# ?dttrsv

Solves a general tridiagonal system of linear equations using the LU factorization computed by ?dttrf.

## Syntax

call sdttrsv(uplo, trans, n, nrhs, dl, d, du, b, ldb, info)

call ddttrsv(uplo, trans, n, nrhs, dl, d, du, b, ldb, info)

call cdttrsv(uplo, trans, n, nrhs, dl, d, du, b, ldb, info)

call zdttrsv(uplo, trans, n, nrhs, dl, d, du, b, ldb, info)

## Description

The ?dttrsvroutine solves one of the following systems of linear equations:

L*X = B, LT*X = B, or LH*X = B,

U*X = B, UT*X = B, or UH*X = B

with factors of the tridiagonal matrix A from the LU factorization computed by ?dttrf.

## Input Parameters

uplo

CHARACTER*1.

Specifies whether to solve with L or U.

trans

CHARACTER. Must be 'N' or 'T' or 'C'.

Indicates the form of the equations:

If trans = 'N', then A*X=B is solved for X (no transpose).

If trans = 'T', then AT*X = B is solved for X (transpose).

If trans = 'C', then AH*X = B is solved for X (conjugate transpose).

n

INTEGER. The order of the matrix A(n 0).

nrhs

INTEGER. The number of right-hand sides, that is, the number of columns in the matrix B(nrhs 0).

dl,d,du,b

REAL for sdttrsv

DOUBLE PRECISION for ddttrsv

COMPLEX for cdttrsv

COMPLEX*16 for zdttrsv.

The array dl of size (n - 1) contains the (n - 1) multipliers that define the matrix L from the LU factorization of A.

The array d of size n contains n diagonal elements of the upper triangular matrix U from the LU factorization of A.

The array du of size (n - 1) contains the (n - 1) elements of the first super-diagonal of U.

On entry, the array b of size (ldb,nrhs) contains the right-hand side of matrix B.

ldb

INTEGER. The leading dimension of the array b; ldb max(1, n).

## Output Parameters

b

Overwritten by the solution matrix X.

info

INTEGER. If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.