File:  [local] / rpl / lapack / lapack / zpftrs.f
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Tue Dec 21 13:48:06 2010 UTC (13 years, 10 months ago) by bertrand
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CVS tags: HEAD
Mise à jour de Lapack vers la version 3.3.0

    1:       SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.3.0)                                    --
    4: *
    5: *  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
    6: *     November 2010
    7: *
    8: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    9: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   10: *
   11: *     .. Scalar Arguments ..
   12:       CHARACTER          TRANSR, UPLO
   13:       INTEGER            INFO, LDB, N, NRHS
   14: *     ..
   15: *     .. Array Arguments ..
   16:       COMPLEX*16         A( 0: * ), B( LDB, * )
   17: *     ..
   18: *
   19: *  Purpose
   20: *  =======
   21: *
   22: *  ZPFTRS solves a system of linear equations A*X = B with a Hermitian
   23: *  positive definite matrix A using the Cholesky factorization
   24: *  A = U**H*U or A = L*L**H computed by ZPFTRF.
   25: *
   26: *  Arguments
   27: *  =========
   28: *
   29: *  TRANSR    (input) CHARACTER*1
   30: *          = 'N':  The Normal TRANSR of RFP A is stored;
   31: *          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
   32: *
   33: *  UPLO    (input) CHARACTER*1
   34: *          = 'U':  Upper triangle of RFP A is stored;
   35: *          = 'L':  Lower triangle of RFP A is stored.
   36: *
   37: *  N       (input) INTEGER
   38: *          The order of the matrix A.  N >= 0.
   39: *
   40: *  NRHS    (input) INTEGER
   41: *          The number of right hand sides, i.e., the number of columns
   42: *          of the matrix B.  NRHS >= 0.
   43: *
   44: *  A       (input) COMPLEX*16 array, dimension ( N*(N+1)/2 );
   45: *          The triangular factor U or L from the Cholesky factorization
   46: *          of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF.
   47: *          See note below for more details about RFP A.
   48: *
   49: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
   50: *          On entry, the right hand side matrix B.
   51: *          On exit, the solution matrix X.
   52: *
   53: *  LDB     (input) INTEGER
   54: *          The leading dimension of the array B.  LDB >= max(1,N).
   55: *
   56: *  INFO    (output) INTEGER
   57: *          = 0:  successful exit
   58: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   59: *
   60: *  Further Details
   61: *  ===============
   62: *
   63: *  We first consider Standard Packed Format when N is even.
   64: *  We give an example where N = 6.
   65: *
   66: *      AP is Upper             AP is Lower
   67: *
   68: *   00 01 02 03 04 05       00
   69: *      11 12 13 14 15       10 11
   70: *         22 23 24 25       20 21 22
   71: *            33 34 35       30 31 32 33
   72: *               44 45       40 41 42 43 44
   73: *                  55       50 51 52 53 54 55
   74: *
   75: *
   76: *  Let TRANSR = 'N'. RFP holds AP as follows:
   77: *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
   78: *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
   79: *  conjugate-transpose of the first three columns of AP upper.
   80: *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
   81: *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
   82: *  conjugate-transpose of the last three columns of AP lower.
   83: *  To denote conjugate we place -- above the element. This covers the
   84: *  case N even and TRANSR = 'N'.
   85: *
   86: *         RFP A                   RFP A
   87: *
   88: *                                -- -- --
   89: *        03 04 05                33 43 53
   90: *                                   -- --
   91: *        13 14 15                00 44 54
   92: *                                      --
   93: *        23 24 25                10 11 55
   94: *
   95: *        33 34 35                20 21 22
   96: *        --
   97: *        00 44 45                30 31 32
   98: *        -- --
   99: *        01 11 55                40 41 42
  100: *        -- -- --
  101: *        02 12 22                50 51 52
  102: *
  103: *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
  104: *  transpose of RFP A above. One therefore gets:
  105: *
  106: *
  107: *           RFP A                   RFP A
  108: *
  109: *     -- -- -- --                -- -- -- -- -- --
  110: *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
  111: *     -- -- -- -- --                -- -- -- -- --
  112: *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
  113: *     -- -- -- -- -- --                -- -- -- --
  114: *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
  115: *
  116: *
  117: *  We next  consider Standard Packed Format when N is odd.
