 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine stbsv ( character UPLO, character TRANS, character DIAG, integer N, integer K, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX )

STBSV

Purpose:
``` STBSV  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 band matrix, with ( k + 1 )
diagonals.

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] K ``` K is INTEGER On entry with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K.``` [in] A ``` A is REAL array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer an upper triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, 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 ( k + 1 ).``` [in,out] X ``` X is REAL array of 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
November 2011
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 191 of file stbsv.f.

191 *
192 * -- Reference BLAS level2 routine (version 3.4.0) --
193 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * November 2011
196 *
197 * .. Scalar Arguments ..
198  INTEGER incx,k,lda,n
199  CHARACTER diag,trans,uplo
200 * ..
201 * .. Array Arguments ..
202  REAL a(lda,*),x(*)
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. Parameters ..
208  REAL zero
209  parameter(zero=0.0e+0)
210 * ..
211 * .. Local Scalars ..
212  REAL temp
213  INTEGER i,info,ix,j,jx,kplus1,kx,l
214  LOGICAL nounit
215 * ..
216 * .. External Functions ..
217  LOGICAL lsame
218  EXTERNAL lsame
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL xerbla
222 * ..
223 * .. Intrinsic Functions ..
224  INTRINSIC max,min
225 * ..
226 *
227 * Test the input parameters.
228 *
229  info = 0
230  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
231  info = 1
232  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
233  + .NOT.lsame(trans,'C')) THEN
234  info = 2
235  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
236  info = 3
237  ELSE IF (n.LT.0) THEN
238  info = 4
239  ELSE IF (k.LT.0) THEN
240  info = 5
241  ELSE IF (lda.LT. (k+1)) THEN
242  info = 7
243  ELSE IF (incx.EQ.0) THEN
244  info = 9
245  END IF
246  IF (info.NE.0) THEN
247  CALL xerbla('STBSV ',info)
248  RETURN
249  END IF
250 *
251 * Quick return if possible.
252 *
253  IF (n.EQ.0) RETURN
254 *
255  nounit = lsame(diag,'N')
256 *
257 * Set up the start point in X if the increment is not unity. This
258 * will be ( N - 1 )*INCX too small for descending loops.
259 *
260  IF (incx.LE.0) THEN
261  kx = 1 - (n-1)*incx
262  ELSE IF (incx.NE.1) THEN
263  kx = 1
264  END IF
265 *
266 * Start the operations. In this version the elements of A are
267 * accessed by sequentially with one pass through A.
268 *
269  IF (lsame(trans,'N')) THEN
270 *
271 * Form x := inv( A )*x.
272 *
273  IF (lsame(uplo,'U')) THEN
274  kplus1 = k + 1
275  IF (incx.EQ.1) THEN
276  DO 20 j = n,1,-1
277  IF (x(j).NE.zero) THEN
278  l = kplus1 - j
279  IF (nounit) x(j) = x(j)/a(kplus1,j)
280  temp = x(j)
281  DO 10 i = j - 1,max(1,j-k),-1
282  x(i) = x(i) - temp*a(l+i,j)
283  10 CONTINUE
284  END IF
285  20 CONTINUE
286  ELSE
287  kx = kx + (n-1)*incx
288  jx = kx
289  DO 40 j = n,1,-1
290  kx = kx - incx
291  IF (x(jx).NE.zero) THEN
292  ix = kx
293  l = kplus1 - j
294  IF (nounit) x(jx) = x(jx)/a(kplus1,j)
295  temp = x(jx)
296  DO 30 i = j - 1,max(1,j-k),-1
297  x(ix) = x(ix) - temp*a(l+i,j)
298  ix = ix - incx
299  30 CONTINUE
300  END IF
301  jx = jx - incx
302  40 CONTINUE
303  END IF
304  ELSE
305  IF (incx.EQ.1) THEN
306  DO 60 j = 1,n
307  IF (x(j).NE.zero) THEN
308  l = 1 - j
309  IF (nounit) x(j) = x(j)/a(1,j)
310  temp = x(j)
311  DO 50 i = j + 1,min(n,j+k)
312  x(i) = x(i) - temp*a(l+i,j)
313  50 CONTINUE
314  END IF
315  60 CONTINUE
316  ELSE
317  jx = kx
318  DO 80 j = 1,n
319  kx = kx + incx
320  IF (x(jx).NE.zero) THEN
321  ix = kx
322  l = 1 - j
323  IF (nounit) x(jx) = x(jx)/a(1,j)
324  temp = x(jx)
325  DO 70 i = j + 1,min(n,j+k)
326  x(ix) = x(ix) - temp*a(l+i,j)
327  ix = ix + incx
328  70 CONTINUE
329  END IF
330  jx = jx + incx
331  80 CONTINUE
332  END IF
333  END IF
334  ELSE
335 *
336 * Form x := inv( A**T)*x.
337 *
338  IF (lsame(uplo,'U')) THEN
339  kplus1 = k + 1
340  IF (incx.EQ.1) THEN
341  DO 100 j = 1,n
342  temp = x(j)
343  l = kplus1 - j
344  DO 90 i = max(1,j-k),j - 1
345  temp = temp - a(l+i,j)*x(i)
346  90 CONTINUE
347  IF (nounit) temp = temp/a(kplus1,j)
348  x(j) = temp
349  100 CONTINUE
350  ELSE
351  jx = kx
352  DO 120 j = 1,n
353  temp = x(jx)
354  ix = kx
355  l = kplus1 - j
356  DO 110 i = max(1,j-k),j - 1
357  temp = temp - a(l+i,j)*x(ix)
358  ix = ix + incx
359  110 CONTINUE
360  IF (nounit) temp = temp/a(kplus1,j)
361  x(jx) = temp
362  jx = jx + incx
363  IF (j.GT.k) kx = kx + incx
364  120 CONTINUE
365  END IF
366  ELSE
367  IF (incx.EQ.1) THEN
368  DO 140 j = n,1,-1
369  temp = x(j)
370  l = 1 - j
371  DO 130 i = min(n,j+k),j + 1,-1
372  temp = temp - a(l+i,j)*x(i)
373  130 CONTINUE
374  IF (nounit) temp = temp/a(1,j)
375  x(j) = temp
376  140 CONTINUE
377  ELSE
378  kx = kx + (n-1)*incx
379  jx = kx
380  DO 160 j = n,1,-1
381  temp = x(jx)
382  ix = kx
383  l = 1 - j
384  DO 150 i = min(n,j+k),j + 1,-1
385  temp = temp - a(l+i,j)*x(ix)
386  ix = ix - incx
387  150 CONTINUE
388  IF (nounit) temp = temp/a(1,j)
389  x(jx) = temp
390  jx = jx - incx
391  IF ((n-j).GE.k) kx = kx - incx
392  160 CONTINUE
393  END IF
394  END IF
395  END IF
396 *
397  RETURN
398 *
399 * End of STBSV .
400 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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