC          MAX
00254 *     ..
00255 *     .. Executable Statements ..
00256 *
00257 *     Test the input parameters.
00258 *
00259       INFO = 0
00260       NORMALTRANSR = LSAME( TRANSR, 'N' )
00261       LOWER = LSAME( UPLO, 'L' )
00262       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
00263          INFO = -1
00264       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
00265          INFO = -2
00266       ELSE IF( N.LT.0 ) THEN
00267          INFO = -3
00268       ELSE IF( NRHS.LT.0 ) THEN
00269          INFO = -4
00270       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00271          INFO = -7
00272       END IF
00273       IF( INFO.NE.0 ) THEN
00274          CALL XERBLA( 'CPFTRS', -INFO )
00275          RETURN
00276       END IF
00277 *
00278 *     Quick return if possible
00279 *
00280       IF( N.EQ.0 .OR. NRHS.EQ.0 )
00281      $   RETURN
00282 *
00283 *     start execution: there are two triangular solves
00284 *
00285       IF( LOWER ) THEN
00286          CALL CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
00287      $               LDB )
00288          CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
00289      $               LDB )
00290       ELSE
00291          CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
00292      $               LDB )
00293          CALL CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
00294      $               LDB )
00295       END IF
00296 *
00297       RETURN
00298 *
00299 *     End of CPFTRS
00300 *
00301       END
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