dlaqsb(l) [redhat man page]

DLAQSB(l)								 )								 DLAQSB(l)

NAME

       DLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S

SYNOPSIS

       SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

	   CHARACTER	  EQUED, UPLO

	   INTEGER	  KD, LDAB, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION AB( LDAB, * ), S( * )

PURPOSE

       DLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.  = 'U':  Upper triangular
	       = 'L':  Lower triangular

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

       KD      (input) INTEGER
	       The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
	       On  entry, 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).

	       On  exit,  if  INFO = 0, the triangular factor U or L from the Cholesky factorization A = U'*U or A = L*L' of the band matrix A, in
	       the same storage format as A.

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

       S       (output) DOUBLE PRECISION array, dimension (N)
	       The scale factors for A.

       SCOND   (input) DOUBLE PRECISION
	       Ratio of the smallest S(i) to the largest S(i).

       AMAX    (input) DOUBLE PRECISION
	       Absolute value of largest matrix entry.

       EQUED   (output) CHARACTER*1
	       Specifies whether or not equilibration was done.  = 'N':  No equilibration.
	       = 'Y':  Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

PARAMETERS

       THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors.	If SCOND < THRESH, scaling
       is done.

       LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element.	If
       AMAX > LARGE or AMAX < SMALL, scaling is done.

LAPACK version 3.0						   15 June 2000 							 DLAQSB(l)

dlaqsb.f(3)							      LAPACK							       dlaqsb.f(3)

NAME

       dlaqsb.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
	   DLAQSB

Function/Subroutine Documentation
   subroutine dlaqsb (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( *
       )S, double precisionSCOND, double precisionAMAX, characterEQUED)
       DLAQSB

       Purpose:

	    DLAQSB equilibrates a symmetric band matrix A using the scaling
	    factors in the vector S.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     symmetric matrix A is stored.
		     = 'U':  Upper triangular
		     = 'L':  Lower triangular

	   N

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

	   KD

		     KD is INTEGER
		     The number of super-diagonals of the matrix A if UPLO = 'U',
		     or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

	   AB

		     AB is DOUBLE PRECISION array, dimension (LDAB,N)
		     On entry, 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).

		     On exit, if INFO = 0, the triangular factor U or L from the
		     Cholesky factorization A = U**T*U or A = L*L**T of the band
		     matrix A, in the same storage format as A.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   S

		     S is DOUBLE PRECISION array, dimension (N)
		     The scale factors for A.

	   SCOND

		     SCOND is DOUBLE PRECISION
		     Ratio of the smallest S(i) to the largest S(i).

	   AMAX

		     AMAX is DOUBLE PRECISION
		     Absolute value of largest matrix entry.

	   EQUED

		     EQUED is CHARACTER*1
		     Specifies whether or not equilibration was done.
		     = 'N':  No equilibration.
		     = 'Y':  Equilibration was done, i.e., A has been replaced by
			     diag(S) * A * diag(S).

       Internal Parameters:

	     THRESH is a threshold value used to decide if scaling should be done
	     based on the ratio of the scaling factors.  If SCOND < THRESH,
	     scaling is done.

	     LARGE and SMALL are threshold values used to decide if scaling should
	     be done based on the absolute size of the largest matrix element.
	     If AMAX > LARGE or AMAX < SMALL, scaling is done.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 141 of file dlaqsb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       dlaqsb.f(3)