claqsb(l) [redhat man page]

CLAQSB(l)								 )								 CLAQSB(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	  EQUED, UPLO

	   INTEGER	  KD, LDAB, N

	   REAL 	  AMAX, SCOND

	   REAL 	  S( * )

	   COMPLEX	  AB( LDAB, * )

PURPOSE

       CLAQSB 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) COMPLEX 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) REAL array, dimension (N)
	       The scale factors for A.

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

       AMAX    (input) REAL
	       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	       = 'Y':  Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 							 CLAQSB(l)

CLAQHB(l)								 )								 CLAQHB(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	  EQUED, UPLO

	   INTEGER	  KD, LDAB, N

	   REAL 	  AMAX, SCOND

	   REAL 	  S( * )

	   COMPLEX	  AB( LDAB, * )

PURPOSE

       CLAQHB 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) COMPLEX 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) REAL array, dimension (N)
	       The scale factors for A.

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

       AMAX    (input) REAL
	       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 							 CLAQHB(l)