1 SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
2 $ INCY )
3 *
4 * -- LAPACK auxiliary routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INCX, INCY, K, LDA, N
11 COMPLEX ALPHA, BETA
12 * ..
13 * .. Array Arguments ..
14 COMPLEX A( LDA, * ), X( * ), Y( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * CSBMV performs the matrix-vector operation
21 *
22 * y := alpha*A*x + beta*y,
23 *
24 * where alpha and beta are scalars, x and y are n element vectors and
25 * A is an n by n symmetric band matrix, with k super-diagonals.
26 *
27 * Arguments
28 * ==========
29 *
30 * UPLO - CHARACTER*1
31 * On entry, UPLO specifies whether the upper or lower
32 * triangular part of the band matrix A is being supplied as
33 * follows:
34 *
35 * UPLO = 'U' or 'u' The upper triangular part of A is
36 * being supplied.
37 *
38 * UPLO = 'L' or 'l' The lower triangular part of A is
39 * being supplied.
40 *
41 * Unchanged on exit.
42 *
43 * N - INTEGER
44 * On entry, N specifies the order of the matrix A.
45 * N must be at least zero.
46 * Unchanged on exit.
47 *
48 * K - INTEGER
49 * On entry, K specifies the number of super-diagonals of the
50 * matrix A. K must satisfy 0 .le. K.
51 * Unchanged on exit.
52 *
53 * ALPHA - COMPLEX
54 * On entry, ALPHA specifies the scalar alpha.
55 * Unchanged on exit.
56 *
57 * A - COMPLEX array, dimension( LDA, N )
58 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
59 * by n part of the array A must contain the upper triangular
60 * band part of the symmetric matrix, supplied column by
61 * column, with the leading diagonal of the matrix in row
62 * ( k + 1 ) of the array, the first super-diagonal starting at
63 * position 2 in row k, and so on. The top left k by k triangle
64 * of the array A is not referenced.
65 * The following program segment will transfer the upper
66 * triangular part of a symmetric band matrix from conventional
67 * full matrix storage to band storage:
68 *
69 * DO 20, J = 1, N
70 * M = K + 1 - J
71 * DO 10, I = MAX( 1, J - K ), J
72 * A( M + I, J ) = matrix( I, J )
73 * 10 CONTINUE
74 * 20 CONTINUE
75 *
76 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
77 * by n part of the array A must contain the lower triangular
78 * band part of the symmetric matrix, supplied column by
79 * column, with the leading diagonal of the matrix in row 1 of
80 * the array, the first sub-diagonal starting at position 1 in
81 * row 2, and so on. The bottom right k by k triangle of the
82 * array A is not referenced.
83 * The following program segment will transfer the lower
84 * triangular part of a symmetric band matrix from conventional
85 * full matrix storage to band storage:
86 *
87 * DO 20, J = 1, N
88 * M = 1 - J
89 * DO 10, I = J, MIN( N, J + K )
90 * A( M + I, J ) = matrix( I, J )
91 * 10 CONTINUE
92 * 20 CONTINUE
93 *
94 * Unchanged on exit.
95 *
96 * LDA - INTEGER
97 * On entry, LDA specifies the first dimension of A as declared
98 * in the calling (sub) program. LDA must be at least
99 * ( k + 1 ).
100 * Unchanged on exit.
101 *
102 * X - COMPLEX array, dimension at least
103 * ( 1 + ( N - 1 )*abs( INCX ) ).
104 * Before entry, the incremented array X must contain the
105 * vector x.
106 * Unchanged on exit.
107 *
108 * INCX - INTEGER
109 * On entry, INCX specifies the increment for the elements of
110 * X. INCX must not be zero.
111 * Unchanged on exit.
112 *
113 * BETA - COMPLEX
114 * On entry, BETA specifies the scalar beta.
115 * Unchanged on exit.
116 *
117 * Y - COMPLEX array, dimension at least
118 * ( 1 + ( N - 1 )*abs( INCY ) ).
