OpenRadioss 2025.1.11
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cdttrsv.f
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1 SUBROUTINE cdttrsv( UPLO, TRANS, N, NRHS, DL, D, DU,
2 $ B, LDB, INFO )
3*
4* -- ScaLAPACK auxiliary routine (version 2.0) --
5* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
6*
7* Written by Andrew J. Cleary, University of Tennessee.
8* August, 1996.
9* Modified from CGTTRS:
10* -- LAPACK routine (preliminary version) --
11* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
12* Courant Institute, Argonne National Lab, and Rice University
13*
14* .. Scalar Arguments ..
15 CHARACTER UPLO, TRANS
16 INTEGER INFO, LDB, N, NRHS
17* ..
18* .. Array Arguments ..
19 COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
20* ..
21*
22* Purpose
23* =======
24*
25* CDTTRSV solves one of the systems of equations
26* L * X = B, L**T * X = B, or L**H * X = B,
27* U * X = B, U**T * X = B, or U**H * X = B,
28* with factors of the tridiagonal matrix A from the LU factorization
29* computed by CDTTRF.
30*
31* Arguments
32* =========
33*
34* UPLO (input) CHARACTER*1
35* Specifies whether to solve with L or U.
36*
37* TRANS (input) CHARACTER
38* Specifies the form of the system of equations:
39* = 'N': A * X = B (No transpose)
40* = 'T': A**T * X = B (Transpose)
41* = 'C': A**H * X = B (Conjugate transpose)
42*
43* N (input) INTEGER
44* The order of the matrix A. N >= 0.
45*
46* NRHS (input) INTEGER
47* The number of right hand sides, i.e., the number of columns
48* of the matrix B. NRHS >= 0.
49*
50* DL (input) COMPLEX array, dimension (N-1)
51* The (n-1) multipliers that define the matrix L from the
52* LU factorization of A.
53*
54* D (input) COMPLEX array, dimension (N)
55* The n diagonal elements of the upper triangular matrix U from
56* the LU factorization of A.
57*
58* DU (input) COMPLEX array, dimension (N-1)
59* The (n-1) elements of the first superdiagonal of U.
60*
61* B (input/output) COMPLEX array, dimension (LDB,NRHS)
62* On entry, the right hand side matrix B.
63* On exit, B is overwritten by the solution matrix X.
64*
65* LDB (input) INTEGER
66* The leading dimension of the array B. LDB >= max(1,N).
67*
68* INFO (output) INTEGER
69* = 0: successful exit
70* < 0: if INFO = -i, the i-th argument had an illegal value
71*
72* =====================================================================
73*
74* .. Local Scalars ..
75 LOGICAL LOWER, NOTRAN
76 INTEGER I, J
77* ..
78* .. External Functions ..
79 LOGICAL LSAME
80 EXTERNAL lsame
81* ..
82* .. External Subroutines ..
83 EXTERNAL xerbla
84* ..
85* .. Intrinsic Functions ..
86 INTRINSIC conjg, max
87* ..
88* .. Executable Statements ..
89*
90 info = 0
91 notran = lsame( trans, 'N' )
92 lower = lsame( uplo, 'L' )
93 IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
94 info = -1
95 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
96 $ lsame( trans, 'C' ) ) THEN
97 info = -2
98 ELSE IF( n.LT.0 ) THEN
99 info = -3
100 ELSE IF( nrhs.LT.0 ) THEN
101 info = -4
102 ELSE IF( ldb.LT.max( n, 1 ) ) THEN
103 info = -9
104 END IF
105 IF( info.NE.0 ) THEN
106 CALL xerbla( 'CDTTRSV', -info )
107 RETURN
108 END IF
109*
110* Quick return if possible
111*
112 IF( n.EQ.0 .OR. nrhs.EQ.0 )
113 $ RETURN
114*
115 IF( notran ) THEN
116*
117 IF( lower ) THEN
118* Solve L*X = B, overwriting B with X.
119*
120 DO 35 j = 1, nrhs
121*
122* Solve L*x = b.
