LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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cptts2.f
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1*> \brief \b CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CPTTS2 + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cptts2.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cptts2.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cptts2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
22*
23* .. Scalar Arguments ..
24* INTEGER IUPLO, LDB, N, NRHS
25* ..
26* .. Array Arguments ..
27* REAL D( * )
28* COMPLEX B( LDB, * ), E( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> CPTTS2 solves a tridiagonal system of the form
38*> A * X = B
39*> using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
40*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
41*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
42*> the vector E, and X and B are N by NRHS matrices.
43*> \endverbatim
44*
45* Arguments:
46* ==========
47*
48*> \param[in] IUPLO
49*> \verbatim
50*> IUPLO is INTEGER
51*> Specifies the form of the factorization and whether the
52*> vector E is the superdiagonal of the upper bidiagonal factor
53*> U or the subdiagonal of the lower bidiagonal factor L.
54*> = 1: A = U**H *D*U, E is the superdiagonal of U
55*> = 0: A = L*D*L**H, E is the subdiagonal of L
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The order of the tridiagonal matrix A. N >= 0.
62*> \endverbatim
63*>
64*> \param[in] NRHS
65*> \verbatim
66*> NRHS is INTEGER
67*> The number of right hand sides, i.e., the number of columns
68*> of the matrix B. NRHS >= 0.
69*> \endverbatim
70*>
71*> \param[in] D
72*> \verbatim
73*> D is REAL array, dimension (N)
74*> The n diagonal elements of the diagonal matrix D from the
75*> factorization A = U**H *D*U or A = L*D*L**H.
76*> \endverbatim
77*>
78*> \param[in] E
79*> \verbatim
80*> E is COMPLEX array, dimension (N-1)
81*> If IUPLO = 1, the (n-1) superdiagonal elements of the unit
82*> bidiagonal factor U from the factorization A = U**H*D*U.
83*> If IUPLO = 0, the (n-1) subdiagonal elements of the unit
84*> bidiagonal factor L from the factorization A = L*D*L**H.
85*> \endverbatim
86*>
87*> \param[in,out] B
88*> \verbatim
89*> B is COMPLEX array, dimension (LDB,NRHS)
90*> On entry, the right hand side vectors B for the system of
91*> linear equations.
92*> On exit, the solution vectors, X.
93*> \endverbatim
94*>
95*> \param[in] LDB
96*> \verbatim
97*> LDB is INTEGER
98*> The leading dimension of the array B. LDB >= max(1,N).
99*> \endverbatim
100*
101* Authors:
102* ========
103*
104*> \author Univ. of Tennessee
105*> \author Univ. of California Berkeley
106*> \author Univ. of Colorado Denver
107*> \author NAG Ltd.
108*
109*> \ingroup complexPTcomputational
110*
111* =====================================================================
112 SUBROUTINE cptts2( IUPLO, N, NRHS, D, E, B, LDB )
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 REAL D( * )
123 COMPLEX B( LDB, * ), E( * )
124* ..
125*
126* =====================================================================
127*
128* .. Local Scalars ..
129 INTEGER I, J
130* ..
131* .. External Subroutines ..
132 EXTERNAL csscal
133* ..
134* .. Intrinsic Functions ..
135 INTRINSIC conjg
136* ..
137* .. Executable Statements ..
138*
139* Quick return if possible
140*
141 IF( n.LE.1 ) THEN
142 IF( n.EQ.1 )
143 $ CALL csscal( nrhs, 1. / 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 5 CONTINUE
155*
156* Solve U**H * x = b.
157*
158 DO 10 i = 2, n
159 b( i, j ) = b( i, j ) - b( i-1, j )*conjg( e( i-1 ) )
160 10 CONTINUE
161*
162* Solve D * U * x = b.
163*
164 DO 20 i = 1, n
165 b( i, j ) = b( i, j ) / d( i )
166 20 CONTINUE
167 DO 30 i = n - 1, 1, -1
168 b( i, j ) = b( i, j ) - b( i+1, j )*e( i )
169 30 CONTINUE
170 IF( j.LT.nrhs ) THEN
171 j = j + 1
172 GO TO 5
173 END IF
174 ELSE
175 DO 60 j = 1, nrhs
176*
177* Solve U**H * x = b.
178*
179 DO 40 i = 2, n
180 b( i, j ) = b( i, j ) - b( i-1, j )*conjg( e( i-1 ) )
181 40 CONTINUE
182*
183* Solve D * U * x = b.
184*
185 b( n, j ) = b( n, j ) / d( n )
186 DO 50 i = n - 1, 1, -1
187 b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
188 50 CONTINUE
189 60 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 65 CONTINUE
199*
200* Solve L * x = b.
201*
202 DO 70 i = 2, n
203 b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
204 70 CONTINUE
205*
206* Solve D * L**H * x = b.
207*
208 DO 80 i = 1, n
209 b( i, j ) = b( i, j ) / d( i )
210 80 CONTINUE
211 DO 90 i = n - 1, 1, -1
212 b( i, j ) = b( i, j ) - b( i+1, j )*conjg( e( i ) )
213 90 CONTINUE
214 IF( j.LT.nrhs ) THEN
215 j = j + 1
216 GO TO 65
217 END IF
218 ELSE
219 DO 120 j = 1, nrhs
220*
221* Solve L * x = b.
222*
223 DO 100 i = 2, n
224 b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
225 100 CONTINUE
226*
227* Solve D * L**H * x = b.
228*
229 b( n, j ) = b( n, j ) / d( n )
230 DO 110 i = n - 1, 1, -1
231 b( i, j ) = b( i, j ) / d( i ) -
232 $ b( i+1, j )*conjg( e( i ) )
233 110 CONTINUE
234 120 CONTINUE
235 END IF
236 END IF
237*
238 RETURN
239*
240* End of CPTTS2
241*
242 END
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine cptts2(IUPLO, N, NRHS, D, E, B, LDB)
CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf...
Definition: cptts2.f:113