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    1: *> \brief \b DPFTRS
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DPFTRS + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftrs.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftrs.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftrs.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          TRANSR, UPLO
   25: *       INTEGER            INFO, LDB, N, NRHS
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   A( 0: * ), B( LDB, * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DPFTRS solves a system of linear equations A*X = B with a symmetric
   38: *> positive definite matrix A using the Cholesky factorization
   39: *> A = U**T*U or A = L*L**T computed by DPFTRF.
   40: *> \endverbatim
   41: *
   42: *  Arguments:
   43: *  ==========
   44: *
   45: *> \param[in] TRANSR
   46: *> \verbatim
   47: *>          TRANSR is CHARACTER*1
   48: *>          = 'N':  The Normal TRANSR of RFP A is stored;
   49: *>          = 'T':  The Transpose TRANSR of RFP A is stored.
   50: *> \endverbatim
   51: *>
   52: *> \param[in] UPLO
   53: *> \verbatim
   54: *>          UPLO is CHARACTER*1
   55: *>          = 'U':  Upper triangle of RFP A is stored;
   56: *>          = 'L':  Lower triangle of RFP A is stored.
   57: *> \endverbatim
   58: *>
   59: *> \param[in] N
   60: *> \verbatim
   61: *>          N is INTEGER
   62: *>          The order of the matrix A.  N >= 0.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] NRHS
   66: *> \verbatim
   67: *>          NRHS is INTEGER
   68: *>          The number of right hand sides, i.e., the number of columns
   69: *>          of the matrix B.  NRHS >= 0.
   70: *> \endverbatim
   71: *>
   72: *> \param[in] A
   73: *> \verbatim
   74: *>          A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
   75: *>          The triangular factor U or L from the Cholesky factorization
   76: *>          of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
   77: *>          See note below for more details about RFP A.
   78: *> \endverbatim
   79: *>
   80: *> \param[in,out] B
   81: *> \verbatim
   82: *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   83: *>          On entry, the right hand side matrix B.
   84: *>          On exit, the solution matrix X.
   85: *> \endverbatim
   86: *>
   87: *> \param[in] LDB
   88: *> \verbatim
   89: *>          LDB is INTEGER
   90: *>          The leading dimension of the array B.  LDB >= max(1,N).
   91: *> \endverbatim
   92: *>
   93: *> \param[out] INFO
   94: *> \verbatim
   95: *>          INFO is INTEGER
   96: *>          = 0:  successful exit
   97: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   98: *> \endverbatim
   99: *
  100: *  Authors:
  101: *  ========
  102: *
  103: *> \author Univ. of Tennessee 
  104: *> \author Univ. of California Berkeley 
  105: *> \author Univ. of Colorado Denver 
  106: *> \author NAG Ltd. 
  107: *
  108: *> \date November 2011
  109: *
  110: *> \ingroup doubleOTHERcomputational
  111: *
  112: *> \par Further Details:
  113: *  =====================
  114: *>
  115: *> \verbatim
  116: *>
  117: *>  We first consider Rectangular Full Packed (RFP) Format when N is
  118: *>  even. We give an example where N = 6.
  119: *>
  120: *>      AP is Upper             AP is Lower
  121: *>
  122: *>   00 01 02 03 04 05       00
  123: *>      11 12 13 14 15       10 11
  124: *>         22 23 24 25       20 21 22
  125: *>            33 34 35       30 31 32 33
  126: *>               44 45       40 41 42 43 44
  127: *>                  55       50 51 52 53 54 55
  128: *>
  129: *>
  130: *>  Let TRANSR = 'N'. RFP holds AP as follows:
  131: *>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
  132: *>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
  133: *>  the transpose of the first three columns of AP upper.
  134: *>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
  135: *>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
  136: *>  the transpose of the last three columns of AP lower.
  137: *>  This covers the case N even and TRANSR = 'N'.
  138: *>
  139: *>         RFP A                   RFP A
  140: *>
  141: *>        03 04 05                33 43 53
  142: *>        13 14 15                00 44 54
  143: *>        23 24 25                10 11 55
  144: *>        33 34 35                20 21 22
  145: *>        00 44 45                30 31 32
  146: *>        01 11 55                40 41 42
  147: *>        02 12 22                50 51 52
  148: *>
  149: *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
  150: *>  transpose of RFP A above. One therefore gets:
  151: *>
  152: *>
  153: *>           RFP A                   RFP A
  154: *>
  155: *>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
  156: *>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
  157: *>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
  158: *>
  159: *>
  160: *>  We then consider Rectangular Full Packed (RFP) Format when N is
  161: *>  odd. We give an example where N = 5.
