LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Functions/Subroutines  
REAL function  clangb (NORM, N, KL, KU, AB, LDAB, WORK) 
CLANGB returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of general band matrix.  
subroutine  claqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) 
CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 
This is the group of complex auxiliary functions for GB matrices
REAL function clangb  (  character  NORM, 
integer  N,  
integer  KL,  
integer  KU,  
complex, dimension( ldab, * )  AB,  
integer  LDAB,  
real, dimension( * )  WORK  
) 
CLANGB returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of general band matrix.
Download CLANGB + dependencies [TGZ] [ZIP] [TXT]CLANGB 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.
CLANGB = ( 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 CLANGB as described above. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANGB 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 COMPLEX 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 REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. 
Definition at line 125 of file clangb.f.
subroutine claqgb  (  integer  M, 
integer  N,  
integer  KL,  
integer  KU,  
complex, dimension( ldab, * )  AB,  
integer  LDAB,  
real, dimension( * )  R,  
real, dimension( * )  C,  
real  ROWCND,  
real  COLCND,  
real  AMAX,  
character  EQUED  
) 
CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
Download CLAQGB + dependencies [TGZ] [ZIP] [TXT]CLAQGB 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 COMPLEX 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 REAL array, dimension (M) The row scale factors for A. 
[in]  C  C is REAL array, dimension (N) The column scale factors for A. 
[in]  ROWCND  ROWCND is REAL Ratio of the smallest R(i) to the largest R(i). 
[in]  COLCND  COLCND is REAL Ratio of the smallest C(i) to the largest C(i). 
[in]  AMAX  AMAX is REAL 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 160 of file claqgb.f.