dgbsvx man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



DGBSVX(3F)							    DGBSVX(3F)

NAME
     DGBSVX - use the LU factorization to compute the solution to a real
     system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

SYNOPSIS
     SUBROUTINE DGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
			IPIV, EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
			WORK, IWORK, INFO )

	 CHARACTER	EQUED, FACT, TRANS

	 INTEGER	INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS

	 DOUBLE		PRECISION RCOND

	 INTEGER	IPIV( * ), IWORK( * )

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

PURPOSE
     DGBSVX uses the LU factorization to compute the solution to a real system
     of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is
     a band matrix of order N with KL subdiagonals and KU superdiagonals, and
     X and B are N-by-NRHS matrices.

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

DESCRIPTION
     The following steps are performed by this subroutine:

     1. If FACT = 'E', real scaling factors are computed to equilibrate
	the system:
	   TRANS = 'N':	 diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B
	   TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
	   TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
	Whether or not the system will be equilibrated depends on the
	scaling of the matrix A, but if equilibration is used, A is
	overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
	or diag(C)*B (if TRANS = 'T' or 'C').

     2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
	matrix A (after equilibration if FACT = 'E') as
	   A = L * U,
	where L is a product of permutation and unit lower triangular
	matrices with KL subdiagonals, and U is upper triangular with
	KL+KU superdiagonals.

     3. The factored form of A is used to estimate the condition number
	of the matrix A.  If the reciprocal of the condition number is

									Page 1

DGBSVX(3F)							    DGBSVX(3F)

	less than machine precision, steps 4-6 are skipped.

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

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

     6. If equilibration was used, the matrix X is premultiplied by
	diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
	that it solves the original system before equilibration.

ARGUMENTS
     FACT    (input) CHARACTER*1
	     Specifies whether or not the factored form of the matrix A is
	     supplied on entry, and if not, whether the matrix A should be
	     equilibrated before it is factored.  = 'F':  On entry, AFB and
	     IPIV contain the factored form of A.  If EQUED is not 'N', the
	     matrix A has been equilibrated with scaling factors given by R
	     and C.  AB, AFB, and IPIV are not modified.  = 'N':  The matrix A
	     will be copied to AFB and factored.
	     = 'E':  The matrix A will be equilibrated if necessary, then
	     copied to AFB and factored.

     TRANS   (input) CHARACTER*1
	     Specifies the form of the system of equations.  = 'N':  A * X = B
	     (No transpose)
	     = 'T':  A**T * X = B  (Transpose)
	     = 'C':  A**H * X = B  (Transpose)

     N	     (input) INTEGER
	     The number of linear equations, i.e., the order of the matrix A.
	     N >= 0.

     KL	     (input) INTEGER
	     The number of subdiagonals within the band of A.  KL >= 0.

     KU	     (input) INTEGER
	     The number of superdiagonals within the band of A.	 KU >= 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/output) DOUBLE PRECISION array, dimension (LDAB,N)
	     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
	     The j-th column of A is stored in the j-th column of the array AB
	     as follows:  AB(KU+1+i-j,j) = A(i,j) for max(1,j-
	     KU)<=i<=min(N,j+kl)

									Page 2

DGBSVX(3F)							    DGBSVX(3F)

	     If FACT = 'F' and EQUED is not 'N', then A must have been
	     equilibrated by the scaling factors in R and/or C.	 AB is not
	     modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N'
	     on exit.

	     On exit, if EQUED .ne. 'N', A is scaled as follows:  EQUED = 'R':
	     A := diag(R) * A
	     EQUED = 'C':  A := A * diag(C)
	     EQUED = 'B':  A := diag(R) * A * diag(C).

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

     AFB     (input or output) DOUBLE PRECISION array, dimension (LDAFB,N)
	     If FACT = 'F', then AFB is an input argument and on entry
	     contains details of the LU factorization of the band matrix A, as
	     computed by DGBTRF.  U is stored as an upper triangular band
	     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
	     multipliers used during the factorization are stored in rows
	     KL+KU+2 to 2*KL+KU+1.  If EQUED .ne. 'N', then AFB is the
	     factored form of the equilibrated matrix A.

