1 SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 COMPLEX AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * CTPSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*x = b, or A**H*x = b,
16 *
17 * where b and x are n element vectors and A is an n by n unit, or
18 * non-unit, upper or lower triangular matrix, supplied in packed form.
19 *
20 * No test for singularity or near-singularity is included in this
21 * routine. Such tests must be performed before calling this routine.
22 *
23 * Arguments
24 * ==========
25 *
26 * UPLO - CHARACTER*1.
27 * On entry, UPLO specifies whether the matrix is an upper or
28 * lower triangular matrix as follows:
29 *
30 * UPLO = 'U' or 'u' A is an upper triangular matrix.
31 *
32 * UPLO = 'L' or 'l' A is a lower triangular matrix.
33 *
34 * Unchanged on exit.
35 *
36 * TRANS - CHARACTER*1.
37 * On entry, TRANS specifies the equations to be solved as
38 * follows:
39 *
40 * TRANS = 'N' or 'n' A*x = b.
41 *
42 * TRANS = 'T' or 't' A**T*x = b.
43 *
44 * TRANS = 'C' or 'c' A**H*x = b.
45 *
46 * Unchanged on exit.
47 *
48 * DIAG - CHARACTER*1.
49 * On entry, DIAG specifies whether or not A is unit
50 * triangular as follows:
51 *
52 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
53 *
54 * DIAG = 'N' or 'n' A is not assumed to be unit
55 * triangular.
56 *
57 * Unchanged on exit.
58 *
59 * N - INTEGER.
60 * On entry, N specifies the order of the matrix A.
61 * N must be at least zero.
62 * Unchanged on exit.
63 *
64 * AP - COMPLEX array of DIMENSION at least
65 * ( ( n*( n + 1 ) )/2 ).
66 * Before entry with UPLO = 'U' or 'u', the array AP must
67 * contain the upper triangular matrix packed sequentially,
68 * column by column, so that AP( 1 ) contains a( 1, 1 ),
69 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
70 * respectively, and so on.
71 * Before entry with UPLO = 'L' or 'l', the array AP must
72 * contain the lower triangular matrix packed sequentially,
73 * column by column, so that AP( 1 ) contains a( 1, 1 ),
74 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
75 * respectively, and so on.
76 * Note that when DIAG = 'U' or 'u', the diagonal elements of
77 * A are not referenced, but are assumed to be unity.
78 * Unchanged on exit.
79 *
80 * X - COMPLEX array of dimension at least
81 * ( 1 + ( n - 1 )*abs( INCX ) ).
82 * Before entry, the incremented array X must contain the n
83 * element right-hand side vector b. On exit, X is overwritten
84 * with the solution vector x.
85 *
86 * INCX - INTEGER.
87 * On entry, INCX specifies the increment for the elements of
88 * X. INCX must not be zero.
89 * Unchanged on exit.
90 *
91 * Further Details
92 * ===============
93 *
94 * Level 2 Blas routine.
95 *
96 * -- Written on 22-October-1986.
97 * Jack Dongarra, Argonne National Lab.
98 * Jeremy Du Croz, Nag Central Office.
99 * Sven Hammarling, Nag Central Office.
100 * Richard Hanson, Sandia National Labs.
101 *
102 * =====================================================================
103 *
104 * .. Parameters ..
105 COMPLEX ZERO
106 PARAMETER (ZERO= (0.0E+0,0.0E+0))
107 * ..
108 * .. Local Scalars ..
109 COMPLEX TEMP
110 INTEGER I,INFO,IX,J,JX,K,KK,KX
111 LOGICAL NOCONJ,NOUNIT
112 * ..
113 * .. External Functions ..
114 LOGICAL LSAME
115 EXTERNAL LSAME
116 * ..
117 * .. External Subroutines ..
118 EXTERNAL XERBLA
119 * ..
120 * .. Intrinsic Functions ..
121 INTRINSIC CONJG
122 * ..
123 *
124 * Test the input parameters.
