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Patches pour OS/2

    1:       SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
    2: *
    3: *  -- LAPACK driver routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          UPLO
   10:       INTEGER            INFO, LDB, N, NRHS
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   AP( * ), B( LDB, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DPPSV computes the solution to a real system of linear equations
   20: *     A * X = B,
   21: *  where A is an N-by-N symmetric positive definite matrix stored in
   22: *  packed format and X and B are N-by-NRHS matrices.
   23: *
   24: *  The Cholesky decomposition is used to factor A as
   25: *     A = U**T* U,  if UPLO = 'U', or
   26: *     A = L * L**T,  if UPLO = 'L',
   27: *  where U is an upper triangular matrix and L is a lower triangular
   28: *  matrix.  The factored form of A is then used to solve the system of
   29: *  equations A * X = B.
   30: *
   31: *  Arguments
   32: *  =========
   33: *
   34: *  UPLO    (input) CHARACTER*1
   35: *          = 'U':  Upper triangle of A is stored;
   36: *          = 'L':  Lower triangle of A is stored.
   37: *
   38: *  N       (input) INTEGER
   39: *          The number of linear equations, i.e., the order of the
   40: *          matrix A.  N >= 0.
   41: *
   42: *  NRHS    (input) INTEGER
   43: *          The number of right hand sides, i.e., the number of columns
   44: *          of the matrix B.  NRHS >= 0.
   45: *
   46: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   47: *          On entry, the upper or lower triangle of the symmetric matrix
   48: *          A, packed columnwise in a linear array.  The j-th column of A
   49: *          is stored in the array AP as follows:
   50: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   51: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   52: *          See below for further details.
   53: *
   54: *          On exit, if INFO = 0, the factor U or L from the Cholesky
   55: *          factorization A = U**T*U or A = L*L**T, in the same storage
   56: *          format as A.
   57: *
   58: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
   59: *          On entry, the N-by-NRHS right hand side matrix B.
   60: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   61: *
   62: *  LDB     (input) INTEGER
   63: *          The leading dimension of the array B.  LDB >= max(1,N).
   64: *
   65: *  INFO    (output) INTEGER
   66: *          = 0:  successful exit
   67: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   68: *          > 0:  if INFO = i, the leading minor of order i of A is not
   69: *                positive definite, so the factorization could not be
   70: *                completed, and the solution has not been computed.
   71: *
   72: *  Further Details
   73: *  ===============
   74: *
   75: *  The packed storage scheme is illustrated by the following example
   76: *  when N = 4, UPLO = 'U':
   77: *
   78: *  Two-dimensional storage of the symmetric matrix A:
   79: *
   80: *     a11 a12 a13 a14
   81: *         a22 a23 a24
   82: *             a33 a34     (aij = conjg(aji))
   83: *                 a44
   84: *
   85: *  Packed storage of the upper triangle of A:
   86: *
   87: *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
   88: *
   89: *  =====================================================================
   90: *
   91: *     .. External Functions ..
   92:       LOGICAL            LSAME
   93:       EXTERNAL           LSAME
   94: *     ..
   95: *     .. External Subroutines ..
   96:       EXTERNAL           DPPTRF, DPPTRS, XERBLA
   97: *     ..
   98: *     .. Intrinsic Functions ..
   99:       INTRINSIC          MAX
  100: *     ..
  101: *     .. Executable Statements ..
  102: *
  103: *     Test the input parameters.
  104: *
  105:       INFO = 0
  106:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  107:          INFO = -1
  108:       ELSE IF( N.LT.0 ) THEN
  109:          INFO = -2
  110:       ELSE IF( NRHS.LT.0 ) THEN
  111:          INFO = -3
  112:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  113:          INFO = -6
  114:       END IF
  115:       IF( INFO.NE.0 ) THEN
  116:          CALL XERBLA( 'DPPSV ', -INFO )
  117:          RETURN
  118:       END IF
  119: *
  120: *     Compute the Cholesky factorization A = U'*U or A = L*L'.
  121: *
  122:       CALL DPPTRF( UPLO, N, AP, INFO )
  123:       IF( INFO.EQ.0 ) THEN
  124: *
  125: *        Solve the system A*X = B, overwriting B with X.
  126: *
  127:          CALL DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
  128: *
  129:       END IF
  130:       RETURN
  131: *
  132: *     End of DPPSV
  133: *
  134:       END