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gtsv(3) LAPACK gtsv(3)

NAME

gtsv - gtsv: factor and solve

SYNOPSIS

Functions


subroutine cgtsv (n, nrhs, dl, d, du, b, ldb, info)
CGTSV computes the solution to system of linear equations A * X = B for GT matrices subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info)
DGTSV computes the solution to system of linear equations A * X = B for GT matrices subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info)
SGTSV computes the solution to system of linear equations A * X = B for GT matrices subroutine zgtsv (n, nrhs, dl, d, du, b, ldb, info)
ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Detailed Description

Function Documentation

subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

!>
!> CGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T *X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

DL

!>          DL is COMPLEX array, dimension (N-1)
!>          On entry, DL must contain the (n-1) subdiagonal elements of
!>          A.
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second superdiagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>

D

!>          D is COMPLEX array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>          On exit, D is overwritten by the n diagonal elements of U.
!>

DU

!>          DU is COMPLEX array, dimension (N-1)
!>          On entry, DU must contain the (n-1) superdiagonal elements
!>          of A.
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          superdiagonal of U.
!>

B

!>          B is COMPLEX 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.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
!>                has not been computed.  The factorization has not been
!>                completed unless i = N.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

!>
!> DGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an n by n tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T*X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

DL

!>          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-2) elements of the
!>          second super-diagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>

D

!>          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 U.
!>

DU

!>          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.
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix of right hand side matrix B.
!>          On exit, if INFO = 0, the N by NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
!>               has not been computed.  The factorization has not been
!>               completed unless i = N.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b, integer ldb, integer info)

SGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

!>
!> SGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an n by n tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T*X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

DL

!>          DL is REAL 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-2) elements of the
!>          second super-diagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>

D

!>          D is REAL array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>
!>          On exit, D is overwritten by the n diagonal elements of U.
!>

DU

!>          DU is REAL 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.
!>

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix of right hand side matrix B.
!>          On exit, if INFO = 0, the N by NRHS solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
!>               has not been computed.  The factorization has not been
!>               completed unless i = N.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

!>
!> ZGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T *X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

DL

!>          DL is COMPLEX*16 array, dimension (N-1)
!>          On entry, DL must contain the (n-1) subdiagonal elements of
!>          A.
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second superdiagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>

D

!>          D is COMPLEX*16 array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>          On exit, D is overwritten by the n diagonal elements of U.
!>

DU

!>          DU is COMPLEX*16 array, dimension (N-1)
!>          On entry, DU must contain the (n-1) superdiagonal elements
!>          of A.
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          superdiagonal of U.
!>

B

!>          B is COMPLEX*16 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.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
!>                has not been computed.  The factorization has not been
!>                completed unless i = N.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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