# gtts2 - Man Page

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**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**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

Generated automatically by Doxygen for LAPACK from the source code.