SLANGB  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the element of  largest absolute value  of an


 n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.

    SLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'


             (


             ( norm1(A),         NORM = '1', 'O' or 'o'


             (


             ( normI(A),         NORM = 'I' or 'i'


             (


             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'


 where  norm1  denotes the  one norm of a matrix (maximum column sum),


 normI  denotes the  infinity norm  of a matrix  (maximum row sum) and


 normF  denotes the  Frobenius norm of a matrix (square root of sum of


 squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.

          NORM is CHARACTER*1


          Specifies the value to be returned in SLANGB as described


          above.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, SLANGB is


          set to zero.

KL

          KL is INTEGER


          The number of sub-diagonals of the matrix A.  KL >= 0.

KU

          KU is INTEGER


          The number of super-diagonals of the matrix A.  KU >= 0.

AB

          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


          follows:


          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

          LDAB is INTEGER


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

WORK

          WORK is REAL array, dimension (MAX(1,LWORK)),


          where LWORK >= N when NORM = 'I'; otherwise, WORK is not


          referenced.

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Univ. of Colorado Denver

NAG Ltd.

 SLAQGB equilibrates a general M by N band matrix A with KL


 subdiagonals and KU superdiagonals using the row and scaling factors


 in the vectors R and C.

          M is INTEGER


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

N

          N is INTEGER


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

KL

          KL is INTEGER


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

KU

          KU is INTEGER


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

AB

          AB is REAL array, dimension (LDAB,N)


          On entry, the matrix A in band storage, 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)


          On exit, the equilibrated matrix, in the same storage format


          as A.  See EQUED for the form of the equilibrated matrix.

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDA >= KL+KU+1.

R

          R is REAL array, dimension (M)


          The row scale factors for A.

C

          C is REAL array, dimension (N)


          The column scale factors for A.

ROWCND

          ROWCND is REAL


          Ratio of the smallest R(i) to the largest R(i).

COLCND

          COLCND is REAL


          Ratio of the smallest C(i) to the largest C(i).

AMAX

          AMAX is REAL


          Absolute value of largest matrix entry.

EQUED

          EQUED is CHARACTER*1


          Specifies the form of equilibration that was done.


          = 'N':  No equilibration


          = 'R':  Row equilibration, i.e., A has been premultiplied by


                  diag(R).


          = 'C':  Column equilibration, i.e., A has been postmultiplied


                  by diag(C).


          = 'B':  Both row and column equilibration, i.e., A has been


                  replaced by diag(R) * A * diag(C).

  THRESH is a threshold value used to decide if row or column scaling


  should be done based on the ratio of the row or column scaling


  factors.  If ROWCND < THRESH, row scaling is done, and if


  COLCND < THRESH, column scaling is done.


  LARGE and SMALL are threshold values used to decide if row scaling


  should be done based on the absolute size of the largest matrix


  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.