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sspgv (3)
  • >> sspgv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sspgv - compute all the  eigenvalues  and,  optionally,  the
         eigenvectors of a real generalized symmetric-definite eigen-
         problem, of the form A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or
         B*A*x=(lambda)*x
    
    SYNOPSIS
         SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W,  Z,  LDZ,
                   WORK, INFO )
    
         CHARACTER JOBZ, UPLO
    
         INTEGER INFO, ITYPE, LDZ, N
    
         REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )
    
    
    
         #include <sunperf.h>
    
         void sspgv(int itype, char jobz, char  uplo,  int  n,  float
                   *sap, float *bp, float *w, float *sz, int ldz, int
                   *info) ;
    
    PURPOSE
         SSPGV computes all  the  eigenvalues  and,  optionally,  the
         eigenvectors of a real generalized symmetric-definite eigen-
         problem, of the form A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or
         B*A*x=(lambda)*x.  Here A and B are assumed to be symmetric,
         stored in packed format, and B is also positive definite.
    
    
    ARGUMENTS
         ITYPE     (input) INTEGER
                   Specifies the problem type to be solved:
                   = 1:  A*x = (lambda)*B*x
                   = 2:  A*B*x = (lambda)*x
                   = 3:  B*A*x = (lambda)*x
    
         JOBZ      (input) CHARACTER*1
                   = 'N':  Compute eigenvalues only;
                   = 'V':  Compute eigenvalues and eigenvectors.
    
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangles of A and B are stored;
                   = 'L':  Lower triangles of A and B are stored.
    
         N         (input) INTEGER
                   The order of the matrices A and B.  N >= 0.
    
         AP        (input/output) REAL array, dimension
                   (N*(N+1)/2) On entry, the upper or lower  triangle
                   of  the symmetric matrix A, packed columnwise in a
                   linear array.  The j-th column of A is  stored  in
                   the  array  AP  as follows:  if UPLO = 'U', AP(i +
                   (j-1)*j/2) = A(i,j) for 1<=i<=j; if  UPLO  =  'L',
                   AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    
                   On exit, the contents of AP are destroyed.
    
         BP        (input/output) REAL array, dimension (N*(N+1)/2)
                   On entry, the upper or lower triangle of the  sym-
                   metric  matrix  B,  packed  columnwise in a linear
                   array.  The j-th column of  B  is  stored  in  the
                   array  BP  as  follows:  if UPLO = 'U', BP(i + (j-
                   1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L',  BP(i
                   + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
    
                   On exit, the triangular factor U  or  L  from  the
                   Cholesky  factorization  B = U**T*U or B = L*L**T,
                   in the same storage format as B.
    
         W         (output) REAL array, dimension (N)
                   If INFO = 0, the eigenvalues in ascending order.
    
         Z         (output) REAL array, dimension (LDZ, N)
                   If JOBZ = 'V', then if INFO = 0,  Z  contains  the
                   matrix  Z  of  eigenvectors.  The eigenvectors are
                   normalized  as  follows:   if  ITYPE  =  1  or  2,
                   Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I.  If
                   JOBZ = 'N', then Z is not referenced.
    
         LDZ       (input) INTEGER
                   The leading dimension of the array Z.  LDZ  >=  1,
                   and if JOBZ = 'V', LDZ >= max(1,N).
    
         WORK      (workspace) REAL array, dimension (3*N)
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  SPPTRF or SSPEV returned an error code:
                   <= N:  if INFO = i, SSPEV failed  to  converge;  i
                   off-diagonal elements of an intermediate tridiago-
                   nal form did not converge to zero.  > N:   if INFO
                   =  n  + i, for 1 <= i <= n, then the leading minor
                   of order i of B is  not  positive  definite.   The
                   factorization  of  B could not be completed and no
                   eigenvalues or eigenvectors were computed.
    
    
    
    


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