 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zgttrs()

 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
 [in] 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)``` [in] N ``` N is INTEGER The order of the matrix A.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] DL ``` DL is COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.``` [in] D ``` D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DU ``` DU is COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.``` [in] DU2 ``` DU2 is COMPLEX*16 array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.``` [in] 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.``` [in,out] 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.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 136 of file zgttrs.f.

138 *
139 * -- LAPACK computational routine --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 *
143 * .. Scalar Arguments ..
144  CHARACTER TRANS
145  INTEGER INFO, LDB, N, NRHS
146 * ..
147 * .. Array Arguments ..
148  INTEGER IPIV( * )
149  COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Local Scalars ..
155  LOGICAL NOTRAN
156  INTEGER ITRANS, J, JB, NB
157 * ..
158 * .. External Functions ..
159  INTEGER ILAENV
160  EXTERNAL ilaenv
161 * ..
162 * .. External Subroutines ..
163  EXTERNAL xerbla, zgtts2
164 * ..
165 * .. Intrinsic Functions ..
166  INTRINSIC max, min
167 * ..
168 * .. Executable Statements ..
169 *
170  info = 0
171  notran = ( trans.EQ.'N' .OR. trans.EQ.'n' )
172  IF( .NOT.notran .AND. .NOT.( trans.EQ.'T' .OR. trans.EQ.
173  \$ 't' ) .AND. .NOT.( trans.EQ.'C' .OR. trans.EQ.'c' ) ) THEN
174  info = -1
175  ELSE IF( n.LT.0 ) THEN
176  info = -2
177  ELSE IF( nrhs.LT.0 ) THEN
178  info = -3
179  ELSE IF( ldb.LT.max( n, 1 ) ) THEN
180  info = -10
181  END IF
182  IF( info.NE.0 ) THEN
183  CALL xerbla( 'ZGTTRS', -info )
184  RETURN
185  END IF
186 *
187 * Quick return if possible
188 *
189  IF( n.EQ.0 .OR. nrhs.EQ.0 )
190  \$ RETURN
191 *
192 * Decode TRANS
193 *
194  IF( notran ) THEN
195  itrans = 0
196  ELSE IF( trans.EQ.'T' .OR. trans.EQ.'t' ) THEN
197  itrans = 1
198  ELSE
199  itrans = 2
200  END IF
201 *
202 * Determine the number of right-hand sides to solve at a time.
203 *
204  IF( nrhs.EQ.1 ) THEN
205  nb = 1
206  ELSE
207  nb = max( 1, ilaenv( 1, 'ZGTTRS', trans, n, nrhs, -1, -1 ) )
208  END IF
209 *
210  IF( nb.GE.nrhs ) THEN
211  CALL zgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )
212  ELSE
213  DO 10 j = 1, nrhs, nb
214  jb = min( nrhs-j+1, nb )
215  CALL zgtts2( itrans, n, jb, dl, d, du, du2, ipiv, b( 1, j ),
216  \$ ldb )
217  10 CONTINUE
218  END IF
219 *
220 * End of ZGTTRS
221 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 compu...
Definition: zgtts2.f:128
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