1 SUBROUTINE STBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
2 * .. Scalar Arguments ..
3 INTEGER INCX,K,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STBSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*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 band matrix, with ( k + 1 )
19 * diagonals.
20 *
21 * No test for singularity or near-singularity is included in this
22 * routine. Such tests must be performed before calling this routine.
23 *
24 * Arguments
25 * ==========
26 *
27 * UPLO - CHARACTER*1.
28 * On entry, UPLO specifies whether the matrix is an upper or
29 * lower triangular matrix as follows:
30 *
31 * UPLO = 'U' or 'u' A is an upper triangular matrix.
32 *
33 * UPLO = 'L' or 'l' A is a lower triangular matrix.
34 *
35 * Unchanged on exit.
36 *
37 * TRANS - CHARACTER*1.
38 * On entry, TRANS specifies the equations to be solved as
39 * follows:
40 *
41 * TRANS = 'N' or 'n' A*x = b.
42 *
43 * TRANS = 'T' or 't' A**T*x = b.
44 *
45 * TRANS = 'C' or 'c' A**T*x = b.
46 *
47 * Unchanged on exit.
48 *
49 * DIAG - CHARACTER*1.
50 * On entry, DIAG specifies whether or not A is unit
51 * triangular as follows:
52 *
53 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
54 *
55 * DIAG = 'N' or 'n' A is not assumed to be unit
56 * triangular.
57 *
58 * Unchanged on exit.
59 *
60 * N - INTEGER.
61 * On entry, N specifies the order of the matrix A.
62 * N must be at least zero.
63 * Unchanged on exit.
64 *
65 * K - INTEGER.
66 * On entry with UPLO = 'U' or 'u', K specifies the number of
67 * super-diagonals of the matrix A.
68 * On entry with UPLO = 'L' or 'l', K specifies the number of
69 * sub-diagonals of the matrix A.
70 * K must satisfy 0 .le. K.
71 * Unchanged on exit.
72 *
73 * A - REAL array of DIMENSION ( LDA, n ).
74 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
75 * by n part of the array A must contain the upper triangular
76 * band part of the matrix of coefficients, supplied column by
77 * column, with the leading diagonal of the matrix in row
78 * ( k + 1 ) of the array, the first super-diagonal starting at
79 * position 2 in row k, and so on. The top left k by k triangle
80 * of the array A is not referenced.
81 * The following program segment will transfer an upper
82 * triangular band matrix from conventional full matrix storage
83 * to band storage:
84 *
85 * DO 20, J = 1, N
86 * M = K + 1 - J
87 * DO 10, I = MAX( 1, J - K ), J
88 * A( M + I, J ) = matrix( I, J )
89 * 10 CONTINUE
90 * 20 CONTINUE
91 *
92 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
93 * by n part of the array A must contain the lower triangular
94 * band part of the matrix of coefficients, supplied column by
95 * column, with the leading diagonal of the matrix in row 1 of
96 * the array, the first sub-diagonal starting at position 1 in
97 * row 2, and so on. The bottom right k by k triangle of the
98 * array A is not referenced.
99 * The following program segment will transfer a lower
100 * triangular band matrix from conventional full matrix storage
101 * to band storage:
102 *
103 * DO 20, J = 1, N
104 * M = 1 - J
105 * DO 10, I = J, MIN( N, J + K )
106 * A( M + I, J ) = matrix( I, J )
107 * 10 CONTINUE
108 * 20 CONTINUE
109 *
110 * Note that when DIAG = 'U' or 'u' the elements of the array A
111 * corresponding to the diagonal elements of the matrix are not
112 * referenced, but are assumed to be unity.
113 * Unchanged on exit.
114 *
115 * LDA - INTEGER.
116 * On entry, LDA specifies the first dimension of A as declared
117 * in the calling (sub) program. LDA must be at least
118 * ( k + 1 ).
119 * Unchanged on exit.
120 *
121 * X - REAL array of dimension at least
122 * ( 1 + ( n - 1 )*abs( INCX ) ).
123 * Before entry, the incremented array X must contain the n
124 * element right-hand side vector b. On exit, X is overwritten
125 * with the solution vector x.
126 *
127 * INCX - INTEGER.
128 * On entry, INCX specifies the increment for the elements of
129 * X. INCX must not be zero.
130 * Unchanged on exit.
131 *
132 * Further Details
133 * ===============
134 *
135 * Level 2 Blas routine.
