spbequ(l) [redhat man page]

SPBEQU(l)								 )								 SPBEQU(l)

NAME

       SPBEQU  - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition num-
       ber (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE SPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  AMAX, SCOND

	   REAL 	  AB( LDAB, * ), S( * )

PURPOSE

       SPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number
       (with  respect  to  the	two-norm).  S  contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements
       B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the condition number of B within a factor N of the smallest pos-
       sible condition number over all possible diagonal scalings.

ARGUMENTS

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

       AB      (input) REAL 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 A.  LDAB >= KD+1.

       S       (output) REAL array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) REAL
	       If  INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i).  If SCOND >= 0.1 and AMAX is neither too large nor too
	       small, it is not worth scaling by S.

       AMAX    (output) REAL
	       Absolute value of largest matrix element.  If AMAX is very close to overflow or very close  to  underflow,  the	matrix	should	be
	       scaled.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  if INFO = i, the i-th diagonal element is nonpositive.

LAPACK version 3.0						   15 June 2000 							 SPBEQU(l)

ZPBEQU(l)								 )								 ZPBEQU(l)

NAME

       ZPBEQU  - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition num-
       ber (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION S( * )

	   COMPLEX*16	  AB( LDAB, * )

PURPOSE

       ZPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number
       (with  respect  to  the	two-norm).  S  contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements
       B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the condition number of B within a factor N of the smallest pos-
       sible condition number over all possible diagonal scalings.

ARGUMENTS

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

       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
	       The  upper  or  lower triangle of the Hermitian 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 A.  LDAB >= KD+1.

       S       (output) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) DOUBLE PRECISION
	       If  INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i).  If SCOND >= 0.1 and AMAX is neither too large nor too
	       small, it is not worth scaling by S.

       AMAX    (output) DOUBLE PRECISION
	       Absolute value of largest matrix element.  If AMAX is very close to overflow or very close  to  underflow,  the	matrix	should	be
	       scaled.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  if INFO = i, the i-th diagonal element is nonpositive.

LAPACK version 3.0						   15 June 2000 							 ZPBEQU(l)