Annotation of rpl/lapack/blas/zhbmv.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZHBMV
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: * Definition:
! 9: * ===========
! 10: *
! 11: * SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * COMPLEX*16 ALPHA,BETA
! 15: * INTEGER INCX,INCY,K,LDA,N
! 16: * CHARACTER UPLO
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> ZHBMV performs the matrix-vector operation
! 29: *>
! 30: *> y := alpha*A*x + beta*y,
! 31: *>
! 32: *> where alpha and beta are scalars, x and y are n element vectors and
! 33: *> A is an n by n hermitian band matrix, with k super-diagonals.
! 34: *> \endverbatim
! 35: *
! 36: * Arguments:
! 37: * ==========
! 38: *
! 39: *> \param[in] UPLO
! 40: *> \verbatim
! 41: *> UPLO is CHARACTER*1
! 42: *> On entry, UPLO specifies whether the upper or lower
! 43: *> triangular part of the band matrix A is being supplied as
! 44: *> follows:
! 45: *>
! 46: *> UPLO = 'U' or 'u' The upper triangular part of A is
! 47: *> being supplied.
! 48: *>
! 49: *> UPLO = 'L' or 'l' The lower triangular part of A is
! 50: *> being supplied.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] N
! 54: *> \verbatim
! 55: *> N is INTEGER
! 56: *> On entry, N specifies the order of the matrix A.
! 57: *> N must be at least zero.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] K
! 61: *> \verbatim
! 62: *> K is INTEGER
! 63: *> On entry, K specifies the number of super-diagonals of the
! 64: *> matrix A. K must satisfy 0 .le. K.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] ALPHA
! 68: *> \verbatim
! 69: *> ALPHA is COMPLEX*16
! 70: *> On entry, ALPHA specifies the scalar alpha.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] A
! 74: *> \verbatim
! 75: *> A is COMPLEX*16 array of DIMENSION ( LDA, n ).
! 76: *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
! 77: *> by n part of the array A must contain the upper triangular
! 78: *> band part of the hermitian matrix, supplied column by
! 79: *> column, with the leading diagonal of the matrix in row
! 80: *> ( k + 1 ) of the array, the first super-diagonal starting at
! 81: *> position 2 in row k, and so on. The top left k by k triangle
! 82: *> of the array A is not referenced.
! 83: *> The following program segment will transfer the upper
! 84: *> triangular part of a hermitian band matrix from conventional
! 85: *> full matrix storage to band storage:
! 86: *>
! 87: *> DO 20, J = 1, N
! 88: *> M = K + 1 - J
! 89: *> DO 10, I = MAX( 1, J - K ), J
! 90: *> A( M + I, J ) = matrix( I, J )
! 91: *> 10 CONTINUE
! 92: *> 20 CONTINUE
! 93: *>
! 94: *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
! 95: *> by n part of the array A must contain the lower triangular
! 96: *> band part of the hermitian matrix, supplied column by
! 97: *> column, with the leading diagonal of the matrix in row 1 of
! 98: *> the array, the first sub-diagonal starting at position 1 in
! 99: *> row 2, and so on. The bottom right k by k triangle of the
! 100: *> array A is not referenced.
! 101: *> The following program segment will transfer the lower
! 102: *> triangular part of a hermitian band matrix from conventional
! 103: *> full matrix storage to band storage:
! 104: *>
! 105: *> DO 20, J = 1, N
! 106: *> M = 1 - J
! 107: *> DO 10, I = J, MIN( N, J + K )
! 108: *> A( M + I, J ) = matrix( I, J )
! 109: *> 10 CONTINUE
! 110: *> 20 CONTINUE
! 111: *>
! 112: *> Note that the imaginary parts of the diagonal elements need
! 113: *> not be set and are assumed to be zero.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] LDA
! 117: *> \verbatim
! 118: *> LDA is INTEGER
! 119: *> On entry, LDA specifies the first dimension of A as declared
! 120: *> in the calling (sub) program. LDA must be at least
! 121: *> ( k + 1 ).
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[in] X
! 125: *> \verbatim
! 126: *> X is COMPLEX*16 array of DIMENSION at least
! 127: *> ( 1 + ( n - 1 )*abs( INCX ) ).