123*
124 DO 10 i = 1, n - 1
125 b( i+1, j ) = b( i+1, j ) - dl( i )*b( i, j )
126 10 CONTINUE 35 CONTINUE * ELSE * Solve U*x = b. * DO 30 J = 1, NRHS B( N, J ) = B( N, J ) / D( N ) IF( N.GT.1 ) $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / $ D( N-1 ) DO 20 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J ) ) / D( I ) 20 CONTINUE 30 CONTINUE * ENDIF * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * IF( .NOT. LOWER ) THEN * Solve U**T * X = B, overwriting B with X. * DO 65 J = 1, NRHS * * Solve U**T * x = b. * B( 1, J ) = B( 1, J ) / D( 1 ) IF( N.GT.1 ) $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) DO 40 I = 3, N B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J ) ) / D( I ) 40 CONTINUE 65 CONTINUE * ELSE * * Solve L**T * X = B, overwriting B with X. DO 60 J = 1, NRHS * * Solve L**T * x = b. * DO 50 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) 50 CONTINUE 60 CONTINUE ENDIF ELSE * IF( .NOT. LOWER ) THEN * Solve U**H * X = B, overwriting B with X. * DO 95 J = 1, NRHS * * Solve U**H * x = b. * B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) ) IF( N.GT.1 ) $ B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) / $ CONJG( D( 2 ) ) DO 70 I = 3, N B( I, J ) = ( B( I, J ) $ -CONJG( DU( I-1 ) )*B( I-1, J ) ) / $ CONJG( D( I ) ) 70 CONTINUE 95 CONTINUE * ELSE * * Solve L**H * X = B, overwriting B with X. DO 90 J = 1, NRHS * * Solve L**H * x = b. * DO 80 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - CONJG( DL( I ) )*B( I+1, J ) 80 CONTINUE 90 CONTINUE ENDIF END IF * * End of CDTTRSV * END CONTINUE
127 35 CONTINUE
128*
129 ELSE
130* Solve U*x = b.
131*
132 DO 30 j = 1, nrhs
133 b( n, j ) = b( n, j ) / d( n )
134 IF( n.GT.1 )
135 $ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) /
136 $ d( n-1 )
137 DO 20 i = n - 2, 1, -1
138 b( i, j ) = ( b( i, j )-du( i )*b( i+1, j ) ) / d( i )
139 20 CONTINUE
140 30 CONTINUE
141*
142 ENDIF
143*
144 ELSE IF( lsame( trans, 'T' ) ) THEN
145*
146 IF( .NOT. lower ) THEN
147* Solve U**T * X = B, overwriting B with X.
148*
149 DO 65 j = 1, nrhs
150*
151* Solve U**T * x = b.
152*
153 b( 1, j ) = b( 1, j ) / d( 1 )
154 IF( n.GT.1 )
155 $ b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
156 DO 40 i = 3, n
157 b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j ) ) / d( i )
158 40 CONTINUE
159 65 CONTINUE
160*
161 ELSE
162*
163* Solve L**T * X = B, overwriting B with X.
164 DO 60 j = 1, nrhs
165*
166* Solve L**T * x = b.
167*
168 DO 50 i = n - 1, 1, -1
169 b( i, j ) = b( i, j ) - dl( i )*b( i+1, j )
170 50 CONTINUE
171 60 CONTINUE
172 ENDIF
173 ELSE
174*
175 IF( .NOT. lower ) THEN
176* Solve U**H * X = B, overwriting B with X.
177*
178 DO 95 j = 1, nrhs
179*
180* Solve U**H * x = b.
181*
182 b( 1, j ) = b( 1, j ) / conjg( d( 1 ) )
183 IF( n.GT.1 )
184 $ b( 2, j ) = ( b( 2, j )-conjg( du( 1 ) )*b( 1, j ) ) /
185 $ conjg( d( 2 ) )
186 DO 70 i = 3, n
187 b( i, j ) = ( b( i, j )
188 $ -conjg( du( i-1 ) )*b( i-1, j ) ) /
189 $ conjg( d( i ) )
190 70 CONTINUE
191 95 CONTINUE
192*
193 ELSE
194*
195* Solve L**H * X = B, overwriting B with X.
196 DO 90 j = 1, nrhs
197*
198* Solve L**H * x = b.
199*
200 DO 80 i = n - 1, 1, -1
201 b( i, j ) = b( i, j ) - conjg( dl( i ) )*b( i+1, j )
202 80 CONTINUE
203 90 CONTINUE
204 ENDIF
205 END IF
206*
207* End of CDTTRSV
208*
209 END
cdttrsv
subroutine cdttrsv(uplo, trans, n, nrhs, dl, d, du, b, ldb, info)
Definition cdttrsv.f:3
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
max
#define max(a, b)
Definition macros.h:21