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gtts2(3) LAPACK 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.

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.

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.

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.

Author

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