sgbequ.f - Man Page



subroutine sgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)

Function/Subroutine Documentation

subroutine sgbequ (integer M, integer N, integer KL, integer KU, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) R, real, dimension( * ) C, real ROWCND, real COLCND, real AMAX, integer INFO)



 SGBEQU computes row and column scalings intended to equilibrate an
 M-by-N band matrix A and reduce its condition number.  R returns the
 row scale factors and C the column scale factors, chosen to try to
 make the largest element in each row and column of the matrix B with
 elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

 R(i) and C(j) are restricted to be between SMLNUM = smallest safe
 number and BIGNUM = largest safe number.  Use of these scaling
 factors is not guaranteed to reduce the condition number of A but
 works well in practice.


          M is INTEGER
          The number of rows of the matrix A.  M >= 0.


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


          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.


          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.


          AB is REAL array, dimension (LDAB,N)
          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
          column of A is stored in the j-th column of the array AB as
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).


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


          R is REAL array, dimension (M)
          If INFO = 0, or INFO > M, R contains the row scale factors
          for A.


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


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


          COLCND is REAL
          If INFO = 0, COLCND contains the ratio of the smallest
          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
          worth scaling by C.


          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, and i is
                <= M:  the i-th row of A is exactly zero
                >  M:  the (i-M)-th column of A is exactly zero

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December 2016

Definition at line 155 of file sgbequ.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page sgbequ(3) is an alias of sgbequ.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK