LAPACK  3.9.1
LAPACK: Linear Algebra PACKage
strsv.f
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1 *> \brief \b STRSV
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER INCX,LDA,N
15 * CHARACTER DIAG,TRANS,UPLO
16 * ..
17 * .. Array Arguments ..
18 * REAL A(LDA,*),X(*)
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> STRSV solves one of the systems of equations
28 *>
29 *> A*x = b, or A**T*x = b,
30 *>
31 *> where b and x are n element vectors and A is an n by n unit, or
32 *> non-unit, upper or lower triangular matrix.
33 *>
34 *> No test for singularity or near-singularity is included in this
35 *> routine. Such tests must be performed before calling this routine.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] UPLO
42 *> \verbatim
43 *> UPLO is CHARACTER*1
44 *> On entry, UPLO specifies whether the matrix is an upper or
45 *> lower triangular matrix as follows:
46 *>
47 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
48 *>
49 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
50 *> \endverbatim
51 *>
52 *> \param[in] TRANS
53 *> \verbatim
54 *> TRANS is CHARACTER*1
55 *> On entry, TRANS specifies the equations to be solved as
56 *> follows:
57 *>
58 *> TRANS = 'N' or 'n' A*x = b.
59 *>
60 *> TRANS = 'T' or 't' A**T*x = b.
61 *>
62 *> TRANS = 'C' or 'c' A**T*x = b.
63 *> \endverbatim
64 *>
65 *> \param[in] DIAG
66 *> \verbatim
67 *> DIAG is CHARACTER*1
68 *> On entry, DIAG specifies whether or not A is unit
69 *> triangular as follows:
70 *>
71 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
72 *>
73 *> DIAG = 'N' or 'n' A is not assumed to be unit
74 *> triangular.
75 *> \endverbatim
76 *>
77 *> \param[in] N
78 *> \verbatim
79 *> N is INTEGER
80 *> On entry, N specifies the order of the matrix A.
81 *> N must be at least zero.
82 *> \endverbatim
83 *>
84 *> \param[in] A
85 *> \verbatim
86 *> A is REAL array, dimension ( LDA, N )
87 *> Before entry with UPLO = 'U' or 'u', the leading n by n
88 *> upper triangular part of the array A must contain the upper
89 *> triangular matrix and the strictly lower triangular part of
90 *> A is not referenced.
91 *> Before entry with UPLO = 'L' or 'l', the leading n by n
92 *> lower triangular part of the array A must contain the lower
93 *> triangular matrix and the strictly upper triangular part of
94 *> A is not referenced.
95 *> Note that when DIAG = 'U' or 'u', the diagonal elements of
96 *> A are not referenced either, but are assumed to be unity.
97 *> \endverbatim
98 *>
99 *> \param[in] LDA
100 *> \verbatim
101 *> LDA is INTEGER
102 *> On entry, LDA specifies the first dimension of A as declared
103 *> in the calling (sub) program. LDA must be at least
104 *> max( 1, n ).
105 *> \endverbatim
106 *>
107 *> \param[in,out] X
108 *> \verbatim
109 *> X is REAL array, dimension at least
110 *> ( 1 + ( n - 1 )*abs( INCX ) ).
111 *> Before entry, the incremented array X must contain the n
112 *> element right-hand side vector b. On exit, X is overwritten
113 *> with the solution vector x.
114 *> \endverbatim
115 *>
116 *> \param[in] INCX
117 *> \verbatim
118 *> INCX is INTEGER
119 *> On entry, INCX specifies the increment for the elements of
120 *> X. INCX must not be zero.
121 *> \endverbatim
122 *
123 * Authors:
124 * ========
125 *
126 *> \author Univ. of Tennessee
127 *> \author Univ. of California Berkeley
128 *> \author Univ. of Colorado Denver
129 *> \author NAG Ltd.
130 *
131 *> \ingroup single_blas_level2
132 *
133 *> \par Further Details:
134 * =====================
135 *>
136 *> \verbatim
137 *>
138 *> Level 2 Blas routine.
139 *>
140 *> -- Written on 22-October-1986.
141 *> Jack Dongarra, Argonne National Lab.
142 *> Jeremy Du Croz, Nag Central Office.
143 *> Sven Hammarling, Nag Central Office.
144 *> Richard Hanson, Sandia National Labs.
145 *> \endverbatim
146 *>
147 * =====================================================================
148  SUBROUTINE strsv(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
149 *
150 * -- Reference BLAS level2 routine --
151 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  INTEGER INCX,LDA,N
156  CHARACTER DIAG,TRANS,UPLO
157 * ..
158 * .. Array Arguments ..
159  REAL A(LDA,*),X(*)
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  REAL ZERO
166  parameter(zero=0.0e+0)
167 * ..
168 * .. Local Scalars ..
