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chbtrd (3)
  • >> chbtrd (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         chbtrd - reduce a complex Hermitian band matrix  A  to  real
         symmetric   tridiagonal  form  T  by  a  unitary  similarity
         transformation
    
    SYNOPSIS
         SUBROUTINE CHBTRD( VECT, UPLO, N, KD, AB,  LDAB,  D,  E,  Q,
                   LDQ, WORK, INFO )
    
         CHARACTER UPLO, VECT
    
         INTEGER INFO, KD, LDAB, LDQ, N
    
         REAL D( * ), E( * )
    
         COMPLEX AB( LDAB, * ), Q( LDQ, * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void chbtrd(char vect, char uplo, int  n,  int  kd,  complex
                   *cab,  int  ldab,  float *d, float *e, complex *q,
                   int ldq, int *info) ;
    
    PURPOSE
         CHBTRD reduces a complex Hermitian band  matrix  A  to  real
         symmetric   tridiagonal  form  T  by  a  unitary  similarity
         transformation:  Q**H * A * Q = T.
    
    
    ARGUMENTS
         VECT      (input) CHARACTER*1
                   = 'N':  do not form Q;
                   = 'V':  form Q;
                   = 'U':  update a matrix X, by forming X*Q.
    
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         KD        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KD >= 0.
    
         AB        (input/output) COMPLEX array, dimension (LDAB,N)
                   On entry, the upper or lower triangle of the  Her-
                   mitian  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, the diagonal ele-
                   ments  of  AB are overwritten by the diagonal ele-
                   ments of the tridiagonal matrix T; if KD > 0,  the
                   elements  on  the  first  superdiagonal (if UPLO =
                   'U') or the first subdiagonal (if UPLO = 'L')  are
                   overwritten  by the offdiagonal elements of T; the
                   rest of AB is overwritten by values generated dur-
                   ing the reduction.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KD+1.
    
         D         (output) REAL array, dimension (N)
                   The diagonal elements of the tridiagonal matrix T.
    
         E         (output) REAL array, dimension (N-1)
                   The  off-diagonal  elements  of  the   tridiagonal
                   matrix  T:   E(i) = T(i,i+1) if UPLO = 'U'; E(i) =
                   T(i+1,i) if UPLO = 'L'.
    
         Q         (input/output) COMPLEX array, dimension (LDQ,N)
                   On entry, if VECT = 'U', then Q  must  contain  an
                   N-by-N matrix X; if VECT = 'N' or 'V', then Q need
                   not be set.
    
                   On exit:  if VECT = 'V',  Q  contains  the  N-by-N
                   unitary  matrix  Q;  if VECT = 'U', Q contains the
                   product X*Q; if VECT = 'N', the  array  Q  is  not
                   referenced.
    
         LDQ       (input) INTEGER
                   The leading dimension of the array Q.  LDQ  >=  1,
                   and LDQ >= N if VECT = 'V' or 'U'.
    
         WORK      (workspace) COMPLEX array, dimension (N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
    
    
    
    


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