125 *
126 INFO = 0
127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
128 INFO = 1
129 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
130 + .NOT.LSAME(TRANS,'C')) THEN
131 INFO = 2
132 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
133 INFO = 3
134 ELSE IF (N.LT.0) THEN
135 INFO = 4
136 ELSE IF (INCX.EQ.0) THEN
137 INFO = 7
138 END IF
139 IF (INFO.NE.0) THEN
140 CALL XERBLA('CTPSV ',INFO)
141 RETURN
142 END IF
143 *
144 * Quick return if possible.
145 *
146 IF (N.EQ.0) RETURN
147 *
148 NOCONJ = LSAME(TRANS,'T')
149 NOUNIT = LSAME(DIAG,'N')
150 *
151 * Set up the start point in X if the increment is not unity. This
152 * will be ( N - 1 )*INCX too small for descending loops.
153 *
154 IF (INCX.LE.0) THEN
155 KX = 1 - (N-1)*INCX
156 ELSE IF (INCX.NE.1) THEN
157 KX = 1
158 END IF
159 *
160 * Start the operations. In this version the elements of AP are
161 * accessed sequentially with one pass through AP.
162 *
163 IF (LSAME(TRANS,'N')) THEN
164 *
165 * Form x := inv( A )*x.
166 *
167 IF (LSAME(UPLO,'U')) THEN
168 KK = (N* (N+1))/2
169 IF (INCX.EQ.1) THEN
170 DO 20 J = N,1,-1
171 IF (X(J).NE.ZERO) THEN
172 IF (NOUNIT) X(J) = X(J)/AP(KK)
173 TEMP = X(J)
174 K = KK - 1
175 DO 10 I = J - 1,1,-1
176 X(I) = X(I) - TEMP*AP(K)
177 K = K - 1
178 10 CONTINUE
179 END IF
180 KK = KK - J
181 20 CONTINUE
182 ELSE
183 JX = KX + (N-1)*INCX
184 DO 40 J = N,1,-1
185 IF (X(JX).NE.ZERO) THEN
186 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
187 TEMP = X(JX)
188 IX = JX
189 DO 30 K = KK - 1,KK - J + 1,-1
190 IX = IX - INCX
191 X(IX) = X(IX) - TEMP*AP(K)
192 30 CONTINUE
193 END IF
194 JX = JX - INCX
195 KK = KK - J
196 40 CONTINUE
197 END IF
198 ELSE
199 KK = 1
200 IF (INCX.EQ.1) THEN
201 DO 60 J = 1,N
202 IF (X(J).NE.ZERO) THEN
203 IF (NOUNIT) X(J) = X(J)/AP(KK)
204 TEMP = X(J)
205 K = KK + 1
206 DO 50 I = J + 1,N
207 X(I) = X(I) - TEMP*AP(K)
208 K = K + 1
209 50 CONTINUE
210 END IF
211 KK = KK + (N-J+1)
212 60 CONTINUE
213 ELSE
214 JX = KX
215 DO 80 J = 1,N
216 IF (X(JX).NE.ZERO) THEN
217 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
218 TEMP = X(JX)
219 IX = JX
220 DO 70 K = KK + 1,KK + N - J
221 IX = IX + INCX
222 X(IX) = X(IX) - TEMP*AP(K)
223 70 CONTINUE
224 END IF
225 JX = JX + INCX
226 KK = KK + (N-J+1)
227 80 CONTINUE
228 END IF
229 END IF
230 ELSE
231 *
232 * Form x := inv( A**T )*x or x := inv( A**H )*x.