119 * Before entry, the incremented array Y must contain the
120 * vector y. On exit, Y is overwritten by the updated vector y.
121 *
122 * INCY - INTEGER
123 * On entry, INCY specifies the increment for the elements of
124 * Y. INCY must not be zero.
125 * Unchanged on exit.
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130 COMPLEX ONE
131 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
132 COMPLEX ZERO
133 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
134 * ..
135 * .. Local Scalars ..
136 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
137 COMPLEX TEMP1, TEMP2
138 * ..
139 * .. External Functions ..
140 LOGICAL LSAME
141 EXTERNAL LSAME
142 * ..
143 * .. External Subroutines ..
144 EXTERNAL XERBLA
145 * ..
146 * .. Intrinsic Functions ..
147 INTRINSIC MAX, MIN
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153 INFO = 0
154 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
155 INFO = 1
156 ELSE IF( N.LT.0 ) THEN
157 INFO = 2
158 ELSE IF( K.LT.0 ) THEN
159 INFO = 3
160 ELSE IF( LDA.LT.( K+1 ) ) THEN
161 INFO = 6
162 ELSE IF( INCX.EQ.0 ) THEN
163 INFO = 8
164 ELSE IF( INCY.EQ.0 ) THEN
165 INFO = 11
166 END IF
167 IF( INFO.NE.0 ) THEN
168 CALL XERBLA( 'CSBMV ', INFO )
169 RETURN
170 END IF
171 *
172 * Quick return if possible.
173 *
174 IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
175 $ RETURN
176 *
177 * Set up the start points in X and Y.
178 *
179 IF( INCX.GT.0 ) THEN
180 KX = 1
181 ELSE
182 KX = 1 - ( N-1 )*INCX
183 END IF
184 IF( INCY.GT.0 ) THEN
185 KY = 1
186 ELSE
187 KY = 1 - ( N-1 )*INCY
188 END IF
189 *
190 * Start the operations. In this version the elements of the array A
191 * are accessed sequentially with one pass through A.
192 *
193 * First form y := beta*y.
194 *
195 IF( BETA.NE.ONE ) THEN
196 IF( INCY.EQ.1 ) THEN
197 IF( BETA.EQ.ZERO ) THEN
198 DO 10 I = 1, N
199 Y( I ) = ZERO
200 10 CONTINUE
201 ELSE
202 DO 20 I = 1, N
203 Y( I ) = BETA*Y( I )
204 20 CONTINUE
205 END IF
206 ELSE
207 IY = KY
208 IF( BETA.EQ.ZERO ) THEN
209 DO 30 I = 1, N
210 Y( IY ) = ZERO
211 IY = IY + INCY
212 30 CONTINUE
213 ELSE
214 DO 40 I = 1, N
215 Y( IY ) = BETA*Y( IY )
216 IY = IY + INCY
217 40 CONTINUE
218 END IF
219 END IF
220 END IF
221 IF( ALPHA.EQ.ZERO )
222 $ RETURN
223 IF( LSAME( UPLO, 'U' ) ) THEN
224 *
225 * Form y when upper triangle of A is stored.
226 *
227 KPLUS1 = K + 1
228 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
229 DO 60 J = 1, N
230 TEMP1 = ALPHA*X( J )
231 TEMP2 = ZERO
232 L = KPLUS1 - J
233 DO 50 I = MAX( 1, J-K ), J - 1
234 Y( I ) = Y( I ) + TEMP1*A( L+I, J )
235 TEMP2 = TEMP2 + A( L+I, J )*X( I )
236 50 CONTINUE
237 Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
238 60 CONTINUE
239 ELSE
240 JX = KX
241 JY = KY
242 DO 80 J = 1, N
243 TEMP1 = ALPHA*X( JX )
244 TEMP2 = ZERO
245 IX = KX
246 IY = KY
247 L = KPLUS1 - J
248 DO 70 I = MAX( 1, J-K ), J - 1
249 Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
250 TEMP2 = TEMP2 + A( L+I, J )*X( IX )
251 IX = IX + INCX
252 IY = IY + INCY
253 70 CONTINUE
254 Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
255 JX = JX + INCX
256 JY = JY + INCY
257 IF( J.GT.K ) THEN
258 KX = KX + INCX
259 KY = KY + INCY
260 END IF
261 80 CONTINUE
262 END IF
263 ELSE
264 *
265 * Form y when lower triangle of A is stored.