	     If FACT = 'N', then AFB is an output argument and on exit returns
	     details of the LU factorization of A.

	     If FACT = 'E', then AFB is an output argument and on exit returns
	     details of the LU factorization of the equilibrated matrix A (see
	     the description of AB for the form of the equilibrated matrix).

     LDAFB   (input) INTEGER
	     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

     IPIV    (input or output) INTEGER array, dimension (N)
	     If FACT = 'F', then IPIV is an input argument and on entry
	     contains the pivot indices from the factorization A = L*U as
	     computed by DGBTRF; row i of the matrix was interchanged with row
	     IPIV(i).

	     If FACT = 'N', then IPIV is an output argument and on exit
	     contains the pivot indices from the factorization A = L*U of the
	     original matrix A.

	     If FACT = 'E', then IPIV is an output argument and on exit
	     contains the pivot indices from the factorization A = L*U of the
	     equilibrated matrix A.

     EQUED   (input or output) CHARACTER*1
	     Specifies the form of equilibration that was done.	 = 'N':	 No
	     equilibration (always true if FACT = 'N').
	     = 'R':  Row equilibration, i.e., A has been premultiplied by
	     diag(R).  = 'C':  Column equilibration, i.e., A has been
	     postmultiplied by diag(C).	 = 'B':	 Both row and column

									Page 3

DGBSVX(3F)							    DGBSVX(3F)

	     equilibration, i.e., A has been replaced by diag(R) * A *
	     diag(C).  EQUED is an input argument if FACT = 'F'; otherwise, it
	     is an output argument.

     R	     (input or output) DOUBLE PRECISION array, dimension (N)
	     The row scale factors for A.  If EQUED = 'R' or 'B', A is
	     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R is
	     not accessed.  R is an input argument if FACT = 'F'; otherwise, R
	     is an output argument.  If FACT = 'F' and EQUED = 'R' or 'B',
	     each element of R must be positive.

     C	     (input or output) DOUBLE PRECISION array, dimension (N)
	     The column scale factors for A.  If EQUED = 'C' or 'B', A is
	     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C is
	     not accessed.  C is an input argument if FACT = 'F'; otherwise, C
	     is an output argument.  If FACT = 'F' and EQUED = 'C' or 'B',
	     each element of C must be positive.

     B	     (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	     On entry, the right hand side matrix B.  On exit, if EQUED = 'N',
	     B is not modified; if TRANS = 'N' and EQUED = 'R' or 'B', B is
	     overwritten by diag(R)*B; if TRANS = 'T' or 'C' and EQUED = 'C'
	     or 'B', B is overwritten by diag(C)*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 to the original
	     system of equations.  Note that A and B are modified on exit if
	     EQUED .ne. 'N', and the solution to the equilibrated system is
	     inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or or 'B'.

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

     RCOND   (output) DOUBLE PRECISION
	     The estimate of the reciprocal condition number of the matrix A
	     after equilibration (if done).  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 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.

									Page 4

DGBSVX(3F)							    DGBSVX(3F)

     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/output) DOUBLE PRECISION array, dimension (3*N)
	     On exit, WORK(1) contains the reciprocal pivot growth factor
	     norm(A)/norm(U). The "max absolute element" norm is used. If
	     WORK(1) is much less than 1, then the stability of the LU
	     factorization of the (equilibrated) matrix A could be poor. This
	     also means that the solution X, condition estimator RCOND, and
	     forward error bound FERR could be unreliable. If factorization
	     fails with 0<INFO<=N, then WORK(1) contains the reciprocal pivot
	     growth factor for the leading INFO columns of A.

     IWORK   (workspace) INTEGER array, dimension (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:  U(i,i) is exactly zero.  The factorization has been
	     completed, but the factor U is exactly singular, so 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 A is singular to working precision, and the
	     solution and error bounds have not been computed.

									Page 5

[top]

List of man pages available for IRIX

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net