! 128: *> Before entry, the incremented array X must contain the
! 129: *> vector x.
! 130: *> \endverbatim
! 131: *>
! 132: *> \param[in] INCX
! 133: *> \verbatim
! 134: *> INCX is INTEGER
! 135: *> On entry, INCX specifies the increment for the elements of
! 136: *> X. INCX must not be zero.
! 137: *> \endverbatim
! 138: *>
! 139: *> \param[in] BETA
! 140: *> \verbatim
! 141: *> BETA is COMPLEX*16
! 142: *> On entry, BETA specifies the scalar beta.
! 143: *> \endverbatim
! 144: *>
! 145: *> \param[in,out] Y
! 146: *> \verbatim
! 147: *> Y is COMPLEX*16 array of DIMENSION at least
! 148: *> ( 1 + ( n - 1 )*abs( INCY ) ).
! 149: *> Before entry, the incremented array Y must contain the
! 150: *> vector y. On exit, Y is overwritten by the updated vector y.
! 151: *> \endverbatim
! 152: *>
! 153: *> \param[in] INCY
! 154: *> \verbatim
! 155: *> INCY is INTEGER
! 156: *> On entry, INCY specifies the increment for the elements of
! 157: *> Y. INCY must not be zero.
! 158: *> \endverbatim
! 159: *
! 160: * Authors:
! 161: * ========
! 162: *
! 163: *> \author Univ. of Tennessee
! 164: *> \author Univ. of California Berkeley
! 165: *> \author Univ. of Colorado Denver
! 166: *> \author NAG Ltd.
! 167: *
! 168: *> \date November 2011
! 169: *
! 170: *> \ingroup complex16_blas_level2
! 171: *
! 172: *> \par Further Details:
! 173: * =====================
! 174: *>
! 175: *> \verbatim
! 176: *>
! 177: *> Level 2 Blas routine.
! 178: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
! 179: *>
! 180: *> -- Written on 22-October-1986.
! 181: *> Jack Dongarra, Argonne National Lab.
! 182: *> Jeremy Du Croz, Nag Central Office.
! 183: *> Sven Hammarling, Nag Central Office.
! 184: *> Richard Hanson, Sandia National Labs.
! 185: *> \endverbatim
! 186: *>
! 187: * =====================================================================
1.1 bertrand 188: SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
1.8 ! bertrand 189: *
! 190: * -- Reference BLAS level2 routine (version 3.4.0) --
! 191: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 192: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 193: * November 2011
! 194: *
1.1 bertrand 195: * .. Scalar Arguments ..
1.8 ! bertrand 196: COMPLEX*16 ALPHA,BETA
1.1 bertrand 197: INTEGER INCX,INCY,K,LDA,N
198: CHARACTER UPLO
199: * ..
200: * .. Array Arguments ..
1.8 ! bertrand 201: COMPLEX*16 A(LDA,*),X(*),Y(*)
1.1 bertrand 202: * ..
203: *
204: * =====================================================================
205: *
206: * .. Parameters ..
1.8 ! bertrand 207: COMPLEX*16 ONE
1.1 bertrand 208: PARAMETER (ONE= (1.0D+0,0.0D+0))
1.8 ! bertrand 209: COMPLEX*16 ZERO
1.1 bertrand 210: PARAMETER (ZERO= (0.0D+0,0.0D+0))
211: * ..
212: * .. Local Scalars ..
1.8 ! bertrand 213: COMPLEX*16 TEMP1,TEMP2
1.1 bertrand 214: INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: EXTERNAL LSAME
219: * ..
220: * .. External Subroutines ..
221: EXTERNAL XERBLA
222: * ..
223: * .. Intrinsic Functions ..
224: INTRINSIC DBLE,DCONJG,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 (N.LT.0) THEN
233: INFO = 2
234: ELSE IF (K.LT.0) THEN
235: INFO = 3
236: ELSE IF (LDA.LT. (K+1)) THEN
237: INFO = 6
238: ELSE IF (INCX.EQ.0) THEN
239: INFO = 8
240: ELSE IF (INCY.EQ.0) THEN
241: INFO = 11
242: END IF
243: IF (INFO.NE.0) THEN
244: CALL XERBLA('ZHBMV ',INFO)
245: RETURN
246: END IF
247: *
248: * Quick return if possible.