136 *
137 * -- Written on 22-October-1986.
138 * Jack Dongarra, Argonne National Lab.
139 * Jeremy Du Croz, Nag Central Office.
140 * Sven Hammarling, Nag Central Office.
141 * Richard Hanson, Sandia National Labs.
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146 REAL ZERO
147 PARAMETER (ZERO=0.0E+0)
148 * ..
149 * .. Local Scalars ..
150 REAL TEMP
151 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
152 LOGICAL NOUNIT
153 * ..
154 * .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL LSAME
157 * ..
158 * .. External Subroutines ..
159 EXTERNAL XERBLA
160 * ..
161 * .. Intrinsic Functions ..
162 INTRINSIC MAX,MIN
163 * ..
164 *
165 * Test the input parameters.
166 *
167 INFO = 0
168 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
169 INFO = 1
170 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
171 + .NOT.LSAME(TRANS,'C')) THEN
172 INFO = 2
173 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
174 INFO = 3
175 ELSE IF (N.LT.0) THEN
176 INFO = 4
177 ELSE IF (K.LT.0) THEN
178 INFO = 5
179 ELSE IF (LDA.LT. (K+1)) THEN
180 INFO = 7
181 ELSE IF (INCX.EQ.0) THEN
182 INFO = 9
183 END IF
184 IF (INFO.NE.0) THEN
185 CALL XERBLA('STBSV ',INFO)
186 RETURN
187 END IF
188 *
189 * Quick return if possible.
190 *
191 IF (N.EQ.0) RETURN
192 *
193 NOUNIT = LSAME(DIAG,'N')
194 *
195 * Set up the start point in X if the increment is not unity. This
196 * will be ( N - 1 )*INCX too small for descending loops.
197 *
198 IF (INCX.LE.0) THEN
199 KX = 1 - (N-1)*INCX
200 ELSE IF (INCX.NE.1) THEN
201 KX = 1
202 END IF
203 *
204 * Start the operations. In this version the elements of A are
205 * accessed by sequentially with one pass through A.
206 *
207 IF (LSAME(TRANS,'N')) THEN
208 *
209 * Form x := inv( A )*x.
210 *
211 IF (LSAME(UPLO,'U')) THEN
212 KPLUS1 = K + 1
213 IF (INCX.EQ.1) THEN
214 DO 20 J = N,1,-1
215 IF (X(J).NE.ZERO) THEN
216 L = KPLUS1 - J
217 IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
218 TEMP = X(J)
219 DO 10 I = J - 1,MAX(1,J-K),-1
220 X(I) = X(I) - TEMP*A(L+I,J)
221 10 CONTINUE
222 END IF
223 20 CONTINUE
224 ELSE
225 KX = KX + (N-1)*INCX
226 JX = KX
227 DO 40 J = N,1,-1
228 KX = KX - INCX
229 IF (X(JX).NE.ZERO) THEN
230 IX = KX
231 L = KPLUS1 - J
232 IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
233 TEMP = X(JX)
234 DO 30 I = J - 1,MAX(1,J-K),-1
235 X(IX) = X(IX) - TEMP*A(L+I,J)
236 IX = IX - INCX
237 30 CONTINUE
238 END IF
239 JX = JX - INCX
240 40 CONTINUE
241 END IF
242 ELSE
243 IF (INCX.EQ.1) THEN
244 DO 60 J = 1,N
245 IF (X(J).NE.ZERO) THEN
246 L = 1 - J
247 IF (NOUNIT) X(J) = X(J)/A(1,J)
248 TEMP = X(J)
249 DO 50 I = J + 1,MIN(N,J+K)
250 X(I) = X(I) - TEMP*A(L+I,J)
251 50 CONTINUE
252 END IF
253 60 CONTINUE
254 ELSE
255 JX = KX
256 DO 80 J = 1,N
257 KX = KX + INCX
258 IF (X(JX).NE.ZERO) THEN
259 IX = KX
260 L = 1 - J
261 IF (NOUNIT) X(JX) = X(JX)/A(1,J)
262 TEMP = X(JX)
263 DO 70 I = J + 1,MIN(N,J+K)
264 X(IX) = X(IX) - TEMP*A(L+I,J)
265 IX = IX + INCX
266 70 CONTINUE
267 END IF
268 JX = JX + INCX
269 80 CONTINUE
270 END IF
271 END IF
272 ELSE
273 *
274 * Form x := inv( A**T)*x.
