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

.in +1c
.ti -1c
.RI "subroutine \fBdgtcon\fP (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO)"
.br
.RI "\fBDGTCON\fP "
.ti -1c
.RI "subroutine \fBdgtrfs\fP (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)"
.br
.RI "\fBDGTRFS\fP "
.ti -1c
.RI "subroutine \fBdgttrf\fP (N, DL, D, DU, DU2, IPIV, INFO)"
.br
.RI "\fBDGTTRF\fP "
.ti -1c
.RI "subroutine \fBdgttrs\fP (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)"
.br
.RI "\fBDGTTRS\fP "
.ti -1c
.RI "subroutine \fBdgtts2\fP (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)"
.br
.RI "\fBDGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. "
.in -1c
.SH "Detailed Description"
.PP 
This is the group of double computational functions for GT matrices 
.SH "Function Documentation"
.PP 
.SS "subroutine dgtcon (character NORM, integer N, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)"

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

.PP
.nf
 DGTCON estimates the reciprocal of the condition number of a real
 tridiagonal matrix A using the LU factorization as computed by
 DGTTRF\&.

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies whether the 1-norm condition number or the
          infinity-norm condition number is required:
          = '1' or 'O':  1-norm;
          = 'I':         Infinity-norm\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by DGTTRF\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
          ANORM is DOUBLE PRECISION
          If NORM = '1' or 'O', the 1-norm of the original matrix A\&.
          If NORM = 'I', the infinity-norm of the original matrix A\&.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of the matrix A,
          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
          estimate of the 1-norm of inv(A) computed in this routine\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (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
.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 dgtrfs (character TRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DLF, double precision, dimension( * ) DF, double precision, dimension( * ) DUF, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)"

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

.PP
.nf
 DGTRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is tridiagonal, and provides
 error bounds and backward error estimates for the solution\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
.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 matrix B\&.  NRHS >= 0\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) superdiagonal elements of A\&.
.fi
.PP
.br
\fIDLF\fP 
.PP
.nf
          DLF is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by DGTTRF\&.
.fi
.PP
.br
\fIDF\fP 
.PP
.nf
          DF is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A\&.
.fi
.PP
.br
\fIDUF\fP 
.PP
.nf
          DUF is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The 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)
          On entry, the solution matrix X, as computed by DGTTRS\&.
          On exit, the improved 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
\fIFERR\fP 
.PP
.nf
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated 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)\&.  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error\&.
.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 (3*N)
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (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
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
  ITMAX is the maximum number of steps of iterative refinement\&.
.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 dgttrf (integer N, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, integer INFO)"

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

.PP
.nf
 DGTTRF computes an LU factorization of a real tridiagonal matrix A
 using elimination with partial pivoting and row interchanges\&.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.fi
.PP
.br
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A\&.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          On entry, D must contain the diagonal elements of A\&.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A\&.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -k, the k-th argument had an illegal value
          > 0:  if INFO = k, U(k,k) is exactly zero\&. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations\&.
.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 dgttrs (character TRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)"

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

.PP
.nf
 DGTTRS solves one of the systems of equations
    A*X = B  or  A**T*X = B,
 with a tridiagonal matrix A using the LU factorization computed
 by DGTTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations\&.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T* X = B  (Transpose)
          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.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
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the matrix of right hand side vectors B\&.
          On exit, B is overwritten by the solution vectors 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
.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 dgtts2 (integer ITRANS, integer N, integer NRHS, double precision, dimension( * ) DL, double precision, dimension( * ) D, double precision, dimension( * ) DU, double precision, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB)"

.PP
\fBDGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGTTS2 solves one of the systems of equations
    A*X = B  or  A**T*X = B,
 with a tridiagonal matrix A using the LU factorization computed
 by DGTTRF\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITRANS\fP 
.PP
.nf
          ITRANS is INTEGER
          Specifies the form of the system of equations\&.
          = 0:  A * X = B  (No transpose)
          = 1:  A**T* X = B  (Transpose)
          = 2:  A**T* X = B  (Conjugate transpose = Transpose)
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.
.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
\fIDL\fP 
.PP
.nf
          DL is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A\&.
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the matrix of right hand side vectors B\&.
          On exit, B is overwritten by the solution vectors X\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,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

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