dptsvx.f3

!>
!> 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.
!> 

!>
!> 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. If the leading principal minor of order i is not positive,
!>    then the routine returns with INFO = i. Otherwise, the factored
!>    form of A is used to estimate the condition number of the matrix
!>    A.  If the reciprocal of the condition number is less than machine
!>    precision, INFO = N+1 is returned as a warning, but the routine
!>    still goes on to solve for X and compute error bounds as
!>    described below.
!>
!> 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.
!> 

FACT

!>          FACT is 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.
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

NRHS

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

D

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

E

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

DF

!>          DF is 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

!>          EF is 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

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

LDB

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

X

!>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.
!> 

LDX

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

RCOND

!>          RCOND is 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.
!> 

FERR

!>          FERR is 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 the magnitude of the
!>          largest element in X(j).
!> 

BERR

!>          BERR is 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

!>          WORK is DOUBLE PRECISION array, dimension (2*N)
!> 

INFO

!>          INFO is 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 principal minor of order i of A
!>                       is not positive, so the factorization could not
!>                       be completed, and the solution has not been
!>                       computed. RCOND = 0 is returned.
!>                = N+1: U is nonsingular, but RCOND is less than machine
!>                       precision, meaning that the matrix is singular
!>                       to working precision.  Nevertheless, the
!>                       solution and error bounds are computed because
!>                       there are a number of situations where the
!>                       computed solution can be more accurate than the
!>                       value of RCOND would suggest.
!> 

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