# gttrs - Man Page

gttrs: triangular solve using factor

## Synopsis

### Functions

subroutine **cgttrs** (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)**CGTTRS**

subroutine **dgttrs** (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)**DGTTRS**

subroutine **sgttrs** (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)**SGTTRS**

subroutine **zgttrs** (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)**ZGTTRS**

## Detailed Description

## Function Documentation

### subroutine cgttrs (character trans, 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, integer info)

**CGTTRS**

**Purpose:**

CGTTRS 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***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': 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).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **cgttrs.f**.

### subroutine dgttrs (character trans, 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, integer info)

**DGTTRS**

**Purpose:**

DGTTRS 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***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T* X = B (Transpose) = 'C': 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).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **dgttrs.f**.

### subroutine sgttrs (character trans, 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, integer info)

**SGTTRS**

**Purpose:**

SGTTRS 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***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T* X = B (Transpose) = 'C': 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).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **sgttrs.f**.

### subroutine zgttrs (character trans, 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, integer info)

**ZGTTRS**

**Purpose:**

ZGTTRS 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***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': 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).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **136** of file **zgttrs.f**.

## Author

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