275 *
276 IF (LSAME(UPLO,'U')) THEN
277 KPLUS1 = K + 1
278 IF (INCX.EQ.1) THEN
279 DO 100 J = 1,N
280 TEMP = X(J)
281 L = KPLUS1 - J
282 DO 90 I = MAX(1,J-K),J - 1
283 TEMP = TEMP - A(L+I,J)*X(I)
284 90 CONTINUE
285 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
286 X(J) = TEMP
287 100 CONTINUE
288 ELSE
289 JX = KX
290 DO 120 J = 1,N
291 TEMP = X(JX)
292 IX = KX
293 L = KPLUS1 - J
294 DO 110 I = MAX(1,J-K),J - 1
295 TEMP = TEMP - A(L+I,J)*X(IX)
296 IX = IX + INCX
297 110 CONTINUE
298 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
299 X(JX) = TEMP
300 JX = JX + INCX
301 IF (J.GT.K) KX = KX + INCX
302 120 CONTINUE
303 END IF
304 ELSE
305 IF (INCX.EQ.1) THEN
306 DO 140 J = N,1,-1
307 TEMP = X(J)
308 L = 1 - J
309 DO 130 I = MIN(N,J+K),J + 1,-1
310 TEMP = TEMP - A(L+I,J)*X(I)
311 130 CONTINUE
312 IF (NOUNIT) TEMP = TEMP/A(1,J)
313 X(J) = TEMP
314 140 CONTINUE
315 ELSE
316 KX = KX + (N-1)*INCX
317 JX = KX
318 DO 160 J = N,1,-1
319 TEMP = X(JX)
320 IX = KX
321 L = 1 - J
322 DO 150 I = MIN(N,J+K),J + 1,-1
323 TEMP = TEMP - A(L+I,J)*X(IX)
324 IX = IX - INCX
325 150 CONTINUE
326 IF (NOUNIT) TEMP = TEMP/A(1,J)
327 X(JX) = TEMP
328 JX = JX - INCX
329 IF ((N-J).GE.K) KX = KX - INCX
330 160 CONTINUE
331 END IF
332 END IF
333 END IF
334 *
335 RETURN
336 *
337 * End of STBSV .
338 *
339 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,K,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STBSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*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 band matrix, with ( k + 1 )
19 * diagonals.
20 *
21 * No test for singularity or near-singularity is included in this
22 * routine. Such tests must be performed before calling this routine.
23 *
24 * Arguments
25 * ==========
26 *
27 * UPLO - CHARACTER*1.
28 * On entry, UPLO specifies whether the matrix is an upper or
29 * lower triangular matrix as follows:
30 *
31 * UPLO = 'U' or 'u' A is an upper triangular matrix.
32 *
33 * UPLO = 'L' or 'l' A is a lower triangular matrix.
34 *
35 * Unchanged on exit.
36 *
37 * TRANS - CHARACTER*1.
38 * On entry, TRANS specifies the equations to be solved as
39 * follows:
40 *
41 * TRANS = 'N' or 'n' A*x = b.
42 *
43 * TRANS = 'T' or 't' A**T*x = b.
44 *
45 * TRANS = 'C' or 'c' A**T*x = b.
46 *
47 * Unchanged on exit.
48 *
49 * DIAG - CHARACTER*1.
50 * On entry, DIAG specifies whether or not A is unit
51 * triangular as follows:
52 *
53 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
54 *
55 * DIAG = 'N' or 'n' A is not assumed to be unit
56 * triangular.
57 *
58 * Unchanged on exit.
59 *
60 * N - INTEGER.
61 * On entry, N specifies the order of the matrix A.
62 * N must be at least zero.
63 * Unchanged on exit.
64 *
65 * K - INTEGER.
66 * On entry with UPLO = 'U' or 'u', K specifies the number of
67 * super-diagonals of the matrix A.
68 * On entry with UPLO = 'L' or 'l', K specifies the number of
69 * sub-diagonals of the matrix A.
70 * K must satisfy 0 .le. K.
71 * Unchanged on exit.
72 *
73 * A - REAL array of DIMENSION ( LDA, n ).
74 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
75 * by n part of the array A must contain the upper triangular
76 * band part of the matrix of coefficients, supplied column by
77 * column, with the leading diagonal of the matrix in row
78 * ( k + 1 ) of the array, the first super-diagonal starting at
79 * position 2 in row k, and so on. The top left k by k triangle
80 * of the array A is not referenced.
