 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ ssbmv()

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

SSBMV

Purpose:
``` SSBMV  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 symmetric 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 REAL On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is REAL 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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``` [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 REAL 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 REAL On entry, BETA specifies the scalar beta.``` [in,out] Y ``` Y is REAL 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 183 of file ssbmv.f.

184 *
185 * -- Reference BLAS level2 routine --
186 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
187 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
188 *
189 * .. Scalar Arguments ..
190  REAL ALPHA,BETA
191  INTEGER INCX,INCY,K,LDA,N
192  CHARACTER UPLO
193 * ..
194 * .. Array Arguments ..
195  REAL A(LDA,*),X(*),Y(*)
196 * ..
197 *
198 * =====================================================================
199 *
200 * .. Parameters ..
201  REAL ONE,ZERO
202  parameter(one=1.0e+0,zero=0.0e+0)
203 * ..
204 * .. Local Scalars ..
205  REAL TEMP1,TEMP2
206  INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
207 * ..
208 * .. External Functions ..
209  LOGICAL LSAME
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL xerbla
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max,min
217 * ..
218 *
219 * Test the input parameters.
220 *
221  info = 0
222  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
223  info = 1
224  ELSE IF (n.LT.0) THEN
225  info = 2
226  ELSE IF (k.LT.0) THEN
227  info = 3
228  ELSE IF (lda.LT. (k+1)) THEN
229  info = 6
230  ELSE IF (incx.EQ.0) THEN
231  info = 8
232  ELSE IF (incy.EQ.0) THEN
233  info = 11
234  END IF
235  IF (info.NE.0) THEN
236  CALL xerbla('SSBMV ',info)
237  RETURN
238  END IF
239 *
240 * Quick return if possible.
241 *
242  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
243 *
244 * Set up the start points in X and Y.
245 *
246  IF (incx.GT.0) THEN
247  kx = 1
248  ELSE
249  kx = 1 - (n-1)*incx
250  END IF
251  IF (incy.GT.0) THEN
252  ky = 1
253  ELSE
254  ky = 1 - (n-1)*incy
255  END IF
256 *
257 * Start the operations. In this version the elements of the array A
258 * are accessed sequentially with one pass through A.
259 *
260 * First form y := beta*y.
261 *
262  IF (beta.NE.one) THEN
263  IF (incy.EQ.1) THEN
264  IF (beta.EQ.zero) THEN
265  DO 10 i = 1,n
266  y(i) = zero
267  10 CONTINUE
268  ELSE
269  DO 20 i = 1,n
270  y(i) = beta*y(i)
271  20 CONTINUE
272  END IF
273  ELSE
274  iy = ky
275  IF (beta.EQ.zero) THEN
276  DO 30 i = 1,n
277  y(iy) = zero
278  iy = iy + incy
279  30 CONTINUE
280  ELSE
281  DO 40 i = 1,n
282  y(iy) = beta*y(iy)
283  iy = iy + incy
284  40 CONTINUE
285  END IF
286  END IF
287  END IF
288  IF (alpha.EQ.zero) RETURN
289  IF (lsame(uplo,'U')) THEN
290 *
291 * Form y when upper triangle of A is stored.
292 *
293  kplus1 = k + 1
294  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
295  DO 60 j = 1,n
296  temp1 = alpha*x(j)
297  temp2 = zero
298  l = kplus1 - j
299  DO 50 i = max(1,j-k),j - 1
300  y(i) = y(i) + temp1*a(l+i,j)
301  temp2 = temp2 + a(l+i,j)*x(i)
302  50 CONTINUE
303  y(j) = y(j) + temp1*a(kplus1,j) + alpha*temp2
304  60 CONTINUE
305  ELSE
306  jx = kx
307  jy = ky
308  DO 80 j = 1,n
309  temp1 = alpha*x(jx)
310  temp2 = zero
311  ix = kx
312  iy = ky
313  l = kplus1 - j
314  DO 70 i = max(1,j-k),j - 1
315  y(iy) = y(iy) + temp1*a(l+i,j)
316  temp2 = temp2 + a(l+i,j)*x(ix)
317  ix = ix + incx
318  iy = iy + incy
319  70 CONTINUE
320  y(jy) = y(jy) + temp1*a(kplus1,j) + alpha*temp2
321  jx = jx + incx
322  jy = jy + incy
323  IF (j.GT.k) THEN
324  kx = kx + incx
325  ky = ky + incy
326  END IF
327  80 CONTINUE
328  END IF
329  ELSE
330 *
331 * Form y when lower triangle of A is stored.
332 *
333  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
334  DO 100 j = 1,n
335  temp1 = alpha*x(j)
336  temp2 = zero
337  y(j) = y(j) + temp1*a(1,j)
338  l = 1 - j
339  DO 90 i = j + 1,min(n,j+k)
340  y(i) = y(i) + temp1*a(l+i,j)
341  temp2 = temp2 + a(l+i,j)*x(i)
342  90 CONTINUE
343  y(j) = y(j) + alpha*temp2
344  100 CONTINUE
345  ELSE
346  jx = kx
347  jy = ky
348  DO 120 j = 1,n
349  temp1 = alpha*x(jx)
350  temp2 = zero
351  y(jy) = y(jy) + temp1*a(1,j)
352  l = 1 - j
353  ix = jx
354  iy = jy
355  DO 110 i = j + 1,min(n,j+k)
356  ix = ix + incx
357  iy = iy + incy
358  y(iy) = y(iy) + temp1*a(l+i,j)
359  temp2 = temp2 + a(l+i,j)*x(ix)
360  110 CONTINUE
361  y(jy) = y(jy) + alpha*temp2
362  jx = jx + incx
363  jy = jy + incy
364  120 CONTINUE
365  END IF
366  END IF
367 *
368  RETURN
369 *
370 * End of SSBMV
371 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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