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Mise à jour de Lapack vers la version 3.3.0

    1:       SUBROUTINE DPFTRS( 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:       DOUBLE PRECISION   A( 0: * ), B( LDB, * )
   17: *     ..
   18: *
   19: *  Purpose
   20: *  =======
   21: *
   22: *  DPFTRS solves a system of linear equations A*X = B with a symmetric
   23: *  positive definite matrix A using the Cholesky factorization
   24: *  A = U**T*U or A = L*L**T computed by DPFTRF.
   25: *
   26: *  Arguments
   27: *  =========
   28: *
   29: *  TRANSR  (input) CHARACTER*1
   30: *          = 'N':  The Normal TRANSR of RFP A is stored;
   31: *          = 'T':  The 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) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
   45: *          The triangular factor U or L from the Cholesky factorization
   46: *          of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
   47: *          See note below for more details about RFP A.
   48: *
   49: *  B       (input/output) DOUBLE PRECISION 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 Rectangular Full Packed (RFP) Format when N is
   64: *  even. 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: *  the 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: *  the transpose of the last three columns of AP lower.
   83: *  This covers the case N even and TRANSR = 'N'.
   84: *
   85: *         RFP A                   RFP A
   86: *
   87: *        03 04 05                33 43 53
   88: *        13 14 15                00 44 54
   89: *        23 24 25                10 11 55
   90: *        33 34 35                20 21 22
   91: *        00 44 45                30 31 32
   92: *        01 11 55                40 41 42
   93: *        02 12 22                50 51 52
   94: *
   95: *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
   96: *  transpose of RFP A above. One therefore gets:
   97: *
   98: *
   99: *           RFP A                   RFP A
  100: *
  101: *     03 13 23 33 00 01 02    33 00 10 20 30 40 50
  102: *     04 14 24 34 44 11 12    43 44 11 21 31 41 51
  103: *     05 15 25 35 45 55 22    53 54 55 22 32 42 52
  104: *
  105: *
  106: *  We then consider Rectangular Full Packed (RFP) Format when N is
  107: *  odd. We give an example where N = 5.
  108: *
  109: *     AP is Upper                 AP is Lower
  110: *
  111: *   00 01 02 03 04              00
  112: *      11 12 13 14              10 11
  113: *         22 23 24              20 21 22
  114: *            33 34              30 31 32 33
  115: *               44              40 41 42 43 44
  116: *
  117: *
  118: *  Let TRANSR = 'N'. RFP holds AP as follows:
  119: *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
  120: *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
  121: *  the transpose of the first two columns of AP upper.
  122: *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
  123: *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
  124: *  the transpose of the last two columns of AP lower.
  125: *  This covers the case N odd and TRANSR = 'N'.
  126: *
  127: *         RFP A                   RFP A
  128: *
  129: *        02 03 04                00 33 43
  130: *        12 13 14                10 11 44
  131: *        22 23 24                20 21 22
  132: *        00 33 34                30 31 32
  133: *        01 11 44                40 41 42
  134: *
  135: *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
  136: *  transpose of RFP A above. One therefore gets:
  137: *
  138: *           RFP A                   RFP A
  139: *
  140: *     02 12 22 00 01             00 10 20 30 40 50
  141: *     03 13 23 33 11             33 11 21 31 41 51
  142: *     04 14 24 34 44             43 44 22 32 42 52
  143: *
  144: *  =====================================================================
  145: *
  146: *     .. Parameters ..
  147:       DOUBLE PRECISION   ONE
  148:       PARAMETER          ( ONE = 1.0D+0 )
  149: *     ..
  150: *     .. Local Scalars ..
  151:       LOGICAL            LOWER, NORMALTRANSR
  152: *     ..
  153: *     .. External Functions ..
  154:       LOGICAL            LSAME
  155:       EXTERNAL           LSAME
  156: *     ..
  157: *     .. External Subroutines ..
  158:       EXTERNAL           XERBLA, DTFSM
  159: *     ..
  160: *     .. Intrinsic Functions ..
  161:       INTRINSIC          MAX
  162: *     ..
  163: *     .. Executable Statements ..
  164: *
  165: *     Test the input parameters.
  166: *
  167:       INFO = 0
  168:       NORMALTRANSR = LSAME( TRANSR, 'N' )
  169:       LOWER = LSAME( UPLO, 'L' )
  170:       IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
  171:          INFO = -1
  172:       ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
  173:          INFO = -2
  174:       ELSE IF( N.LT.0 ) THEN
  175:          INFO = -3
  176:       ELSE IF( NRHS.LT.0 ) THEN
  177:          INFO = -4
  178:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  179:          INFO = -7
  180:       END IF
  181:       IF( INFO.NE.0 ) THEN
  182:          CALL XERBLA( 'DPFTRS', -INFO )
  183:          RETURN
  184:       END IF
  185: *
  186: *     Quick return if possible
  187: *
  188:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  189:      +   RETURN
  190: *
  191: *     start execution: there are two triangular solves
  192: *
  193:       IF( LOWER ) THEN
  194:          CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
  195:      +               LDB )
  196:          CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
  197:      +               LDB )
  198:       ELSE
  199:          CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
  200:      +               LDB )
  201:          CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
  202:      +               LDB )
  203:       END IF
  204: *
  205:       RETURN
  206: *
  207: *     End of DPFTRS
  208: *
  209:       END