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sgbequ (3)
  • >> sgbequ (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgbequ - compute row and column scalings intended to equili-
         brate  an  M-by-N  band  matrix  A  and reduce its condition
         number
    
    SYNOPSIS
         SUBROUTINE SGBEQU( M, N, KL, KU, AB,  LDAB,  R,  C,  ROWCND,
                   COLCND, AMAX, INFO )
    
         INTEGER INFO, KL, KU, LDAB, M, N
    
         REAL AMAX, COLCND, ROWCND
    
         REAL AB( LDAB, * ), C( * ), R( * )
    
    
    
         #include <sunperf.h>
    
         void sgbequ(int m, int n, int kl, int ku,  float  *sab,  int
                   ldab,  float  *r,  float *sc, float *rowcnd, float
                   *colcnd, float *amax, int *info);
    
    PURPOSE
         SGBEQU computes row and column scalings intended to  equili-
         brate  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.
    
    
    ARGUMENTS
         M         (input) INTEGER
                   The number of rows of the matrix A.  M >= 0.
    
         N         (input) INTEGER
                   The number of columns of the matrix A.  N >= 0.
    
         KL        (input) INTEGER
                   The number of subdiagonals within the band  of  A.
                   KL >= 0.
    
         KU        (input) INTEGER
                   The number of superdiagonals within the band of A.
                   KU >= 0.
    
         AB        (input) 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  follows:   AB(ku+1+i-j,j)  =
                   A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KL+KU+1.
    
         R         (output) REAL array, dimension (M)
                   If INFO = 0, or INFO > M, R contains the row scale
                   factors for A.
    
         C         (output) REAL array, dimension (N)
                   If INFO = 0, C contains the column  scale  factors
                   for A.
    
         ROWCND    (output) 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    (output) 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      (output) REAL
                   Absolute value of largest matrix element.  If AMAX
                   is  very close to overflow or very close to under-
                   flow, the matrix should be scaled.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal 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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