.TH "SRC/chpgv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/chpgv.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBchpgv\fP (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)"
.br
.RI "\fBCHPGV\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine chpgv (integer itype, character jobz, character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) bp, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)"

.PP
\fBCHPGV\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CHPGV computes all the eigenvalues and, optionally, the eigenvectors
 of a complex generalized Hermitian-definite eigenproblem, 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 Hermitian, stored in packed format,
 and B is also positive definite\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
          ITYPE is 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
.fi
.PP
.br
\fIJOBZ\fP 
.PP
.nf
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrices A and B\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangle of the Hermitian 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\&.
.fi
.PP
.br
\fIBP\fP 
.PP
.nf
          BP is COMPLEX array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, in the same storage
          format as B\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is COMPLEX 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**H*B*Z = I;
          if ITYPE = 3, Z**H*inv(B)*Z = I\&.
          If JOBZ = 'N', then Z is not referenced\&.
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
          LDZ is INTEGER
          The leading dimension of the array Z\&.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (max(1, 2*N-1))
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (max(1, 3*N-2))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  CPPTRF or CHPEV returned an error code:
             <= N:  if INFO = i, CHPEV failed to converge;
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not convergeto zero;
             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
                    principal minor of order i of B is not positive\&.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB163\fP of file \fBchpgv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.