169  REAL TEMP
170  INTEGER I,INFO,IX,J,JX,KX
171  LOGICAL NOUNIT
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max
182 * ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
188  info = 1
189  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
190  + .NOT.lsame(trans,'C')) THEN
191  info = 2
192  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
193  info = 3
194  ELSE IF (n.LT.0) THEN
195  info = 4
196  ELSE IF (lda.LT.max(1,n)) THEN
197  info = 6
198  ELSE IF (incx.EQ.0) THEN
199  info = 8
200  END IF
201  IF (info.NE.0) THEN
202  CALL xerbla('STRSV ',info)
203  RETURN
204  END IF
205 *
206 * Quick return if possible.
207 *
208  IF (n.EQ.0) RETURN
209 *
210  nounit = lsame(diag,'N')
211 *
212 * Set up the start point in X if the increment is not unity. This
213 * will be ( N - 1 )*INCX too small for descending loops.
214 *
215  IF (incx.LE.0) THEN
216  kx = 1 - (n-1)*incx
217  ELSE IF (incx.NE.1) THEN
218  kx = 1
219  END IF
220 *
221 * Start the operations. In this version the elements of A are
222 * accessed sequentially with one pass through A.
223 *
224  IF (lsame(trans,'N')) THEN
225 *
226 * Form x := inv( A )*x.
227 *
228  IF (lsame(uplo,'U')) THEN
229  IF (incx.EQ.1) THEN
230  DO 20 j = n,1,-1
231  IF (x(j).NE.zero) THEN
232  IF (nounit) x(j) = x(j)/a(j,j)
233  temp = x(j)
234  DO 10 i = j - 1,1,-1
235  x(i) = x(i) - temp*a(i,j)
236  10 CONTINUE
237  END IF
238  20 CONTINUE
239  ELSE
240  jx = kx + (n-1)*incx
241  DO 40 j = n,1,-1
242  IF (x(jx).NE.zero) THEN
243  IF (nounit) x(jx) = x(jx)/a(j,j)
244  temp = x(jx)
245  ix = jx
246  DO 30 i = j - 1,1,-1
247  ix = ix - incx
248  x(ix) = x(ix) - temp*a(i,j)
249  30 CONTINUE
250  END IF
251  jx = jx - incx
252  40 CONTINUE
253  END IF
254  ELSE
255  IF (incx.EQ.1) THEN
256  DO 60 j = 1,n
257  IF (x(j).NE.zero) THEN
258  IF (nounit) x(j) = x(j)/a(j,j)
259  temp = x(j)
260  DO 50 i = j + 1,n
261  x(i) = x(i) - temp*a(i,j)
262  50 CONTINUE
263  END IF
264  60 CONTINUE
265  ELSE
266  jx = kx
267  DO 80 j = 1,n
268  IF (x(jx).NE.zero) THEN
269  IF (nounit) x(jx) = x(jx)/a(j,j)
270  temp = x(jx)
271  ix = jx
272  DO 70 i = j + 1,n
273  ix = ix + incx
274  x(ix) = x(ix) - temp*a(i,j)
275  70 CONTINUE
276  END IF
277  jx = jx + incx
278  80 CONTINUE
279  END IF
280  END IF
281  ELSE
282 *
283 * Form x := inv( A**T )*x.
284 *
285  IF (lsame(uplo,'U')) THEN
286  IF (incx.EQ.1) THEN
287  DO 100 j = 1,n
288  temp = x(j)
289  DO 90 i = 1,j - 1
290  temp = temp - a(i,j)*x(i)
291  90 CONTINUE
292  IF (nounit) temp = temp/a(j,j)
293  x(j) = temp
294  100 CONTINUE
295  ELSE
296  jx = kx
297  DO 120 j = 1,n
298  temp = x(jx)
299  ix = kx
300  DO 110 i = 1,j - 1
301  temp = temp - a(i,j)*x(ix)
302  ix = ix + incx
303  110 CONTINUE
304  IF (nounit) temp = temp/a(j,j)
305  x(jx) = temp
306  jx = jx + incx
307  120 CONTINUE
308  END IF
309  ELSE
310  IF (incx.EQ.1) THEN
311  DO 140 j = n,1,-1
312  temp = x(j)
313  DO 130 i = n,j + 1,-1
314  temp = temp - a(i,j)*x(i)
315  130 CONTINUE
316  IF (nounit) temp = temp/a(j,j)
317  x(j) = temp
318  140 CONTINUE
319  ELSE
320  kx = kx + (n-1)*incx
321  jx = kx
322  DO 160 j = n,1,-1
323  temp = x(jx)
324  ix = kx
325  DO 150 i = n,j + 1,-1
326  temp = temp - a(i,j)*x(ix)
327  ix = ix - incx
328  150 CONTINUE
329  IF (nounit) temp = temp/a(j,j)
330  x(jx) = temp
331  jx = jx - incx
332  160 CONTINUE
333  END IF
334  END IF
335  END IF
336 *
337  RETURN
338 *
339 * End of STRSV .
340 *
341  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine strsv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRSV
Definition: strsv.f:149