81 * The following program segment will transfer an upper
82 * triangular band matrix from conventional full matrix storage
83 * to band storage:
84 *
85 * DO 20, J = 1, N
86 * M = K + 1 - J
87 * DO 10, I = MAX( 1, J - K ), J
88 * A( M + I, J ) = matrix( I, J )
89 * 10 CONTINUE
90 * 20 CONTINUE
91 *
92 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
93 * by n part of the array A must contain the lower triangular
94 * band part of the matrix of coefficients, supplied column by
95 * column, with the leading diagonal of the matrix in row 1 of
96 * the array, the first sub-diagonal starting at position 1 in
97 * row 2, and so on. The bottom right k by k triangle of the
98 * array A is not referenced.
99 * The following program segment will transfer a lower
100 * triangular band matrix from conventional full matrix storage
101 * to band storage:
102 *
103 * DO 20, J = 1, N
104 * M = 1 - J
105 * DO 10, I = J, MIN( N, J + K )
106 * A( M + I, J ) = matrix( I, J )
107 * 10 CONTINUE
108 * 20 CONTINUE
109 *
110 * Note that when DIAG = 'U' or 'u' the elements of the array A
111 * corresponding to the diagonal elements of the matrix are not
112 * referenced, but are assumed to be unity.
113 * Unchanged on exit.
114 *
115 * LDA - INTEGER.
116 * On entry, LDA specifies the first dimension of A as declared
117 * in the calling (sub) program. LDA must be at least
118 * ( k + 1 ).
119 * Unchanged on exit.
120 *
121 * X - REAL array of dimension at least
122 * ( 1 + ( n - 1 )*abs( INCX ) ).
123 * Before entry, the incremented array X must contain the n
124 * element right-hand side vector b. On exit, X is overwritten
125 * with the solution vector x.
126 *
127 * INCX - INTEGER.
128 * On entry, INCX specifies the increment for the elements of
129 * X. INCX must not be zero.
130 * Unchanged on exit.
131 *
132 * Further Details
133 * ===============
134 *
135 * Level 2 Blas routine.
136 *
137 * -- Written on 22-October-1986.
138 * Jack Dongarra, Argonne National Lab.
139 * Jeremy Du Croz, Nag Central Office.
140 * Sven Hammarling, Nag Central Office.
141 * Richard Hanson, Sandia National Labs.
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146 REAL ZERO
147 PARAMETER (ZERO=0.0E+0)
148 * ..
149 * .. Local Scalars ..
150 REAL TEMP
151 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
152 LOGICAL NOUNIT
153 * ..
154 * .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL LSAME
157 * ..
158 * .. External Subroutines ..
159 EXTERNAL XERBLA
160 * ..
161 * .. Intrinsic Functions ..
162 INTRINSIC MAX,MIN
163 * ..
164 *
165 * Test the input parameters.
166 *
167 INFO = 0
168 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
169 INFO = 1
170 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
171 + .NOT.LSAME(TRANS,'C')) THEN
172 INFO = 2
173 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
174 INFO = 3
175 ELSE IF (N.LT.0) THEN
176 INFO = 4
177 ELSE IF (K.LT.0) THEN
178 INFO = 5
179 ELSE IF (LDA.LT. (K+1)) THEN
180 INFO = 7
181 ELSE IF (INCX.EQ.0) THEN
182 INFO = 9
183 END IF
184 IF (INFO.NE.0) THEN
185 CALL XERBLA('STBSV ',INFO)
186 RETURN
187 END IF
188 *
189 * Quick return if possible.
190 *
191 IF (N.EQ.0) RETURN
192 *
193 NOUNIT = LSAME(DIAG,'N')
194 *
195 * Set up the start point in X if the increment is not unity. This
196 * will be ( N - 1 )*INCX too small for descending loops.
197 *
198 IF (INCX.LE.0) THEN
199 KX = 1 - (N-1)*INCX
200 ELSE IF (INCX.NE.1) THEN
201 KX = 1
202 END IF
203 *
204 * Start the operations. In this version the elements of A are
205 * accessed by sequentially with one pass through A.
206 *
207 IF (LSAME(TRANS,'N')) THEN
208 *
209 * Form x := inv( A )*x.