233 *
234 IF (LSAME(UPLO,'U')) THEN
235 KK = 1
236 IF (INCX.EQ.1) THEN
237 DO 110 J = 1,N
238 TEMP = X(J)
239 K = KK
240 IF (NOCONJ) THEN
241 DO 90 I = 1,J - 1
242 TEMP = TEMP - AP(K)*X(I)
243 K = K + 1
244 90 CONTINUE
245 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
246 ELSE
247 DO 100 I = 1,J - 1
248 TEMP = TEMP - CONJG(AP(K))*X(I)
249 K = K + 1
250 100 CONTINUE
251 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
252 END IF
253 X(J) = TEMP
254 KK = KK + J
255 110 CONTINUE
256 ELSE
257 JX = KX
258 DO 140 J = 1,N
259 TEMP = X(JX)
260 IX = KX
261 IF (NOCONJ) THEN
262 DO 120 K = KK,KK + J - 2
263 TEMP = TEMP - AP(K)*X(IX)
264 IX = IX + INCX
265 120 CONTINUE
266 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
267 ELSE
268 DO 130 K = KK,KK + J - 2
269 TEMP = TEMP - CONJG(AP(K))*X(IX)
270 IX = IX + INCX
271 130 CONTINUE
272 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
273 END IF
274 X(JX) = TEMP
275 JX = JX + INCX
276 KK = KK + J
277 140 CONTINUE
278 END IF
279 ELSE
280 KK = (N* (N+1))/2
281 IF (INCX.EQ.1) THEN
282 DO 170 J = N,1,-1
283 TEMP = X(J)
284 K = KK
285 IF (NOCONJ) THEN
286 DO 150 I = N,J + 1,-1
287 TEMP = TEMP - AP(K)*X(I)
288 K = K - 1
289 150 CONTINUE
290 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
291 ELSE
292 DO 160 I = N,J + 1,-1
293 TEMP = TEMP - CONJG(AP(K))*X(I)
294 K = K - 1
295 160 CONTINUE
296 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
297 END IF
298 X(J) = TEMP
299 KK = KK - (N-J+1)
300 170 CONTINUE
301 ELSE
302 KX = KX + (N-1)*INCX
303 JX = KX
304 DO 200 J = N,1,-1
305 TEMP = X(JX)
306 IX = KX
307 IF (NOCONJ) THEN
308 DO 180 K = KK,KK - (N- (J+1)),-1
309 TEMP = TEMP - AP(K)*X(IX)
310 IX = IX - INCX
311 180 CONTINUE
312 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
313 ELSE
314 DO 190 K = KK,KK - (N- (J+1)),-1
315 TEMP = TEMP - CONJG(AP(K))*X(IX)
316 IX = IX - INCX
317 190 CONTINUE
318 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
319 END IF
320 X(JX) = TEMP
321 JX = JX - INCX
322 KK = KK - (N-J+1)
323 200 CONTINUE
324 END IF
325 END IF
326 END IF
327 *
328 RETURN
329 *
330 * End of CTPSV .
331 *
332 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 COMPLEX AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * CTPSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*x = b, or A**H*x = b,
16 *
17 * where b and x are n element vectors and A is an n by n unit, or
18 * non-unit, upper or lower triangular matrix, supplied in packed form.
19 *
20 * No test for singularity or near-singularity is included in this
21 * routine. Such tests must be performed before calling this routine.
22 *
23 * Arguments
24 * ==========
25 *
26 * UPLO - CHARACTER*1.
27 * On entry, UPLO specifies whether the matrix is an upper or
28 * lower triangular matrix as follows:
29 *
30 * UPLO = 'U' or 'u' A is an upper triangular matrix.
31 *
32 * UPLO = 'L' or 'l' A is a lower triangular matrix.
33 *
34 * Unchanged on exit.
35 *
36 * TRANS - CHARACTER*1.
37 * On entry, TRANS specifies the equations to be solved as
38 * follows:
39 *
40 * TRANS = 'N' or 'n' A*x = b.
41 *
42 * TRANS = 'T' or 't' A**T*x = b.
43 *
44 * TRANS = 'C' or 'c' A**H*x = b.
45 *
46 * Unchanged on exit.
47 *
48 * DIAG - CHARACTER*1.
49 * On entry, DIAG specifies whether or not A is unit
50 * triangular as follows:
51 *
52 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
53 *
54 * DIAG = 'N' or 'n' A is not assumed to be unit
55 * triangular.
56 *
57 * Unchanged on exit.
58 *
59 * N - INTEGER.
60 * On entry, N specifies the order of the matrix A.
61 * N must be at least zero.
62 * Unchanged on exit.
63 *
64 * AP - COMPLEX array of DIMENSION at least
65 * ( ( n*( n + 1 ) )/2 ).
66 * Before entry with UPLO = 'U' or 'u', the array AP must
67 * contain the upper triangular matrix packed sequentially,
68 * column by column, so that AP( 1 ) contains a( 1, 1 ),
69 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
70 * respectively, and so on.
71 * Before entry with UPLO = 'L' or 'l', the array AP must
72 * contain the lower triangular matrix packed sequentially,
73 * column by column, so that AP( 1 ) contains a( 1, 1 ),
74 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
75 * respectively, and so on.
