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zpbtf2 (3)
  • >> zpbtf2 (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zpbtf2 - compute the Cholesky  factorization  of  a  complex
         Hermitian positive definite band matrix A
    
    SYNOPSIS
         SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, N
    
         COMPLEX*16 AB( LDAB, * )
    
    
    
         #include <sunperf.h>
    
         void zpbtf2(char uplo, int n, int  kd,  doublecomplex  *zab,
                   int ldab, int *info) ;
    
    PURPOSE
         ZPBTF2 computes the Cholesky factorization of a complex Her-
         mitian positive definite band matrix A.
    
         The factorization has the form
            A = U' * U ,  if UPLO = 'U', or
            A = L  * L',  if UPLO = 'L',
         where U is an upper triangular matrix, U' is  the  conjugate
         transpose of U, and L is lower triangular.
    
         This is the unblocked  version  of  the  algorithm,  calling
         Level 2 BLAS.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   Specifies whether the upper  or  lower  triangular
                   part of the Hermitian matrix A is stored:
                   = 'U':  Upper triangular
                   = 'L':  Lower triangular
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KD        (input) INTEGER
                   The number of super-diagonals of the matrix  A  if
                   UPLO = 'U', or the number of sub-diagonals if UPLO
                   = 'L'.  KD >= 0.
    
         AB        (input/output)   COMPLEX*16    array,    dimension
                   (LDAB,N)
                   On entry, the  upper  or  lower  triangle  of  the
                   Hermitian  band matrix A, stored in the first KD+1
                   rows of the array.  The j-th column of A is stored
                   in the j-th column of the array AB as follows:  if
                   UPLO = 'U', AB(kd+1+i-j,j) = A(i,j)  for  max(1,j-
                   kd)<=i<=j;  if UPLO = 'L', AB(1+i-j,j)    = A(i,j)
                   for j<=i<=min(n,j+kd).
    
                   On exit, if INFO = 0, the triangular factor U or L
                   from  the  Cholesky  factorization A = U'*U or A =
                   L*L' of the band matrix A,  in  the  same  storage
                   format as A.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KD+1.
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -k, the k-th argument had an  ille-
                   gal value
                   > 0: if INFO = k, the leading minor of order k  is
                   not positive definite, and the factorization could
                   not be completed.
    
    FURTHER DETAILS
         The band storage scheme  is  illustrated  by  the  following
         example, when N = 6, KD = 2, and UPLO = 'U':
    
         On entry:                       On exit:
    
             *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
             *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
            a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    
         Similarly, if UPLO = 'L' the format of A is as follows:
    
         On entry:                       On exit:
    
            a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
            a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
            a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    
         Array elements marked * are not used by the routine.
    
    
    
    


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