  162: *>
  163: *>     AP is Upper                 AP is Lower
  164: *>
  165: *>   00 01 02 03 04              00
  166: *>      11 12 13 14              10 11
  167: *>         22 23 24              20 21 22
  168: *>            33 34              30 31 32 33
  169: *>               44              40 41 42 43 44
  170: *>
  171: *>
  172: *>  Let TRANSR = 'N'. RFP holds AP as follows:
  173: *>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
  174: *>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
  175: *>  the transpose of the first two columns of AP upper.
  176: *>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
  177: *>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
  178: *>  the transpose of the last two columns of AP lower.
  179: *>  This covers the case N odd and TRANSR = 'N'.
  180: *>
  181: *>         RFP A                   RFP A
  182: *>
  183: *>        02 03 04                00 33 43
  184: *>        12 13 14                10 11 44
  185: *>        22 23 24                20 21 22
  186: *>        00 33 34                30 31 32
  187: *>        01 11 44                40 41 42
  188: *>
  189: *>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
  190: *>  transpose of RFP A above. One therefore gets:
  191: *>
  192: *>           RFP A                   RFP A
  193: *>
  194: *>     02 12 22 00 01             00 10 20 30 40 50
  195: *>     03 13 23 33 11             33 11 21 31 41 51
  196: *>     04 14 24 34 44             43 44 22 32 42 52
  197: *> \endverbatim
  198: *>
  199: *  =====================================================================
  200:       SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
  201: *
  202: *  -- LAPACK computational routine (version 3.4.0) --
  203: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  204: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  205: *     November 2011
  206: *
  207: *     .. Scalar Arguments ..
  208:       CHARACTER          TRANSR, UPLO
  209:       INTEGER            INFO, LDB, N, NRHS
  210: *     ..
  211: *     .. Array Arguments ..
  212:       DOUBLE PRECISION   A( 0: * ), B( LDB, * )
  213: *     ..
  214: *
  215: *  =====================================================================
  216: *
  217: *     .. Parameters ..
  218:       DOUBLE PRECISION   ONE
  219:       PARAMETER          ( ONE = 1.0D+0 )
  220: *     ..
  221: *     .. Local Scalars ..
  222:       LOGICAL            LOWER, NORMALTRANSR
  223: *     ..
  224: *     .. External Functions ..
  225:       LOGICAL            LSAME
  226:       EXTERNAL           LSAME
  227: *     ..
  228: *     .. External Subroutines ..
  229:       EXTERNAL           XERBLA, DTFSM
  230: *     ..
  231: *     .. Intrinsic Functions ..
  232:       INTRINSIC          MAX
  233: *     ..
  234: *     .. Executable Statements ..
  235: *
  236: *     Test the input parameters.
  237: *
  238:       INFO = 0
  239:       NORMALTRANSR = LSAME( TRANSR, 'N' )
  240:       LOWER = LSAME( UPLO, 'L' )
  241:       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
  242:          INFO = -1
  243:       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
  244:          INFO = -2
  245:       ELSE IF( N.LT.0 ) THEN
  246:          INFO = -3
  247:       ELSE IF( NRHS.LT.0 ) THEN
  248:          INFO = -4
  249:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  250:          INFO = -7
  251:       END IF
  252:       IF( INFO.NE.0 ) THEN
  253:          CALL XERBLA( 'DPFTRS', -INFO )
  254:          RETURN
  255:       END IF
  256: *
  257: *     Quick return if possible
  258: *
  259:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  260:      $   RETURN
  261: *
  262: *     start execution: there are two triangular solves
  263: *
  264:       IF( LOWER ) THEN
  265:          CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
  266:      $               LDB )
  267:          CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
  268:      $               LDB )
  269:       ELSE
  270:          CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
  271:      $               LDB )
  272:          CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
  273:      $               LDB )
  274:       END IF
  275: *
  276:       RETURN
  277: *
  278: *     End of DPFTRS
  279: *
  280:       END