LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ ctbmv()

 subroutine ctbmv ( character UPLO, character TRANS, character DIAG, integer N, integer K, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX )

CTBMV

Purpose:
``` CTBMV  performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and  A is an n by n unit, or non-unit,
upper or lower triangular band matrix, with ( k + 1 ) diagonals.```
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 operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**H*x.``` [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 COMPLEX array, 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 COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.```
Further Details:
```  Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 185 of file ctbmv.f.

186 *
187 * -- Reference BLAS level2 routine --
188 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
189 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190 *
191 * .. Scalar Arguments ..
192  INTEGER INCX,K,LDA,N
193  CHARACTER DIAG,TRANS,UPLO
194 * ..
195 * .. Array Arguments ..
196  COMPLEX A(LDA,*),X(*)
197 * ..
198 *
199 * =====================================================================
200 *
201 * .. Parameters ..
202  COMPLEX ZERO
203  parameter(zero= (0.0e+0,0.0e+0))
204 * ..
205 * .. Local Scalars ..
206  COMPLEX TEMP
207  INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
208  LOGICAL NOCONJ,NOUNIT
209 * ..
210 * .. External Functions ..
211  LOGICAL LSAME
212  EXTERNAL lsame
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL xerbla
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC conjg,max,min
219 * ..
220 *
221 * Test the input parameters.
222 *
223  info = 0
224  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
225  info = 1
226  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
227  + .NOT.lsame(trans,'C')) THEN
228  info = 2
229  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
230  info = 3
231  ELSE IF (n.LT.0) THEN
232  info = 4
233  ELSE IF (k.LT.0) THEN
234  info = 5
235  ELSE IF (lda.LT. (k+1)) THEN
236  info = 7
237  ELSE IF (incx.EQ.0) THEN
238  info = 9
239  END IF
240  IF (info.NE.0) THEN
241  CALL xerbla('CTBMV ',info)
242  RETURN
243  END IF
244 *
245 * Quick return if possible.
246 *
247  IF (n.EQ.0) RETURN
248 *
249  noconj = lsame(trans,'T')
250  nounit = lsame(diag,'N')
251 *
252 * Set up the start point in X if the increment is not unity. This
253 * will be ( N - 1 )*INCX too small for descending loops.
254 *
255  IF (incx.LE.0) THEN
256  kx = 1 - (n-1)*incx
257  ELSE IF (incx.NE.1) THEN
258  kx = 1
259  END IF
260 *
261 * Start the operations. In this version the elements of A are
262 * accessed sequentially with one pass through A.
263 *
264  IF (lsame(trans,'N')) THEN
265 *
266 * Form x := A*x.
267 *
268  IF (lsame(uplo,'U')) THEN
269  kplus1 = k + 1
270  IF (incx.EQ.1) THEN
271  DO 20 j = 1,n
272  IF (x(j).NE.zero) THEN
273  temp = x(j)
274  l = kplus1 - j
275  DO 10 i = max(1,j-k),j - 1
276  x(i) = x(i) + temp*a(l+i,j)
277  10 CONTINUE
278  IF (nounit) x(j) = x(j)*a(kplus1,j)
279  END IF
280  20 CONTINUE
281  ELSE
282  jx = kx
283  DO 40 j = 1,n
284  IF (x(jx).NE.zero) THEN
