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Patches pour OS/2

    1:       SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, 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:       INTEGER            IPIV( * )
   14:       DOUBLE PRECISION   AP( * ), B( LDB, * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DSPSV computes the solution to a real system of linear equations
   21: *     A * X = B,
   22: *  where A is an N-by-N symmetric matrix stored in packed format and X
   23: *  and B are N-by-NRHS matrices.
   24: *
   25: *  The diagonal pivoting method is used to factor A as
   26: *     A = U * D * U**T,  if UPLO = 'U', or
   27: *     A = L * D * L**T,  if UPLO = 'L',
   28: *  where U (or L) is a product of permutation and unit upper (lower)
   29: *  triangular matrices, D is symmetric and block diagonal with 1-by-1
   30: *  and 2-by-2 diagonal blocks.  The factored form of A is then used to
   31: *  solve the system of equations A * X = B.
   32: *
   33: *  Arguments
   34: *  =========
   35: *
   36: *  UPLO    (input) CHARACTER*1
   37: *          = 'U':  Upper triangle of A is stored;
   38: *          = 'L':  Lower triangle of A is stored.
   39: *
   40: *  N       (input) INTEGER
   41: *          The number of linear equations, i.e., the order of the
   42: *          matrix A.  N >= 0.
   43: *
   44: *  NRHS    (input) INTEGER
   45: *          The number of right hand sides, i.e., the number of columns
   46: *          of the matrix B.  NRHS >= 0.
   47: *
   48: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   49: *          On entry, the upper or lower triangle of the symmetric matrix
   50: *          A, packed columnwise in a linear array.  The j-th column of A
   51: *          is stored in the array AP as follows:
   52: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   53: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   54: *          See below for further details.
   55: *
   56: *          On exit, the block diagonal matrix D and the multipliers used
   57: *          to obtain the factor U or L from the factorization
   58: *          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
   59: *          a packed triangular matrix in the same storage format as A.
   60: *
   61: *  IPIV    (output) INTEGER array, dimension (N)
   62: *          Details of the interchanges and the block structure of D, as
   63: *          determined by DSPTRF.  If IPIV(k) > 0, then rows and columns
   64: *          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
   65: *          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
   66: *          then rows and columns k-1 and -IPIV(k) were interchanged and
   67: *          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
   68: *          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
   69: *          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
   70: *          diagonal block.
   71: *
   72: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
   73: *          On entry, the N-by-NRHS right hand side matrix B.
   74: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   75: *
   76: *  LDB     (input) INTEGER
   77: *          The leading dimension of the array B.  LDB >= max(1,N).
   78: *
   79: *  INFO    (output) INTEGER
   80: *          = 0:  successful exit
   81: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   82: *          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
   83: *                has been completed, but the block diagonal matrix D is
   84: *                exactly singular, so the solution could not be
   85: *                computed.
   86: *
   87: *  Further Details
   88: *  ===============
   89: *
   90: *  The packed storage scheme is illustrated by the following example
   91: *  when N = 4, UPLO = 'U':
   92: *
   93: *  Two-dimensional storage of the symmetric matrix A:
   94: *
   95: *     a11 a12 a13 a14
   96: *         a22 a23 a24
   97: *             a33 a34     (aij = aji)
   98: *                 a44
   99: *
  100: *  Packed storage of the upper triangle of A:
  101: *
  102: *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
  103: *
  104: *  =====================================================================
  105: *
  106: *     .. External Functions ..
  107:       LOGICAL            LSAME
  108:       EXTERNAL           LSAME
  109: *     ..
  110: *     .. External Subroutines ..
  111:       EXTERNAL           DSPTRF, DSPTRS, XERBLA
  112: *     ..
  113: *     .. Intrinsic Functions ..
  114:       INTRINSIC          MAX
  115: *     ..
  116: *     .. Executable Statements ..
  117: *
  118: *     Test the input parameters.
  119: *
  120:       INFO = 0
  121:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  122:          INFO = -1
  123:       ELSE IF( N.LT.0 ) THEN
  124:          INFO = -2
  125:       ELSE IF( NRHS.LT.0 ) THEN
  126:          INFO = -3
  127:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  128:          INFO = -7
  129:       END IF
  130:       IF( INFO.NE.0 ) THEN
  131:          CALL XERBLA( 'DSPSV ', -INFO )
  132:          RETURN
  133:       END IF
  134: *
  135: *     Compute the factorization A = U*D*U' or A = L*D*L'.
  136: *
  137:       CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
  138:       IF( INFO.EQ.0 ) THEN
  139: *
  140: *        Solve the system A*X = B, overwriting B with X.
  141: *
  142:          CALL DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
  143: *
  144:       END IF
  145:       RETURN
  146: *
  147: *     End of DSPSV
  148: *
  149:       END