266 *
267 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
268 DO 100 J = 1, N
269 TEMP1 = ALPHA*X( J )
270 TEMP2 = ZERO
271 Y( J ) = Y( J ) + TEMP1*A( 1, J )
272 L = 1 - J
273 DO 90 I = J + 1, MIN( N, J+K )
274 Y( I ) = Y( I ) + TEMP1*A( L+I, J )
275 TEMP2 = TEMP2 + A( L+I, J )*X( I )
276 90 CONTINUE
277 Y( J ) = Y( J ) + ALPHA*TEMP2
278 100 CONTINUE
279 ELSE
280 JX = KX
281 JY = KY
282 DO 120 J = 1, N
283 TEMP1 = ALPHA*X( JX )
284 TEMP2 = ZERO
285 Y( JY ) = Y( JY ) + TEMP1*A( 1, J )
286 L = 1 - J
287 IX = JX
288 IY = JY
289 DO 110 I = J + 1, MIN( N, J+K )
290 IX = IX + INCX
291 IY = IY + INCY
292 Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
293 TEMP2 = TEMP2 + A( L+I, J )*X( IX )
294 110 CONTINUE
295 Y( JY ) = Y( JY ) + ALPHA*TEMP2
296 JX = JX + INCX
297 JY = JY + INCY
298 120 CONTINUE
299 END IF
300 END IF
301 *
302 RETURN
303 *
304 * End of CSBMV
305 *
306 END
2 $ INCY )
3 *
4 * -- LAPACK auxiliary routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INCX, INCY, K, LDA, N
11 COMPLEX ALPHA, BETA
12 * ..
13 * .. Array Arguments ..
14 COMPLEX A( LDA, * ), X( * ), Y( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * CSBMV performs the matrix-vector operation
21 *
22 * y := alpha*A*x + beta*y,
23 *
24 * where alpha and beta are scalars, x and y are n element vectors and
25 * A is an n by n symmetric band matrix, with k super-diagonals.
26 *
27 * Arguments
28 * ==========
29 *
30 * UPLO - CHARACTER*1
31 * On entry, UPLO specifies whether the upper or lower
32 * triangular part of the band matrix A is being supplied as
33 * follows:
34 *
35 * UPLO = 'U' or 'u' The upper triangular part of A is
36 * being supplied.
37 *
38 * UPLO = 'L' or 'l' The lower triangular part of A is
39 * being supplied.
40 *
41 * Unchanged on exit.
42 *
43 * N - INTEGER
44 * On entry, N specifies the order of the matrix A.
45 * N must be at least zero.
46 * Unchanged on exit.
47 *
48 * K - INTEGER
49 * On entry, K specifies the number of super-diagonals of the
50 * matrix A. K must satisfy 0 .le. K.
51 * Unchanged on exit.
52 *
53 * ALPHA - COMPLEX
54 * On entry, ALPHA specifies the scalar alpha.
55 * Unchanged on exit.
56 *
57 * A - COMPLEX array, dimension( LDA, N )
58 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
59 * by n part of the array A must contain the upper triangular
60 * band part of the symmetric matrix, supplied column by
61 * column, with the leading diagonal of the matrix in row
62 * ( k + 1 ) of the array, the first super-diagonal starting at
63 * position 2 in row k, and so on. The top left k by k triangle
64 * of the array A is not referenced.