249: *
250: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
251: *
252: * Set up the start points in X and Y.
253: *
254: IF (INCX.GT.0) THEN
255: KX = 1
256: ELSE
257: KX = 1 - (N-1)*INCX
258: END IF
259: IF (INCY.GT.0) THEN
260: KY = 1
261: ELSE
262: KY = 1 - (N-1)*INCY
263: END IF
264: *
265: * Start the operations. In this version the elements of the array A
266: * are accessed sequentially with one pass through A.
267: *
268: * First form y := beta*y.
269: *
270: IF (BETA.NE.ONE) THEN
271: IF (INCY.EQ.1) THEN
272: IF (BETA.EQ.ZERO) THEN
273: DO 10 I = 1,N
274: Y(I) = ZERO
275: 10 CONTINUE
276: ELSE
277: DO 20 I = 1,N
278: Y(I) = BETA*Y(I)
279: 20 CONTINUE
280: END IF
281: ELSE
282: IY = KY
283: IF (BETA.EQ.ZERO) THEN
284: DO 30 I = 1,N
285: Y(IY) = ZERO
286: IY = IY + INCY
287: 30 CONTINUE
288: ELSE
289: DO 40 I = 1,N
290: Y(IY) = BETA*Y(IY)
291: IY = IY + INCY
292: 40 CONTINUE
293: END IF
294: END IF
295: END IF
296: IF (ALPHA.EQ.ZERO) RETURN
297: IF (LSAME(UPLO,'U')) THEN
298: *
299: * Form y when upper triangle of A is stored.
300: *
301: KPLUS1 = K + 1
302: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
303: DO 60 J = 1,N
304: TEMP1 = ALPHA*X(J)
305: TEMP2 = ZERO
306: L = KPLUS1 - J
307: DO 50 I = MAX(1,J-K),J - 1
308: Y(I) = Y(I) + TEMP1*A(L+I,J)
309: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
310: 50 CONTINUE
311: Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
312: 60 CONTINUE
313: ELSE
314: JX = KX
315: JY = KY
316: DO 80 J = 1,N
317: TEMP1 = ALPHA*X(JX)
318: TEMP2 = ZERO
319: IX = KX
320: IY = KY
321: L = KPLUS1 - J
322: DO 70 I = MAX(1,J-K),J - 1
323: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
324: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
325: IX = IX + INCX
326: IY = IY + INCY
327: 70 CONTINUE
328: Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
329: JX = JX + INCX
330: JY = JY + INCY
331: IF (J.GT.K) THEN
332: KX = KX + INCX
333: KY = KY + INCY
334: END IF
335: 80 CONTINUE
336: END IF
337: ELSE
338: *
339: * Form y when lower triangle of A is stored.
340: *
341: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
342: DO 100 J = 1,N
343: TEMP1 = ALPHA*X(J)
344: TEMP2 = ZERO
345: Y(J) = Y(J) + TEMP1*DBLE(A(1,J))
346: L = 1 - J
347: DO 90 I = J + 1,MIN(N,J+K)
348: Y(I) = Y(I) + TEMP1*A(L+I,J)
349: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
350: 90 CONTINUE
351: Y(J) = Y(J) + ALPHA*TEMP2
352: 100 CONTINUE
353: ELSE
354: JX = KX
355: JY = KY
356: DO 120 J = 1,N
357: TEMP1 = ALPHA*X(JX)
358: TEMP2 = ZERO
359: Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J))
360: L = 1 - J
361: IX = JX
362: IY = JY
363: DO 110 I = J + 1,MIN(N,J+K)
364: IX = IX + INCX
365: IY = IY + INCY
366: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
367: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
368: 110 CONTINUE
369: Y(JY) = Y(JY) + ALPHA*TEMP2
370: JX = JX + INCX
371: JY = JY + INCY
372: 120 CONTINUE
373: END IF
374: END IF
375: *
376: RETURN
377: *
378: * End of ZHBMV .
379: *
380: END
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