*nix Documentation Project
·  Home
 +   man pages
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

  man pages->IRIX man pages -> complib/stbrfs (3)              
Title
Content
Arch
Section
 

Contents


STBRFS(3F)							    STBRFS(3F)


NAME    [Toc]    [Back]

     STBRFS - provide error bounds and backward	error estimates	for the
     solution to a system of linear equations with a triangular	band
     coefficient matrix

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	STBRFS(	UPLO, TRANS, DIAG, N, KD, NRHS,	AB, LDAB, B, LDB, X,
			LDX, FERR, BERR, WORK, IWORK, INFO )

	 CHARACTER	DIAG, TRANS, UPLO

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

	 INTEGER	IWORK( * )

	 REAL		AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ),
			WORK( *	), X( LDX, * )

PURPOSE    [Toc]    [Back]

     STBRFS provides error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular	band
     coefficient matrix.

     The solution matrix X must	be computed by STBTRS or some other means
     before entering this routine.  STBRFS does	not do iterative refinement
     because doing so cannot improve the backward error.

ARGUMENTS    [Toc]    [Back]

     UPLO    (input) CHARACTER*1
	     = 'U':  A is upper	triangular;
	     = 'L':  A is lower	triangular.

     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  (Conjugate transpose	= Transpose)

     DIAG    (input) CHARACTER*1
	     = 'N':  A is non-unit triangular;
	     = 'U':  A is unit triangular.

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

     KD	     (input) INTEGER
	     The number	of superdiagonals or subdiagonals of the triangular
	     band matrix A.  KD	>= 0.






									Page 1






STBRFS(3F)							    STBRFS(3F)



     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) REAL array, dimension (LDAB,N)
	     The upper or lower	triangular band	matrix A, stored in the	first
	     kd+1 rows of the array. The j-th column of	A is stored in the jth
	column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,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).  If DIAG =	'U', the diagonal
	     elements of A are not referenced and are assumed to be 1.

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

     B	     (input) REAL 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) REAL array, dimension (LDX,NRHS)
	     The solution matrix X.

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

     FERR    (output) REAL 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) REAL 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) REAL 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
STBRFS(3F)							    STBRFS(3F)


NAME    [Toc]    [Back]

     STBRFS - provide error bounds and backward	error estimates	for the
     solution to a system of linear equations with a triangular	band
     coefficient matrix

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	STBRFS(	UPLO, TRANS, DIAG, N, KD, NRHS,	AB, LDAB, B, LDB, X,
			LDX, FERR, BERR, WORK, IWORK, INFO )

	 CHARACTER	DIAG, TRANS, UPLO

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

	 INTEGER	IWORK( * )

	 REAL		AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ),
			WORK( *	), X( LDX, * )

PURPOSE    [Toc]    [Back]

     STBRFS provides error bounds and backward error estimates for the
     solution to a system of linear equations with a triangular	band
     coefficient matrix.

     The solution matrix X must	be computed by STBTRS or some other means
     before entering this routine.  STBRFS does	not do iterative refinement
     because doing so cannot improve the backward error.

ARGUMENTS    [Toc]    [Back]

     UPLO    (input) CHARACTER*1
	     = 'U':  A is upper	triangular;
	     = 'L':  A is lower	triangular.

     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  (Conjugate transpose	= Transpose)

     DIAG    (input) CHARACTER*1
	     = 'N':  A is non-unit triangular;
	     = 'U':  A is unit triangular.

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

     KD	     (input) INTEGER
	     The number	of superdiagonals or subdiagonals of the triangular
	     band matrix A.  KD	>= 0.






									Page 1






STBRFS(3F)							    STBRFS(3F)



     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) REAL array, dimension (LDAB,N)
	     The upper or lower	triangular band	matrix A, stored in the	first
	     kd+1 rows of the array. The j-th column of	A is stored in the jth
	column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,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).  If DIAG =	'U', the diagonal
	     elements of A are not referenced and are assumed to be 1.

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

     B	     (input) REAL 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) REAL array, dimension (LDX,NRHS)
	     The solution matrix X.

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

     FERR    (output) REAL 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) REAL 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) REAL 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


									PPPPaaaaggggeeee 2222
[ Back ]
 Similar pages
Name OS Title
zgerfs IRIX improve the computed solution to a system of linear equations and provides error bounds and backward error est
sgerfs IRIX improve the computed solution to a system of linear equations and provides error bounds and backward error est
dgerfs IRIX improve the computed solution to a system of linear equations and provides error bounds and backward error est
cgerfs IRIX improve the computed solution to a system of linear equations and provides error bounds and backward error est
zpprfs IRIX when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward
spbrfs IRIX when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward
dpbrfs IRIX when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward
cpprfs IRIX when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward
zpbrfs IRIX when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward
dpprfs IRIX when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward
Copyright © 2004-2005 DeniX Solutions SRL
newsletter delivery service