285  temp = x(jx)
286  ix = kx
287  l = kplus1 - j
288  DO 30 i = max(1,j-k),j - 1
289  x(ix) = x(ix) + temp*a(l+i,j)
290  ix = ix + incx
291  30 CONTINUE
292  IF (nounit) x(jx) = x(jx)*a(kplus1,j)
293  END IF
294  jx = jx + incx
295  IF (j.GT.k) kx = kx + incx
296  40 CONTINUE
297  END IF
298  ELSE
299  IF (incx.EQ.1) THEN
300  DO 60 j = n,1,-1
301  IF (x(j).NE.zero) THEN
302  temp = x(j)
303  l = 1 - j
304  DO 50 i = min(n,j+k),j + 1,-1
305  x(i) = x(i) + temp*a(l+i,j)
306  50 CONTINUE
307  IF (nounit) x(j) = x(j)*a(1,j)
308  END IF
309  60 CONTINUE
310  ELSE
311  kx = kx + (n-1)*incx
312  jx = kx
313  DO 80 j = n,1,-1
314  IF (x(jx).NE.zero) THEN
315  temp = x(jx)
316  ix = kx
317  l = 1 - j
318  DO 70 i = min(n,j+k),j + 1,-1
319  x(ix) = x(ix) + temp*a(l+i,j)
320  ix = ix - incx
321  70 CONTINUE
322  IF (nounit) x(jx) = x(jx)*a(1,j)
323  END IF
324  jx = jx - incx
325  IF ((n-j).GE.k) kx = kx - incx
326  80 CONTINUE
327  END IF
328  END IF
329  ELSE
330 *
331 * Form x := A**T*x or x := A**H*x.
332 *
333  IF (lsame(uplo,'U')) THEN
334  kplus1 = k + 1
335  IF (incx.EQ.1) THEN
336  DO 110 j = n,1,-1
337  temp = x(j)
338  l = kplus1 - j
339  IF (noconj) THEN
340  IF (nounit) temp = temp*a(kplus1,j)
341  DO 90 i = j - 1,max(1,j-k),-1
342  temp = temp + a(l+i,j)*x(i)
343  90 CONTINUE
344  ELSE
345  IF (nounit) temp = temp*conjg(a(kplus1,j))
346  DO 100 i = j - 1,max(1,j-k),-1
347  temp = temp + conjg(a(l+i,j))*x(i)
348  100 CONTINUE
349  END IF
350  x(j) = temp
351  110 CONTINUE
352  ELSE
353  kx = kx + (n-1)*incx
354  jx = kx
355  DO 140 j = n,1,-1
356  temp = x(jx)
357  kx = kx - incx
358  ix = kx
359  l = kplus1 - j
360  IF (noconj) THEN
361  IF (nounit) temp = temp*a(kplus1,j)
362  DO 120 i = j - 1,max(1,j-k),-1
363  temp = temp + a(l+i,j)*x(ix)
364  ix = ix - incx
365  120 CONTINUE
366  ELSE
367  IF (nounit) temp = temp*conjg(a(kplus1,j))
368  DO 130 i = j - 1,max(1,j-k),-1
369  temp = temp + conjg(a(l+i,j))*x(ix)
370  ix = ix - incx
371  130 CONTINUE
372  END IF
373  x(jx) = temp
374  jx = jx - incx
375  140 CONTINUE
376  END IF
377  ELSE
378  IF (incx.EQ.1) THEN
379  DO 170 j = 1,n
380  temp = x(j)
381  l = 1 - j
382  IF (noconj) THEN
383  IF (nounit) temp = temp*a(1,j)
384  DO 150 i = j + 1,min(n,j+k)
385  temp = temp + a(l+i,j)*x(i)
386  150 CONTINUE
387  ELSE
388  IF (nounit) temp = temp*conjg(a(1,j))
389  DO 160 i = j + 1,min(n,j+k)
390  temp = temp + conjg(a(l+i,j))*x(i)
391  160 CONTINUE
392  END IF
393  x(j) = temp
394  170 CONTINUE
395  ELSE
396  jx = kx
397  DO 200 j = 1,n
398  temp = x(jx)
399  kx = kx + incx
400  ix = kx
401  l = 1 - j
402  IF (noconj) THEN
403  IF (nounit) temp = temp*a(1,j)
404  DO 180 i = j + 1,min(n,j+k)
405  temp = temp + a(l+i,j)*x(ix)
406  ix = ix + incx
407  180 CONTINUE
408  ELSE
409  IF (nounit) temp = temp*conjg(a(1,j))
410  DO 190 i = j + 1,min(n,j+k)
411  temp = temp + conjg(a(l+i,j))*x(ix)
412  ix = ix + incx
413  190 CONTINUE
414  END IF
415  x(jx) = temp
416  jx = jx + incx
417  200 CONTINUE
418  END IF
419  END IF
420  END IF
421 *
422  RETURN
423 *
424 * End of CTBMV
425 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
Here is the call graph for this function:
Here is the caller graph for this function: