.TH "hpgst" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hpgst \- {hp,sp}gst: reduction to standard form, packed
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchpgst\fP (itype, uplo, n, ap, bp, info)"
.br
.RI "\fBCHPGST\fP "
.ti -1c
.RI "subroutine \fBdspgst\fP (itype, uplo, n, ap, bp, info)"
.br
.RI "\fBDSPGST\fP "
.ti -1c
.RI "subroutine \fBsspgst\fP (itype, uplo, n, ap, bp, info)"
.br
.RI "\fBSSPGST\fP "
.ti -1c
.RI "subroutine \fBzhpgst\fP (itype, uplo, n, ap, bp, info)"
.br
.RI "\fBZHPGST\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chpgst (integer itype, character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) bp, integer info)"

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

.PP
.nf
!>
!> CHPGST reduces a complex Hermitian-definite generalized
!> eigenproblem to standard form, using packed storage\&.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L\&.
!>
!> B must have been previously factorized as U**H*U or L*L**H by CPPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
!>          ITYPE is INTEGER
!>          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
!>          = 2 or 3: compute U*A*U**H or L**H*A*L\&.
!> 
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored and B is factored as
!>                  U**H*U;
!>          = 'L':  Lower triangle of A is stored and B is factored as
!>                  L*L**H\&.
!> 
.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)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A\&.
!> 
.fi
.PP
.br
\fIBP\fP 
.PP
.nf
!>          BP is COMPLEX array, dimension (N*(N+1)/2)
!>          The triangular factor from the Cholesky factorization of B,
!>          stored in the same format as A, as returned by CPPTRF\&.
!> 
.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
!> 
.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 \fB112\fP of file \fBchpgst\&.f\fP\&.
.SS "subroutine dspgst (integer itype, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) bp, integer info)"

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

.PP
.nf
!>
!> DSPGST reduces a real symmetric-definite generalized eigenproblem
!> to standard form, using packed storage\&.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L\&.
!>
!> B must have been previously factorized as U**T*U or L*L**T by DPPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
!>          ITYPE is INTEGER
!>          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
!>          = 2 or 3: compute U*A*U**T or L**T*A*L\&.
!> 
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored and B is factored as
!>                  U**T*U;
!>          = 'L':  Lower triangle of A is stored and B is factored as
!>                  L*L**T\&.
!> 
.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 DOUBLE PRECISION 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)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A\&.
!> 
.fi
.PP
.br
\fIBP\fP 
.PP
.nf
!>          BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The triangular factor from the Cholesky factorization of B,
!>          stored in the same format as A, as returned by DPPTRF\&.
!> 
.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
!> 
.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 \fB112\fP of file \fBdspgst\&.f\fP\&.
.SS "subroutine sspgst (integer itype, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) bp, integer info)"

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

.PP
.nf
!>
!> SSPGST reduces a real symmetric-definite generalized eigenproblem
!> to standard form, using packed storage\&.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L\&.
!>
!> B must have been previously factorized as U**T*U or L*L**T by SPPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
!>          ITYPE is INTEGER
!>          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
!>          = 2 or 3: compute U*A*U**T or L**T*A*L\&.
!> 
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored and B is factored as
!>                  U**T*U;
!>          = 'L':  Lower triangle of A is stored and B is factored as
!>                  L*L**T\&.
!> 
.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 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)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A\&.
!> 
.fi
.PP
.br
\fIBP\fP 
.PP
.nf
!>          BP is REAL array, dimension (N*(N+1)/2)
!>          The triangular factor from the Cholesky factorization of B,
!>          stored in the same format as A, as returned by SPPTRF\&.
!> 
.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
!> 
.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 \fB112\fP of file \fBsspgst\&.f\fP\&.
.SS "subroutine zhpgst (integer itype, character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, integer info)"

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

.PP
.nf
!>
!> ZHPGST reduces a complex Hermitian-definite generalized
!> eigenproblem to standard form, using packed storage\&.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L\&.
!>
!> B must have been previously factorized as U**H*U or L*L**H by ZPPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
!>          ITYPE is INTEGER
!>          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
!>          = 2 or 3: compute U*A*U**H or L**H*A*L\&.
!> 
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored and B is factored as
!>                  U**H*U;
!>          = 'L':  Lower triangle of A is stored and B is factored as
!>                  L*L**H\&.
!> 
.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*16 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)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A\&.
!> 
.fi
.PP
.br
\fIBP\fP 
.PP
.nf
!>          BP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The triangular factor from the Cholesky factorization of B,
!>          stored in the same format as A, as returned by ZPPTRF\&.
!> 
.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
!> 
.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 \fB112\fP of file \fBzhpgst\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.