 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ chbmv()

 subroutine chbmv ( character UPLO, integer N, integer K, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY )

CHBMV

Purpose:
``` CHBMV  performs the matrix-vector  operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian band matrix, with k super-diagonals.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied.``` [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, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.``` [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 hermitian matrix, 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 the upper triangular part of a hermitian 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 hermitian matrix, 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 the lower triangular part of a hermitian 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 the imaginary parts of the diagonal elements need not be set and are assumed to be zero.``` [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] X ``` X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta.``` [in,out] Y ``` Y is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY 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 186 of file chbmv.f.

187 *
188 * -- Reference BLAS level2 routine --
189 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
190 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191 *
192 * .. Scalar Arguments ..
193  COMPLEX ALPHA,BETA
194  INTEGER INCX,INCY,K,LDA,N
195  CHARACTER UPLO
196 * ..
197 * .. Array Arguments ..
198  COMPLEX A(LDA,*),X(*),Y(*)
199 * ..
200 *
201 * =====================================================================
202 *
203 * .. Parameters ..
204  COMPLEX ONE
205  parameter(one= (1.0e+0,0.0e+0))
206  COMPLEX ZERO
207  parameter(zero= (0.0e+0,0.0e+0))
208 * ..
209 * .. Local Scalars ..
210  COMPLEX TEMP1,TEMP2
211  INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
212 * ..
213 * .. External Functions ..
214  LOGICAL LSAME
215  EXTERNAL lsame
216 * ..
217 * .. External Subroutines ..
218  EXTERNAL xerbla
219 * ..
220 * .. Intrinsic Functions ..
221  INTRINSIC conjg,max,min,real
222 * ..
223 *
224 * Test the input parameters.
225 *
226  info = 0
227  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
228  info = 1
229  ELSE IF (n.LT.0) THEN
230  info = 2
231  ELSE IF (k.LT.0) THEN
232  info = 3
233  ELSE IF (lda.LT. (k+1)) THEN
234  info = 6
235  ELSE IF (incx.EQ.0) THEN
236  info = 8
237  ELSE IF (incy.EQ.0) THEN
238  info = 11
239  END IF
240  IF (info.NE.0) THEN
241  CALL xerbla('CHBMV ',info)
242  RETURN
243  END IF
244 *
245 * Quick return if possible.
246 *
247  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
248 *
249 * Set up the start points in X and Y.
250 *
251  IF (incx.GT.0) THEN
252  kx = 1
253  ELSE
254  kx = 1 - (n-1)*incx
255  END IF
256  IF (incy.GT.0) THEN
257  ky = 1
258  ELSE
259  ky = 1 - (n-1)*incy
260  END IF
261 *
262 * Start the operations. In this version the elements of the array A
263 * are accessed sequentially with one pass through A.
264 *
265 * First form y := beta*y.
266 *
267  IF (beta.NE.one) THEN
268  IF (incy.EQ.1) THEN
269  IF (beta.EQ.zero) THEN
270  DO 10 i = 1,n
271  y(i) = zero
272  10 CONTINUE
273  ELSE
274  DO 20 i = 1,n
275  y(i) = beta*y(i)
276  20 CONTINUE
277  END IF
278  ELSE
279  iy = ky
280  IF (beta.EQ.zero) THEN
281  DO 30 i = 1,n
282  y(iy) = zero
283  iy = iy + incy
284  30 CONTINUE
285  ELSE
286  DO 40 i = 1,n
287  y(iy) = beta*y(iy)
288  iy = iy + incy
289  40 CONTINUE
290  END IF
291  END IF
292  END IF
293  IF (alpha.EQ.zero) RETURN
294  IF (lsame(uplo,'U')) THEN
295 *
296 * Form y when upper triangle of A is stored.
297 *
298  kplus1 = k + 1
299  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
300  DO 60 j = 1,n
301  temp1 = alpha*x(j)
302  temp2 = zero
303  l = kplus1 - j
304  DO 50 i = max(1,j-k),j - 1
305  y(i) = y(i) + temp1*a(l+i,j)
306  temp2 = temp2 + conjg(a(l+i,j))*x(i)
307  50 CONTINUE
308  y(j) = y(j) + temp1*real(a(kplus1,j)) + alpha*temp2
309  60 CONTINUE
310  ELSE
311  jx = kx
312  jy = ky
313  DO 80 j = 1,n
314  temp1 = alpha*x(jx)
315  temp2 = zero
316  ix = kx
317  iy = ky
318  l = kplus1 - j
319  DO 70 i = max(1,j-k),j - 1
320  y(iy) = y(iy) + temp1*a(l+i,j)
321  temp2 = temp2 + conjg(a(l+i,j))*x(ix)
322  ix = ix + incx
323  iy = iy + incy
324  70 CONTINUE
325  y(jy) = y(jy) + temp1*real(a(kplus1,j)) + alpha*temp2
326  jx = jx + incx
327  jy = jy + incy
328  IF (j.GT.k) THEN
329  kx = kx + incx
330  ky = ky + incy
331  END IF
332  80 CONTINUE
333  END IF
334  ELSE
335 *
336 * Form y when lower triangle of A is stored.
337 *
338  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
339  DO 100 j = 1,n
340  temp1 = alpha*x(j)
341  temp2 = zero
342  y(j) = y(j) + temp1*real(a(1,j))
343  l = 1 - j
344  DO 90 i = j + 1,min(n,j+k)
345  y(i) = y(i) + temp1*a(l+i,j)
346  temp2 = temp2 + conjg(a(l+i,j))*x(i)
347  90 CONTINUE
348  y(j) = y(j) + alpha*temp2
349  100 CONTINUE
350  ELSE
351  jx = kx
352  jy = ky
353  DO 120 j = 1,n
354  temp1 = alpha*x(jx)
355  temp2 = zero
356  y(jy) = y(jy) + temp1*real(a(1,j))
357  l = 1 - j
358  ix = jx
359  iy = jy
360  DO 110 i = j + 1,min(n,j+k)
361  ix = ix + incx
362  iy = iy + incy
363  y(iy) = y(iy) + temp1*a(l+i,j)
364  temp2 = temp2 + conjg(a(l+i,j))*x(ix)
365  110 CONTINUE
366  y(jy) = y(jy) + alpha*temp2
367  jx = jx + incx
368  jy = jy + incy
369  120 CONTINUE
370  END IF
371  END IF
372 *
373  RETURN
374 *
375 * End of CHBMV
376 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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