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