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 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 is COMPLEX array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A.



          D is COMPLEX array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          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 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 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 is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A.



          D is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          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 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 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 is REAL array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A.



          D is REAL array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          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 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, complex16, dimension( ) dl, complex16, dimension( ) d, complex16, dimension( ) du, complex16, dimension( ) du2, integer, dimension( * ) ipiv, complex16, 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 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 is COMPLEX*16 array, dimension (N-1)


          The (n-1) multipliers that define the matrix L from the


          LU factorization of A.



          D is COMPLEX*16 array, dimension (N)


          The n diagonal elements of the upper triangular matrix U from


          the LU factorization of A.



          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 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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