dpbrfs man page on Scientific

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DPBRFS(1)		 LAPACK routine (version 3.2)		     DPBRFS(1)

NAME
       DPBRFS - improves the computed solution to a system of linear equations
       when the coefficient matrix is symmetric positive definite and  banded,
       and provides error bounds and backward error estimates for the solution

SYNOPSIS
       SUBROUTINE DPBRFS( UPLO,	 N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X,
			  LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, LDAFB, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB,  *
			  ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE
       DPBRFS  improves	 the computed solution to a system of linear equations
       when the coefficient matrix is symmetric positive definite and  banded,
       and  provides  error  bounds and backward error estimates for the solu‐
       tion.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

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

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U',  or
	       the number of subdiagonals if UPLO = 'L'.  KD >= 0.

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

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
	       The upper or lower triangle of the  symmetric  band  matrix  A,
	       stored in the first KD+1 rows of the array.  The j-th column of
	       A is stored in the j-th column of the array AB as  follows:  if
	       UPLO  =	'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if
	       UPLO = 'L', AB(1+i-j,j)	  = A(i,j) for j<=i<=min(n,j+kd).

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)
	       The triangular factor U or L from the Cholesky factorization  A
	       = U**T*U or A = L*L**T of the band matrix A as computed by DPB‐
	       TRF, in the same storage format as A (see AB).

       LDAFB   (input) INTEGER
	       The leading dimension of the array AFB.	LDAFB >= KD+1.

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

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

       X       (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as  computed  by  DPBTRS.   On
	       exit, the improved solution matrix X.

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

       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The estimated 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).
	       The estimate is as reliable as the estimate for RCOND,  and  is
	       almost always a slight overestimate of the true error.

       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor 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 (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.

 LAPACK routine (version 3.2)	 November 2008			     DPBRFS(1)
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