65 * The following program segment will transfer the upper
66 * triangular part of a symmetric band matrix from conventional
67 * full matrix storage to band storage:
68 *
69 * DO 20, J = 1, N
70 * M = K + 1 - J
71 * DO 10, I = MAX( 1, J - K ), J
72 * A( M + I, J ) = matrix( I, J )
73 * 10 CONTINUE
74 * 20 CONTINUE
75 *
76 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
77 * by n part of the array A must contain the lower triangular
78 * band part of the symmetric matrix, supplied column by
79 * column, with the leading diagonal of the matrix in row 1 of
80 * the array, the first sub-diagonal starting at position 1 in
81 * row 2, and so on. The bottom right k by k triangle of the
82 * array A is not referenced.
83 * The following program segment will transfer the lower
84 * triangular part of a symmetric band matrix from conventional
85 * full matrix storage to band storage:
86 *
87 * DO 20, J = 1, N
88 * M = 1 - J
89 * DO 10, I = J, MIN( N, J + K )
90 * A( M + I, J ) = matrix( I, J )
91 * 10 CONTINUE
92 * 20 CONTINUE
93 *
94 * Unchanged on exit.
95 *
96 * LDA - INTEGER
97 * On entry, LDA specifies the first dimension of A as declared
98 * in the calling (sub) program. LDA must be at least
99 * ( k + 1 ).
100 * Unchanged on exit.
101 *
102 * X - COMPLEX array, dimension at least
103 * ( 1 + ( N - 1 )*abs( INCX ) ).
104 * Before entry, the incremented array X must contain the
105 * vector x.
106 * Unchanged on exit.
107 *
108 * INCX - INTEGER
109 * On entry, INCX specifies the increment for the elements of
110 * X. INCX must not be zero.
111 * Unchanged on exit.
112 *
113 * BETA - COMPLEX
114 * On entry, BETA specifies the scalar beta.
115 * Unchanged on exit.
116 *
117 * Y - COMPLEX array, dimension at least
118 * ( 1 + ( N - 1 )*abs( INCY ) ).
119 * Before entry, the incremented array Y must contain the
120 * vector y. On exit, Y is overwritten by the updated vector y.
121 *
122 * INCY - INTEGER
123 * On entry, INCY specifies the increment for the elements of
124 * Y. INCY must not be zero.
125 * Unchanged on exit.
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130 COMPLEX ONE
131 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
132 COMPLEX ZERO
133 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
134 * ..
135 * .. Local Scalars ..
136 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
137 COMPLEX TEMP1, TEMP2
138 * ..
139 * .. External Functions ..
140 LOGICAL LSAME
141 EXTERNAL LSAME
142 * ..
143 * .. External Subroutines ..
144 EXTERNAL XERBLA
145 * ..
146 * .. Intrinsic Functions ..
147 INTRINSIC MAX, MIN
148 * ..
149 * .. Executable Statements ..
150 *
151 * Test the input parameters.
152 *
153 INFO = 0
154 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
155 INFO = 1
156 ELSE IF( N.LT.0 ) THEN
157 INFO = 2
158 ELSE IF( K.LT.0 ) THEN
159 INFO = 3
160 ELSE IF( LDA.LT.( K+1 ) ) THEN
161 INFO = 6
162 ELSE IF( INCX.EQ.0 ) THEN
163 INFO = 8
164 ELSE IF( INCY.EQ.0 ) THEN
165 INFO = 11
166 END IF
167 IF( INFO.NE.0 ) THEN
168 CALL XERBLA( 'CSBMV ', INFO )
169 RETURN
170 END IF
171 *
172 * Quick return if possible.
173 *
174 IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
175 $ RETURN
176 *
177 * Set up the start points in X and Y.
178 *
179 IF( INCX.GT.0 ) THEN
180 KX = 1
181 ELSE
182 KX = 1 - ( N-1 )*INCX
183 END IF
184 IF( INCY.GT.0 ) THEN
185 KY = 1
186 ELSE
187 KY = 1 - ( N-1 )*INCY
188 END IF
189 *
190 * Start the operations. In this version the elements of the array A
191 * are accessed sequentially with one pass through A.
