gtsv - Man Page

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.

Definition at line 123 of file cgtsv.f.

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.

Definition at line 126 of file dgtsv.f.

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.

Definition at line 126 of file sgtsv.f.

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.

Definition at line 123 of file zgtsv.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK