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gtts2(3) Library Functions Manual gtts2(3)

NAME

gtts2 - gtts2: triangular solve using factor

SYNOPSIS

Functions


subroutine CGTTS2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine DGTTS2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine SGTTS2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine ZGTTS2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Detailed Description

Function Documentation

subroutine CGTTS2 (integer itrans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb)

CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

!>
!> CGTTS2 solves one of the systems of equations
!>    A * X = B,  A**T * X = B,  or  A**H * X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by CGTTRF.
!>

Parameters

ITRANS 

!>          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**H * X = B  (Conjugate transpose)
!>

N

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

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)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

D

!>          D is COMPLEX array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

DU

!>          DU is COMPLEX array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is COMPLEX array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          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.
!>

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by the solution vectors X.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file cgtts2.f.

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)

DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

!>
!> 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.
!>

Parameters

ITRANS 

!>          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)
!>

N

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

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)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

DU

!>          DU is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is DOUBLE PRECISION array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          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.
!>

B

!>          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.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file dgtts2.f.

subroutine SGTTS2 (integer itrans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb)

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

!>
!> SGTTS2 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 SGTTRF.
!>

Parameters

ITRANS 

!>          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)
!>

N

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

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)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

D

!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

DU

!>          DU is REAL array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is REAL array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          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.
!>

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by the solution vectors X.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file sgtts2.f.

subroutine ZGTTS2 (integer itrans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb)

ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

!>
!> ZGTTS2 solves one of the systems of equations
!>    A * X = B,  A**T * X = B,  or  A**H * X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by ZGTTRF.
!>

Parameters

ITRANS 

!>          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**H * X = B  (Conjugate transpose)
!>

N

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

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)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

D

!>          D is COMPLEX*16 array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

DU

!>          DU is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is COMPLEX*16 array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          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.
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by the solution vectors X.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file zgtts2.f.

Author

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