192 *
193 * First form y := beta*y.
194 *
195 IF( BETA.NE.ONE ) THEN
196 IF( INCY.EQ.1 ) THEN
197 IF( BETA.EQ.ZERO ) THEN
198 DO 10 I = 1, N
199 Y( I ) = ZERO
200 10 CONTINUE
201 ELSE
202 DO 20 I = 1, N
203 Y( I ) = BETA*Y( I )
204 20 CONTINUE
205 END IF
206 ELSE
207 IY = KY
208 IF( BETA.EQ.ZERO ) THEN
209 DO 30 I = 1, N
210 Y( IY ) = ZERO
211 IY = IY + INCY
212 30 CONTINUE
213 ELSE
214 DO 40 I = 1, N
215 Y( IY ) = BETA*Y( IY )
216 IY = IY + INCY
217 40 CONTINUE
218 END IF
219 END IF
220 END IF
221 IF( ALPHA.EQ.ZERO )
222 $ RETURN
223 IF( LSAME( UPLO, 'U' ) ) THEN
224 *
225 * Form y when upper triangle of A is stored.
226 *
227 KPLUS1 = K + 1
228 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
229 DO 60 J = 1, N
230 TEMP1 = ALPHA*X( J )
231 TEMP2 = ZERO
232 L = KPLUS1 - J
233 DO 50 I = MAX( 1, J-K ), J - 1
234 Y( I ) = Y( I ) + TEMP1*A( L+I, J )
235 TEMP2 = TEMP2 + A( L+I, J )*X( I )
236 50 CONTINUE
237 Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
238 60 CONTINUE
239 ELSE
240 JX = KX
241 JY = KY
242 DO 80 J = 1, N
243 TEMP1 = ALPHA*X( JX )
244 TEMP2 = ZERO
245 IX = KX
246 IY = KY
247 L = KPLUS1 - J
248 DO 70 I = MAX( 1, J-K ), J - 1
249 Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
250 TEMP2 = TEMP2 + A( L+I, J )*X( IX )
251 IX = IX + INCX
252 IY = IY + INCY
253 70 CONTINUE
254 Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
255 JX = JX + INCX
256 JY = JY + INCY
257 IF( J.GT.K ) THEN
258 KX = KX + INCX
259 KY = KY + INCY
260 END IF
261 80 CONTINUE
262 END IF
263 ELSE
264 *
265 * Form y when lower triangle of A is stored.
266 *
267 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
268 DO 100 J = 1, N
269 TEMP1 = ALPHA*X( J )
270 TEMP2 = ZERO
271 Y( J ) = Y( J ) + TEMP1*A( 1, J )
272 L = 1 - J
273 DO 90 I = J + 1, MIN( N, J+K )
274 Y( I ) = Y( I ) + TEMP1*A( L+I, J )
275 TEMP2 = TEMP2 + A( L+I, J )*X( I )
276 90 CONTINUE
277 Y( J ) = Y( J ) + ALPHA*TEMP2
278 100 CONTINUE
279 ELSE
280 JX = KX
281 JY = KY
282 DO 120 J = 1, N
283 TEMP1 = ALPHA*X( JX )
284 TEMP2 = ZERO
285 Y( JY ) = Y( JY ) + TEMP1*A( 1, J )
286 L = 1 - J
287 IX = JX
288 IY = JY
289 DO 110 I = J + 1, MIN( N, J+K )
290 IX = IX + INCX
291 IY = IY + INCY
292 Y( IY ) = Y( IY ) + TEMP1*A( L+I, J )
293 TEMP2 = TEMP2 + A( L+I, J )*X( IX )
294 110 CONTINUE
295 Y( JY ) = Y( JY ) + ALPHA*TEMP2
296 JX = JX + INCX
297 JY = JY + INCY
298 120 CONTINUE
299 END IF
300 END IF
301 *
302 RETURN
303 *
304 * End of CSBMV
305 *
306 END