76 * Note that when DIAG = 'U' or 'u', the diagonal elements of
77 * A are not referenced, but are assumed to be unity.
78 * Unchanged on exit.
79 *
80 * X - COMPLEX array of dimension at least
81 * ( 1 + ( n - 1 )*abs( INCX ) ).
82 * Before entry, the incremented array X must contain the n
83 * element right-hand side vector b. On exit, X is overwritten
84 * with the solution vector x.
85 *
86 * INCX - INTEGER.
87 * On entry, INCX specifies the increment for the elements of
88 * X. INCX must not be zero.
89 * Unchanged on exit.
90 *
91 * Further Details
92 * ===============
93 *
94 * Level 2 Blas routine.
95 *
96 * -- Written on 22-October-1986.
97 * Jack Dongarra, Argonne National Lab.
98 * Jeremy Du Croz, Nag Central Office.
99 * Sven Hammarling, Nag Central Office.
100 * Richard Hanson, Sandia National Labs.
101 *
102 * =====================================================================
103 *
104 * .. Parameters ..
105 COMPLEX ZERO
106 PARAMETER (ZERO= (0.0E+0,0.0E+0))
107 * ..
108 * .. Local Scalars ..
109 COMPLEX TEMP
110 INTEGER I,INFO,IX,J,JX,K,KK,KX
111 LOGICAL NOCONJ,NOUNIT
112 * ..
113 * .. External Functions ..
114 LOGICAL LSAME
115 EXTERNAL LSAME
116 * ..
117 * .. External Subroutines ..
118 EXTERNAL XERBLA
119 * ..
120 * .. Intrinsic Functions ..
121 INTRINSIC CONJG
122 * ..
123 *
124 * Test the input parameters.
125 *
126 INFO = 0
127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
128 INFO = 1
129 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
130 + .NOT.LSAME(TRANS,'C')) THEN
131 INFO = 2
132 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
133 INFO = 3
134 ELSE IF (N.LT.0) THEN
135 INFO = 4
136 ELSE IF (INCX.EQ.0) THEN
137 INFO = 7
138 END IF
139 IF (INFO.NE.0) THEN
140 CALL XERBLA('CTPSV ',INFO)
141 RETURN
142 END IF
143 *
144 * Quick return if possible.
145 *
146 IF (N.EQ.0) RETURN
147 *
148 NOCONJ = LSAME(TRANS,'T')
149 NOUNIT = LSAME(DIAG,'N')
150 *
151 * Set up the start point in X if the increment is not unity. This
152 * will be ( N - 1 )*INCX too small for descending loops.
153 *
154 IF (INCX.LE.0) THEN
155 KX = 1 - (N-1)*INCX
156 ELSE IF (INCX.NE.1) THEN
157 KX = 1
158 END IF
159 *
160 * Start the operations. In this version the elements of AP are
161 * accessed sequentially with one pass through AP.
162 *
163 IF (LSAME(TRANS,'N')) THEN
164 *
165 * Form x := inv( A )*x.
