IRIX 6.2 Development Libraries/SGI IRIX 6.2 Development Libraries.iso/dist/complib.idb/usr/share/catman/p_man/cat3/complib/dptsvx.z/dptsvx

Text File | 1996-03-14 | 7KB | 199 lines

DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))                                                          DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))



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     DPTSVX - use the factorization A = L*D*L**T to compute the solution to a
     real system of linear equations A*X = B, where A is an N-by-N symmetric
     positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

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     SUBROUTINE DPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND,
                        FERR, BERR, WORK, INFO )

         CHARACTER      FACT

         INTEGER        INFO, LDB, LDX, N, NRHS

         DOUBLE         PRECISION RCOND

         DOUBLE         PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), E(
                        * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )

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     DPTSVX uses the factorization A = L*D*L**T to compute the solution to a
     real system of linear equations A*X = B, where A is an N-by-N symmetric
     positive definite tridiagonal matrix and X and B are N-by-NRHS matrices.

     Error bounds on the solution and a condition estimate are also provided.


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     The following steps are performed:

     1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
        is a unit lower bidiagonal matrix and D is diagonal.  The
        factorization can also be regarded as having the form
        A = U**T*D*U.

     2. The factored form of A is used to compute the condition number
        of the matrix A.  If the reciprocal of the condition number is
        less than machine precision, steps 3 and 4 are skipped.

     3. The system of equations is solved for X using the factored form
        of A.

     4. Iterative refinement is applied to improve the computed solution
        matrix and calculate error bounds and backward error estimates
        for it.


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     FACT    (input) CHARACTER*1
             Specifies whether or not the factored form of A has been supplied
             on entry.  = 'F':  On entry, DF and EF contain the factored form
             of A.  D, E, DF, and EF will not be modified.  = 'N':  The matrix
             A will be copied to DF and EF and factored.



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DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))                                                          DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))



     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrices B and X.  NRHS >= 0.

     D       (input) DOUBLE PRECISION array, dimension (N)
             The n diagonal elements of the tridiagonal matrix A.

     E       (input) DOUBLE PRECISION array, dimension (N-1)
             The (n-1) subdiagonal elements of the tridiagonal matrix A.

     DF      (input or output) DOUBLE PRECISION array, dimension (N)
             If FACT = 'F', then DF is an input argument and on entry contains
             the n diagonal elements of the diagonal matrix D from the
             L*D*L**T factorization of A.  If FACT = 'N', then DF is an output
             argument and on exit contains the n diagonal elements of the
             diagonal matrix D from the L*D*L**T factorization of A.

     EF      (input or output) DOUBLE PRECISION array, dimension (N-1)
             If FACT = 'F', then EF is an input argument and on entry contains
             the (n-1) subdiagonal elements of the unit bidiagonal factor L
             from the L*D*L**T factorization of A.  If FACT = 'N', then EF is
             an output argument and on exit contains the (n-1) subdiagonal
             elements of the unit bidiagonal factor L from the L*D*L**T
             factorization of A.

     B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
             The N-by-NRHS right hand side matrix B.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
             If INFO = 0, the N-by-NRHS solution matrix X.

     LDX     (input) INTEGER
             The leading dimension of the array X.  LDX >= max(1,N).

     RCOND   (output) DOUBLE PRECISION
             The reciprocal condition number of the matrix A.  If RCOND is
             less than the machine precision (in particular, if RCOND = 0),
             the matrix is singular to working precision.  This condition is
             indicated by a return code of INFO > 0, and the solution and
             error bounds are not computed.

     FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
             The forward error bound for each solution vector X(j) (the j-th
             column of the solution matrix X).  If XTRUE is the true solution
             corresponding to X(j), FERR(j) is an estimated upper bound for
             the magnitude of the largest element in (X(j) - XTRUE) divided by



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DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))                                                          DDDDPPPPTTTTSSSSVVVVXXXX((((3333FFFF))))



             the magnitude of the largest element in X(j).

     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
             The componentwise relative backward error of each solution vector
             X(j) (i.e., the smallest relative change in any element of A or B
             that makes X(j) an exact solution).

     WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, and i is <= N  the leading minor of order i of
             A is not positive definite, so the factorization could not be
             completed unless i = N, and the solution and error bounds could
             not be computed.  = N+1 RCOND is less than machine precision.
             The factorization has been completed, but the matrix is singular
             to working precision, and the solution and error bounds have not
             been computed.




































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