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spbequ.f(3)				      LAPACK				      spbequ.f(3)

       spbequ.f -

       subroutine spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)

Function/Subroutine Documentation
   subroutine spbequ (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB,
       integerLDAB, real, dimension( * )S, realSCOND, realAMAX, integerINFO)


	    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 possible condition number over all possible diagonal


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


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


		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.


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


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


		     SCOND is 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 is 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 is 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.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Definition at line 130 of file spbequ.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      spbequ.f(3)
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