  118: *  We give an example where N = 5.
  119: *
  120: *     AP is Upper                 AP is Lower
  121: *
  122: *   00 01 02 03 04              00
  123: *      11 12 13 14              10 11
  124: *         22 23 24              20 21 22
  125: *            33 34              30 31 32 33
  126: *               44              40 41 42 43 44
  127: *
  128: *
  129: *  Let TRANSR = 'N'. RFP holds AP as follows:
  130: *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
  131: *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
  132: *  conjugate-transpose of the first two   columns of AP upper.
  133: *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
  134: *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
  135: *  conjugate-transpose of the last two   columns of AP lower.
  136: *  To denote conjugate we place -- above the element. This covers the
  137: *  case N odd  and TRANSR = 'N'.
  138: *
  139: *         RFP A                   RFP A
  140: *
  141: *                                   -- --
  142: *        02 03 04                00 33 43
  143: *                                      --
  144: *        12 13 14                10 11 44
  145: *
  146: *        22 23 24                20 21 22
  147: *        --
  148: *        00 33 34                30 31 32
  149: *        -- --
  150: *        01 11 44                40 41 42
  151: *
  152: *  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
  153: *  transpose of RFP A above. One therefore gets:
  154: *
  155: *
  156: *           RFP A                   RFP A
  157: *
  158: *     -- -- --                   -- -- -- -- -- --
  159: *     02 12 22 00 01             00 10 20 30 40 50
  160: *     -- -- -- --                   -- -- -- -- --
  161: *     03 13 23 33 11             33 11 21 31 41 51
  162: *     -- -- -- -- --                   -- -- -- --
  163: *     04 14 24 34 44             43 44 22 32 42 52
  164: *
  165: *  =====================================================================
  166: *
  167: *     .. Parameters ..
  168:       COMPLEX*16         CONE
  169:       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
  170: *     ..
  171: *     .. Local Scalars ..
  172:       LOGICAL            LOWER, NORMALTRANSR
  173: *     ..
  174: *     .. External Functions ..
  175:       LOGICAL            LSAME
  176:       EXTERNAL           LSAME
  177: *     ..
  178: *     .. External Subroutines ..
  179:       EXTERNAL           XERBLA, ZTFSM
  180: *     ..
  181: *     .. Intrinsic Functions ..
  182:       INTRINSIC          MAX
  183: *     ..
  184: *     .. Executable Statements ..
  185: *
  186: *     Test the input parameters.
  187: *
  188:       INFO = 0
  189:       NORMALTRANSR = LSAME( TRANSR, 'N' )
  190:       LOWER = LSAME( UPLO, 'L' )
  191:       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
  192:          INFO = -1
  193:       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
  194:          INFO = -2
  195:       ELSE IF( N.LT.0 ) THEN
  196:          INFO = -3
  197:       ELSE IF( NRHS.LT.0 ) THEN
  198:          INFO = -4
  199:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  200:          INFO = -7
  201:       END IF
  202:       IF( INFO.NE.0 ) THEN
  203:          CALL XERBLA( 'ZPFTRS', -INFO )
  204:          RETURN
  205:       END IF
  206: *
  207: *     Quick return if possible
  208: *
  209:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  210:      +   RETURN
  211: *
  212: *     start execution: there are two triangular solves
  213: *
  214:       IF( LOWER ) THEN
  215:          CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
  216:      +               LDB )
  217:          CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
  218:      +               LDB )
  219:       ELSE
  220:          CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
  221:      +               LDB )
  222:          CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
  223:      +               LDB )
  224:       END IF
  225: *
  226:       RETURN
  227: *
  228: *     End of ZPFTRS
  229: *
  230:       END

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