166 *
167 IF (LSAME(UPLO,'U')) THEN
168 KK = (N* (N+1))/2
169 IF (INCX.EQ.1) THEN
170 DO 20 J = N,1,-1
171 IF (X(J).NE.ZERO) THEN
172 IF (NOUNIT) X(J) = X(J)/AP(KK)
173 TEMP = X(J)
174 K = KK - 1
175 DO 10 I = J - 1,1,-1
176 X(I) = X(I) - TEMP*AP(K)
177 K = K - 1
178 10 CONTINUE
179 END IF
180 KK = KK - J
181 20 CONTINUE
182 ELSE
183 JX = KX + (N-1)*INCX
184 DO 40 J = N,1,-1
185 IF (X(JX).NE.ZERO) THEN
186 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
187 TEMP = X(JX)
188 IX = JX
189 DO 30 K = KK - 1,KK - J + 1,-1
190 IX = IX - INCX
191 X(IX) = X(IX) - TEMP*AP(K)
192 30 CONTINUE
193 END IF
194 JX = JX - INCX
195 KK = KK - J
196 40 CONTINUE
197 END IF
198 ELSE
199 KK = 1
200 IF (INCX.EQ.1) THEN
201 DO 60 J = 1,N
202 IF (X(J).NE.ZERO) THEN
203 IF (NOUNIT) X(J) = X(J)/AP(KK)
204 TEMP = X(J)
205 K = KK + 1
206 DO 50 I = J + 1,N
207 X(I) = X(I) - TEMP*AP(K)
208 K = K + 1
209 50 CONTINUE
210 END IF
211 KK = KK + (N-J+1)
212 60 CONTINUE
213 ELSE
214 JX = KX
215 DO 80 J = 1,N
216 IF (X(JX).NE.ZERO) THEN
217 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
218 TEMP = X(JX)
219 IX = JX
220 DO 70 K = KK + 1,KK + N - J
221 IX = IX + INCX
222 X(IX) = X(IX) - TEMP*AP(K)
223 70 CONTINUE
224 END IF
225 JX = JX + INCX
226 KK = KK + (N-J+1)
227 80 CONTINUE
228 END IF
229 END IF
230 ELSE
231 *
232 * Form x := inv( A**T )*x or x := inv( A**H )*x.
233 *
234 IF (LSAME(UPLO,'U')) THEN
235 KK = 1
236 IF (INCX.EQ.1) THEN
237 DO 110 J = 1,N
238 TEMP = X(J)
239 K = KK
240 IF (NOCONJ) THEN
241 DO 90 I = 1,J - 1
242 TEMP = TEMP - AP(K)*X(I)
243 K = K + 1
244 90 CONTINUE
245 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
246 ELSE
247 DO 100 I = 1,J - 1
248 TEMP = TEMP - CONJG(AP(K))*X(I)
249 K = K + 1
250 100 CONTINUE
251 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
252 END IF
253 X(J) = TEMP
254 KK = KK + J
255 110 CONTINUE
256 ELSE
257 JX = KX
258 DO 140 J = 1,N
259 TEMP = X(JX)
260 IX = KX
261 IF (NOCONJ) THEN
262 DO 120 K = KK,KK + J - 2
263 TEMP = TEMP - AP(K)*X(IX)
264 IX = IX + INCX
265 120 CONTINUE
266 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
267 ELSE
268 DO 130 K = KK,KK + J - 2
269 TEMP = TEMP - CONJG(AP(K))*X(IX)
270 IX = IX + INCX
271 130 CONTINUE
272 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1))
273 END IF
274 X(JX) = TEMP
275 JX = JX + INCX
276 KK = KK + J
277 140 CONTINUE
278 END IF
279 ELSE
280 KK = (N* (N+1))/2
281 IF (INCX.EQ.1) THEN
282 DO 170 J = N,1,-1
283 TEMP = X(J)
284 K = KK
285 IF (NOCONJ) THEN
286 DO 150 I = N,J + 1,-1
287 TEMP = TEMP - AP(K)*X(I)
288 K = K - 1
289 150 CONTINUE
290 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
291 ELSE
292 DO 160 I = N,J + 1,-1
293 TEMP = TEMP - CONJG(AP(K))*X(I)
294 K = K - 1
295 160 CONTINUE
296 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
297 END IF
298 X(J) = TEMP
299 KK = KK - (N-J+1)
300 170 CONTINUE
301 ELSE
302 KX = KX + (N-1)*INCX
303 JX = KX
304 DO 200 J = N,1,-1
305 TEMP = X(JX)
306 IX = KX
307 IF (NOCONJ) THEN
308 DO 180 K = KK,KK - (N- (J+1)),-1
309 TEMP = TEMP - AP(K)*X(IX)
310 IX = IX - INCX
311 180 CONTINUE
312 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
313 ELSE
314 DO 190 K = KK,KK - (N- (J+1)),-1
315 TEMP = TEMP - CONJG(AP(K))*X(IX)
316 IX = IX - INCX
317 190 CONTINUE
318 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J))
319 END IF
320 X(JX) = TEMP
321 JX = JX - INCX
322 KK = KK - (N-J+1)
323 200 CONTINUE
324 END IF
325 END IF
326 END IF
327 *
328 RETURN
329 *
330 * End of CTPSV .
331 *
332 END