LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
DOUBLE PRECISION function  dlangb (NORM, N, KL, KU, AB, LDAB, WORK) 
DLANGB returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of general band matrix.  
subroutine  dlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) 
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 
This is the group of double auxiliary functions for GB matrices
DOUBLE PRECISION function dlangb  (  character  NORM, 
integer  N,  
integer  KL,  
integer  KU,  
double precision, dimension( ldab, * )  AB,  
integer  LDAB,  
double precision, dimension( * )  WORK  
) 
DLANGB returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of general band matrix.
Download DLANGB + dependencies [TGZ] [ZIP] [TXT]DLANGB 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 subdiagonals and ku superdiagonals.
DLANGB = ( 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.
[in]  NORM  NORM is CHARACTER*1 Specifies the value to be returned in DLANGB as described above. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero. 
[in]  KL  KL is INTEGER The number of subdiagonals of the matrix A. KL >= 0. 
[in]  KU  KU is INTEGER The number of superdiagonals of the matrix A. KU >= 0. 
[in]  AB  AB is DOUBLE PRECISION array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=i<=min(n,j+kl). 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. 
Definition at line 124 of file dlangb.f.
subroutine dlaqgb  (  integer  M, 
integer  N,  
integer  KL,  
integer  KU,  
double precision, dimension( ldab, * )  AB,  
integer  LDAB,  
double precision, dimension( * )  R,  
double precision, dimension( * )  C,  
double precision  ROWCND,  
double precision  COLCND,  
double precision  AMAX,  
character  EQUED  
) 
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
Download DLAQGB + dependencies [TGZ] [ZIP] [TXT]DLAQGB 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.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in]  KL  KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. 
[in]  KU  KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. 
[in,out]  AB  AB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=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. 
[in]  LDAB  LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1. 
[in]  R  R is DOUBLE PRECISION array, dimension (M) The row scale factors for A. 
[in]  C  C is DOUBLE PRECISION array, dimension (N) The column scale factors for A. 
[in]  ROWCND  ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i). 
[in]  COLCND  COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i). 
[in]  AMAX  AMAX is DOUBLE PRECISION Absolute value of largest matrix entry. 
[out]  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.
Definition at line 159 of file dlaqgb.f.