---
name: "gtsv"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/gtsv"
---

# gtsv(3)

gtsv: factor and solve

## NAME

gtsv - gtsv: factor and solve

## SYNOPSIS

### Functions

subroutine **cgtsv** (n, nrhs, dl, d, du, b, ldb, info)\
  **CGTSV computes the solution to system of linear equations A \* X = B for GT matrices**   subroutine **dgtsv** (n, nrhs, dl, d, du, b, ldb, info)\
  **DGTSV computes the solution to system of linear equations A \* X = B for GT matrices**   subroutine **sgtsv** (n, nrhs, dl, d, du, b, ldb, info)\
  **SGTSV computes the solution to system of linear equations A \* X = B for GT matrices**   subroutine **zgtsv** (n, nrhs, dl, d, du, b, ldb, info)\
  **ZGTSV computes the solution to system of linear equations A \* X = B for GT matrices**

## Detailed Description

## Function Documentation

### subroutine cgtsv (integer n, integer nrhs, complex, dimension( \* ) dl, complex, dimension( \* ) d, complex, dimension( \* ) du, complex, dimension( ldb, \* ) b, integer ldb, integer info)

 **CGTSV computes the solution to system of linear equations A \* X = B for GT matrices**

**Purpose:**

```
!>
!> CGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T *X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*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)
!>          On entry, DL must contain the (n-1) subdiagonal elements of
!>          A.
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second superdiagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>
```

*D*

```
!>          D is COMPLEX array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>          On exit, D is overwritten by the n diagonal elements of U.
!>
```

*DU*

```
!>          DU is COMPLEX array, dimension (N-1)
!>          On entry, DU must contain the (n-1) superdiagonal elements
!>          of A.
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          superdiagonal of U.
!>
```

*B*

```
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix 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
!>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
!>                has not been computed.  The factorization has not been
!>                completed unless i = N.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **cgtsv.f**.

### subroutine dgtsv (integer n, integer nrhs, double precision, dimension( \* ) dl, double precision, dimension( \* ) d, double precision, dimension( \* ) du, double precision, dimension( ldb, \* ) b, integer ldb, integer info)

 **DGTSV computes the solution to system of linear equations A \* X = B for GT matrices**

**Purpose:**

```
!>
!> DGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an n by n tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T*X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*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)
!>          On entry, DL must contain the (n-1) sub-diagonal elements of
!>          A.
!>
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second super-diagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>
!>          On exit, D is overwritten by the n diagonal elements of U.
!>
```

*DU*

```
!>          DU is DOUBLE PRECISION array, dimension (N-1)
!>          On entry, DU must contain the (n-1) super-diagonal elements
!>          of A.
!>
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          super-diagonal of U.
!>
```

*B*

```
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix of right hand side matrix B.
!>          On exit, if INFO = 0, the N by NRHS solution matrix 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
!>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
!>               has not been computed.  The factorization has not been
!>               completed unless i = N.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **dgtsv.f**.

### subroutine sgtsv (integer n, integer nrhs, real, dimension( \* ) dl, real, dimension( \* ) d, real, dimension( \* ) du, real, dimension( ldb, \* ) b, integer ldb, integer info)

 **SGTSV computes the solution to system of linear equations A \* X = B for GT matrices**

**Purpose:**

```
!>
!> SGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an n by n tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T*X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*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)
!>          On entry, DL must contain the (n-1) sub-diagonal elements of
!>          A.
!>
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second super-diagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>
```

*D*

```
!>          D is REAL array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>
!>          On exit, D is overwritten by the n diagonal elements of U.
!>
```

*DU*

```
!>          DU is REAL array, dimension (N-1)
!>          On entry, DU must contain the (n-1) super-diagonal elements
!>          of A.
!>
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          super-diagonal of U.
!>
```

*B*

```
!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix of right hand side matrix B.
!>          On exit, if INFO = 0, the N by NRHS solution matrix 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
!>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
!>               has not been computed.  The factorization has not been
!>               completed unless i = N.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **126** of file **sgtsv.f**.

### subroutine zgtsv (integer n, integer nrhs, complex\*16, dimension( \* ) dl, complex\*16, dimension( \* ) d, complex\*16, dimension( \* ) du, complex\*16, dimension( ldb, \* ) b, integer ldb, integer info)

 **ZGTSV computes the solution to system of linear equations A \* X = B for GT matrices**

**Purpose:**

```
!>
!> ZGTSV  solves the equation
!>
!>    A*X = B,
!>
!> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
!> partial pivoting.
!>
!> Note that the equation  A**T *X = B  may be solved by interchanging the
!> order of the arguments DU and DL.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*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)
!>          On entry, DL must contain the (n-1) subdiagonal elements of
!>          A.
!>          On exit, DL is overwritten by the (n-2) elements of the
!>          second superdiagonal of the upper triangular matrix U from
!>          the LU factorization of A, in DL(1), ..., DL(n-2).
!>
```

*D*

```
!>          D is COMPLEX*16 array, dimension (N)
!>          On entry, D must contain the diagonal elements of A.
!>          On exit, D is overwritten by the n diagonal elements of U.
!>
```

*DU*

```
!>          DU is COMPLEX*16 array, dimension (N-1)
!>          On entry, DU must contain the (n-1) superdiagonal elements
!>          of A.
!>          On exit, DU is overwritten by the (n-1) elements of the first
!>          superdiagonal of U.
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix 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
!>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
!>                has not been computed.  The factorization has not been
!>                completed unless i = N.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **zgtsv.f**.

## Author

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