LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zptts2()

 subroutine zptts2 ( integer IUPLO, integer N, integer NRHS, double precision, dimension( * ) D, complex*16, dimension( * ) E, complex*16, dimension( ldb, * ) B, integer LDB )

ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Purpose:
``` ZPTTS2 solves a tridiagonal system of the form
A * X = B
using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
D is a diagonal matrix specified in the vector D, U (or L) is a unit
bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
the vector E, and X and B are N by NRHS matrices.```
Parameters
 [in] IUPLO ``` IUPLO is INTEGER Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = 1: A = U**H *D*U, E is the superdiagonal of U = 0: A = L*D*L**H, E is the subdiagonal of L``` [in] N ``` N is INTEGER The order of the tridiagonal matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.``` [in] E ``` E is COMPLEX*16 array, dimension (N-1) If IUPLO = 1, the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If IUPLO = 0, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).```

Definition at line 112 of file zptts2.f.

113*
114* -- LAPACK computational routine --
115* -- LAPACK is a software package provided by Univ. of Tennessee, --
116* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118* .. Scalar Arguments ..
119 INTEGER IUPLO, LDB, N, NRHS
120* ..
121* .. Array Arguments ..
122 DOUBLE PRECISION D( * )
123 COMPLEX*16 B( LDB, * ), E( * )
124* ..
125*
126* =====================================================================
127*
128* .. Local Scalars ..
129 INTEGER I, J
130* ..
131* .. External Subroutines ..
132 EXTERNAL zdscal
133* ..
134* .. Intrinsic Functions ..
135 INTRINSIC dconjg
136* ..
137* .. Executable Statements ..
138*
139* Quick return if possible
140*
141 IF( n.LE.1 ) THEN
142 IF( n.EQ.1 )
143 \$ CALL zdscal( nrhs, 1.d0 / d( 1 ), b, ldb )
144 RETURN
145 END IF
146*
147 IF( iuplo.EQ.1 ) THEN
148*
149* Solve A * X = B using the factorization A = U**H *D*U,
150* overwriting each right hand side vector with its solution.
151*
152 IF( nrhs.LE.2 ) THEN
153 j = 1
154 10 CONTINUE
155*
156* Solve U**H * x = b.
157*
158 DO 20 i = 2, n
159 b( i, j ) = b( i, j ) - b( i-1, j )*dconjg( e( i-1 ) )
160 20 CONTINUE
161*
162* Solve D * U * x = b.
163*
164 DO 30 i = 1, n
165 b( i, j ) = b( i, j ) / d( i )
166 30 CONTINUE
167 DO 40 i = n - 1, 1, -1
168 b( i, j ) = b( i, j ) - b( i+1, j )*e( i )
169 40 CONTINUE
170 IF( j.LT.nrhs ) THEN
171 j = j + 1
172 GO TO 10
173 END IF
174 ELSE
175 DO 70 j = 1, nrhs
176*
177* Solve U**H * x = b.
178*
179 DO 50 i = 2, n
180 b( i, j ) = b( i, j ) - b( i-1, j )*dconjg( e( i-1 ) )
181 50 CONTINUE
182*
183* Solve D * U * x = b.
184*
185 b( n, j ) = b( n, j ) / d( n )
186 DO 60 i = n - 1, 1, -1
187 b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
188 60 CONTINUE
189 70 CONTINUE
190 END IF
191 ELSE
192*
193* Solve A * X = B using the factorization A = L*D*L**H,
194* overwriting each right hand side vector with its solution.
195*
196 IF( nrhs.LE.2 ) THEN
197 j = 1
198 80 CONTINUE
199*
200* Solve L * x = b.
201*
202 DO 90 i = 2, n
203 b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
204 90 CONTINUE
205*
206* Solve D * L**H * x = b.
207*
208 DO 100 i = 1, n
209 b( i, j ) = b( i, j ) / d( i )
210 100 CONTINUE
211 DO 110 i = n - 1, 1, -1
212 b( i, j ) = b( i, j ) - b( i+1, j )*dconjg( e( i ) )
213 110 CONTINUE
214 IF( j.LT.nrhs ) THEN
215 j = j + 1
216 GO TO 80
217 END IF
218 ELSE
219 DO 140 j = 1, nrhs
220*
221* Solve L * x = b.
222*
223 DO 120 i = 2, n
224 b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
225 120 CONTINUE
226*
227* Solve D * L**H * x = b.
228*
229 b( n, j ) = b( n, j ) / d( n )
230 DO 130 i = n - 1, 1, -1
231 b( i, j ) = b( i, j ) / d( i ) -
232 \$ b( i+1, j )*dconjg( e( i ) )
233 130 CONTINUE
234 140 CONTINUE
235 END IF
236 END IF
237*
238 RETURN
239*
240* End of ZPTTS2
241*
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
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