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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,

```NAME
LAPACK-3  - solves one of the systems of equations  A * X = B, A**T * X
= B, or A**H * X = B,

SYNOPSIS
SUBROUTINE ZGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO )

CHARACTER      TRANS

INTEGER        INFO, LDB, N, NRHS

INTEGER        IPIV( * )

COMPLEX*16     B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )

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.

ARGUMENTS
TRANS   (input) 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       (input) INTEGER
The order of the matrix A.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

DL      (input) COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A.

D       (input) COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.

DU      (input) COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first super-diagonal of U.

DU2     (input) COMPLEX*16 array, dimension (N-2)
The (n-2) elements of the second super-diagonal of U.

IPIV    (input) 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       (input/output) 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     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -k, the k-th argument had an illegal value

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
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