 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ strsv()

 subroutine strsv ( character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX )

STRSV

Purpose:
``` STRSV  solves one of the systems of equations

A*x = b,   or   A**T*x = b,

where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.

No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.``` [in] TRANS ``` TRANS is CHARACTER*1 On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**T*x = b.``` [in] DIAG ``` DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.``` [in] A ``` A is REAL array, dimension ( LDA, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).``` [in,out] X ``` X is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.```
Date
December 2016
Further Details:
```  Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.```

Definition at line 151 of file strsv.f.

151 *
152 * -- Reference BLAS level2 routine (version 3.7.0) --
153 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 * December 2016
156 *
157 * .. Scalar Arguments ..
158  INTEGER incx,lda,n
159  CHARACTER diag,trans,uplo
160 * ..
161 * .. Array Arguments ..
162  REAL a(lda,*),x(*)
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  REAL zero
169  parameter(zero=0.0e+0)
170 * ..
171 * .. Local Scalars ..
172  REAL temp
173  INTEGER i,info,ix,j,jx,kx
174  LOGICAL nounit
175 * ..
176 * .. External Functions ..
177  LOGICAL lsame
178  EXTERNAL lsame
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL xerbla
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 *
187 * Test the input parameters.
188 *
189  info = 0
190  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
191  info = 1
192  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
193  + .NOT.lsame(trans,'C')) THEN
194  info = 2
195  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
196  info = 3
197  ELSE IF (n.LT.0) THEN
198  info = 4
199  ELSE IF (lda.LT.max(1,n)) THEN
200  info = 6
201  ELSE IF (incx.EQ.0) THEN
202  info = 8
203  END IF
204  IF (info.NE.0) THEN
205  CALL xerbla('STRSV ',info)
206  RETURN
207  END IF
208 *
209 * Quick return if possible.
210 *
211  IF (n.EQ.0) RETURN
212 *
213  nounit = lsame(diag,'N')
214 *
215 * Set up the start point in X if the increment is not unity. This
216 * will be ( N - 1 )*INCX too small for descending loops.
217 *
218  IF (incx.LE.0) THEN
219  kx = 1 - (n-1)*incx
220  ELSE IF (incx.NE.1) THEN
221  kx = 1
222  END IF
223 *
224 * Start the operations. In this version the elements of A are
225 * accessed sequentially with one pass through A.
226 *
227  IF (lsame(trans,'N')) THEN
228 *
229 * Form x := inv( A )*x.
230 *
231  IF (lsame(uplo,'U')) THEN
232  IF (incx.EQ.1) THEN
233  DO 20 j = n,1,-1
234  IF (x(j).NE.zero) THEN
235  IF (nounit) x(j) = x(j)/a(j,j)
236  temp = x(j)
237  DO 10 i = j - 1,1,-1
238  x(i) = x(i) - temp*a(i,j)
239  10 CONTINUE
240  END IF
241  20 CONTINUE
242  ELSE
243  jx = kx + (n-1)*incx
244  DO 40 j = n,1,-1
245  IF (x(jx).NE.zero) THEN
246  IF (nounit) x(jx) = x(jx)/a(j,j)
247  temp = x(jx)
248  ix = jx
249  DO 30 i = j - 1,1,-1
250  ix = ix - incx
251  x(ix) = x(ix) - temp*a(i,j)
252  30 CONTINUE
253  END IF
254  jx = jx - incx
255  40 CONTINUE
256  END IF
257  ELSE
258  IF (incx.EQ.1) THEN
259  DO 60 j = 1,n
260  IF (x(j).NE.zero) THEN
261  IF (nounit) x(j) = x(j)/a(j,j)
262  temp = x(j)
263  DO 50 i = j + 1,n
264  x(i) = x(i) - temp*a(i,j)
265  50 CONTINUE
266  END IF
267  60 CONTINUE
268  ELSE
269  jx = kx
270  DO 80 j = 1,n
271  IF (x(jx).NE.zero) THEN
272  IF (nounit) x(jx) = x(jx)/a(j,j)
273  temp = x(jx)
274  ix = jx
275  DO 70 i = j + 1,n
276  ix = ix + incx
277  x(ix) = x(ix) - temp*a(i,j)
278  70 CONTINUE
279  END IF
280  jx = jx + incx
281  80 CONTINUE
282  END IF
283  END IF
284  ELSE
285 *
286 * Form x := inv( A**T )*x.
287 *
288  IF (lsame(uplo,'U')) THEN
289  IF (incx.EQ.1) THEN
290  DO 100 j = 1,n
291  temp = x(j)
292  DO 90 i = 1,j - 1
293  temp = temp - a(i,j)*x(i)
294  90 CONTINUE
295  IF (nounit) temp = temp/a(j,j)
296  x(j) = temp
297  100 CONTINUE
298  ELSE
299  jx = kx
300  DO 120 j = 1,n
301  temp = x(jx)
302  ix = kx
303  DO 110 i = 1,j - 1
304  temp = temp - a(i,j)*x(ix)
305  ix = ix + incx
306  110 CONTINUE
307  IF (nounit) temp = temp/a(j,j)
308  x(jx) = temp
309  jx = jx + incx
310  120 CONTINUE
311  END IF
312  ELSE
313  IF (incx.EQ.1) THEN
314  DO 140 j = n,1,-1
315  temp = x(j)
316  DO 130 i = n,j + 1,-1
317  temp = temp - a(i,j)*x(i)
318  130 CONTINUE
319  IF (nounit) temp = temp/a(j,j)
320  x(j) = temp
321  140 CONTINUE
322  ELSE
323  kx = kx + (n-1)*incx
324  jx = kx
325  DO 160 j = n,1,-1
326  temp = x(jx)
327  ix = kx
328  DO 150 i = n,j + 1,-1
329  temp = temp - a(i,j)*x(ix)
330  ix = ix - incx
331  150 CONTINUE
332  IF (nounit) temp = temp/a(j,j)
333  x(jx) = temp
334  jx = jx - incx
335  160 CONTINUE
336  END IF
337  END IF
338  END IF
339 *
340  RETURN
341 *
342 * End of STRSV .
343 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
Here is the call graph for this function:
Here is the caller graph for this function: