.TH "doublePTsolve" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
doublePTsolve \- double
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdptsv\fP (N, NRHS, D, E, B, LDB, INFO)"
.br
.RI "\fB DPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP "
.ti -1c
.RI "subroutine \fBdptsvx\fP (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, INFO)"
.br
.RI "\fB DPTSVX computes the solution to system of linear equations A * X = B for PT matrices\fP "
.in -1c
.SH "Detailed Description"
.PP 
This is the group of double solve driver functions for PT matrices 
.SH "Function Documentation"
.PP 
.SS "subroutine dptsv (integer N, integer NRHS, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)"

.PP
\fB DPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DPTSV computes the solution to a real system of linear equations
 A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
 matrix, and X and B are N-by-NRHS matrices\&.

 A is factored as A = L*D*L**T, and the factored form of A is then
 used to solve the system of equations\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
          The number of right hand sides, i\&.e\&., the number of columns
          of the matrix B\&.  NRHS >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix
          A\&.  On exit, the n diagonal elements of the diagonal matrix
          D from the factorization A = L*D*L**T\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix A\&.  On exit, the (n-1) subdiagonal elements of the
          unit bidiagonal factor L from the L*D*L**T factorization of
          A\&.  (E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**T*D*U factorization of A\&.)
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B\&.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
.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:  if INFO = i, the leading minor of order i is not
                positive definite, and the solution has not been
                computed\&.  The factorization has not been completed
                unless i = N\&.
.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

.SS "subroutine dptsvx (character FACT, integer N, integer NRHS, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( * ) DF, double precision, dimension( * ) EF, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision RCOND, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer INFO)"

.PP
\fB DPTSVX computes the solution to system of linear equations A * X = B for PT matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DPTSVX uses the factorization A = L*D*L**T to compute the solution
 to a real system of linear equations A*X = B, where A is an N-by-N
 symmetric positive definite tridiagonal matrix and X and B are
 N-by-NRHS matrices\&.

 Error bounds on the solution and a condition estimate are also
 provided\&.
.fi
.PP
 
.RE
.PP
\fBDescription:\fP
.RS 4

.PP
.nf
 The following steps are performed:

 1\&. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
    is a unit lower bidiagonal matrix and D is diagonal\&.  The
    factorization can also be regarded as having the form
    A = U**T*D*U\&.

 2\&. If the leading i-by-i principal minor is not positive definite,
    then the routine returns with INFO = i\&. Otherwise, the factored
    form of A is used to estimate the condition number of the matrix
    A\&.  If the reciprocal of the condition number is less than machine
    precision, INFO = N+1 is returned as a warning, but the routine
    still goes on to solve for X and compute error bounds as
    described below\&.

 3\&. The system of equations is solved for X using the factored form
    of A\&.

 4\&. Iterative refinement is applied to improve the computed solution
    matrix and calculate error bounds and backward error estimates
    for it\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIFACT\fP 
.PP
.nf
          FACT is CHARACTER*1
          Specifies whether or not the factored form of A has been
          supplied on entry\&.
          = 'F':  On entry, DF and EF contain the factored form of A\&.
                  D, E, DF, and EF will not be modified\&.
          = 'N':  The matrix A will be copied to DF and EF and
                  factored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
          The number of right hand sides, i\&.e\&., the number of columns
          of the matrices B and X\&.  NRHS >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A\&.
.fi
.PP
.br
\fIDF\fP 
.PP
.nf
          DF is DOUBLE PRECISION array, dimension (N)
          If FACT = 'F', then DF is an input argument and on entry
          contains the n diagonal elements of the diagonal matrix D
          from the L*D*L**T factorization of A\&.
          If FACT = 'N', then DF is an output argument and on exit
          contains the n diagonal elements of the diagonal matrix D
          from the L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIEF\fP 
.PP
.nf
          EF is DOUBLE PRECISION array, dimension (N-1)
          If FACT = 'F', then EF is an input argument and on entry
          contains the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the L*D*L**T factorization of A\&.
          If FACT = 'N', then EF is an output argument and on exit
          contains the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The N-by-NRHS right hand side matrix B\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
          If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X\&.
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
          LDX is INTEGER
          The leading dimension of the array X\&.  LDX >= max(1,N)\&.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          RCOND is DOUBLE PRECISION
          The reciprocal condition number of the matrix A\&.  If RCOND
          is less than the machine precision (in particular, if
          RCOND = 0), the matrix is singular to working precision\&.
          This condition is indicated by a return code of INFO > 0\&.
.fi
.PP
.br
\fIFERR\fP 
.PP
.nf
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X)\&.
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j)\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i\&.e\&., the smallest relative change in any
          element of A or B that makes X(j) an exact solution)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
.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:  if INFO = i, and i is
                <= N:  the leading minor of order i of A is
                       not positive definite, so the factorization
                       could not be completed, and the solution has not
                       been computed\&. RCOND = 0 is returned\&.
                = N+1: U is nonsingular, but RCOND is less than machine
                       precision, meaning that the matrix is singular
                       to working precision\&.  Nevertheless, the
                       solution and error bounds are computed because
                       there are a number of situations where the
                       computed solution can be more accurate than the
                       value of RCOND would suggest\&.
.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.