210 *
211 IF (LSAME(UPLO,'U')) THEN
212 KPLUS1 = K + 1
213 IF (INCX.EQ.1) THEN
214 DO 20 J = N,1,-1
215 IF (X(J).NE.ZERO) THEN
216 L = KPLUS1 - J
217 IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
218 TEMP = X(J)
219 DO 10 I = J - 1,MAX(1,J-K),-1
220 X(I) = X(I) - TEMP*A(L+I,J)
221 10 CONTINUE
222 END IF
223 20 CONTINUE
224 ELSE
225 KX = KX + (N-1)*INCX
226 JX = KX
227 DO 40 J = N,1,-1
228 KX = KX - INCX
229 IF (X(JX).NE.ZERO) THEN
230 IX = KX
231 L = KPLUS1 - J
232 IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
233 TEMP = X(JX)
234 DO 30 I = J - 1,MAX(1,J-K),-1
235 X(IX) = X(IX) - TEMP*A(L+I,J)
236 IX = IX - INCX
237 30 CONTINUE
238 END IF
239 JX = JX - INCX
240 40 CONTINUE
241 END IF
242 ELSE
243 IF (INCX.EQ.1) THEN
244 DO 60 J = 1,N
245 IF (X(J).NE.ZERO) THEN
246 L = 1 - J
247 IF (NOUNIT) X(J) = X(J)/A(1,J)
248 TEMP = X(J)
249 DO 50 I = J + 1,MIN(N,J+K)
250 X(I) = X(I) - TEMP*A(L+I,J)
251 50 CONTINUE
252 END IF
253 60 CONTINUE
254 ELSE
255 JX = KX
256 DO 80 J = 1,N
257 KX = KX + INCX
258 IF (X(JX).NE.ZERO) THEN
259 IX = KX
260 L = 1 - J
261 IF (NOUNIT) X(JX) = X(JX)/A(1,J)
262 TEMP = X(JX)
263 DO 70 I = J + 1,MIN(N,J+K)
264 X(IX) = X(IX) - TEMP*A(L+I,J)
265 IX = IX + INCX
266 70 CONTINUE
267 END IF
268 JX = JX + INCX
269 80 CONTINUE
270 END IF
271 END IF
272 ELSE
273 *
274 * Form x := inv( A**T)*x.
275 *
276 IF (LSAME(UPLO,'U')) THEN
277 KPLUS1 = K + 1
278 IF (INCX.EQ.1) THEN
279 DO 100 J = 1,N
280 TEMP = X(J)
281 L = KPLUS1 - J
282 DO 90 I = MAX(1,J-K),J - 1
283 TEMP = TEMP - A(L+I,J)*X(I)
284 90 CONTINUE
285 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
286 X(J) = TEMP
287 100 CONTINUE
288 ELSE
289 JX = KX
290 DO 120 J = 1,N
291 TEMP = X(JX)
292 IX = KX
293 L = KPLUS1 - J
294 DO 110 I = MAX(1,J-K),J - 1
295 TEMP = TEMP - A(L+I,J)*X(IX)
296 IX = IX + INCX
297 110 CONTINUE
298 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
299 X(JX) = TEMP
300 JX = JX + INCX
301 IF (J.GT.K) KX = KX + INCX
302 120 CONTINUE
303 END IF
304 ELSE
305 IF (INCX.EQ.1) THEN
306 DO 140 J = N,1,-1
307 TEMP = X(J)
308 L = 1 - J
309 DO 130 I = MIN(N,J+K),J + 1,-1
310 TEMP = TEMP - A(L+I,J)*X(I)
311 130 CONTINUE
312 IF (NOUNIT) TEMP = TEMP/A(1,J)
313 X(J) = TEMP
314 140 CONTINUE
315 ELSE
316 KX = KX + (N-1)*INCX
317 JX = KX
318 DO 160 J = N,1,-1
319 TEMP = X(JX)
320 IX = KX
321 L = 1 - J
322 DO 150 I = MIN(N,J+K),J + 1,-1
323 TEMP = TEMP - A(L+I,J)*X(IX)
324 IX = IX - INCX
325 150 CONTINUE
326 IF (NOUNIT) TEMP = TEMP/A(1,J)
327 X(JX) = TEMP
328 JX = JX - INCX
329 IF ((N-J).GE.K) KX = KX - INCX
330 160 CONTINUE
331 END IF
332 END IF
333 END IF
334 *
335 RETURN
336 *
337 * End of STBSV .
338 *
339 END