Annotation of rpl/lapack/blas/dgbmv.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DGBMV
! 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 DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * DOUBLE PRECISION ALPHA,BETA
! 15: * INTEGER INCX,INCY,KL,KU,LDA,M,N
! 16: * CHARACTER TRANS
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> DGBMV performs one of the matrix-vector operations
! 29: *>
! 30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
! 31: *>
! 32: *> where alpha and beta are scalars, x and y are vectors and A is an
! 33: *> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
! 34: *> \endverbatim
! 35: *
! 36: * Arguments:
! 37: * ==========
! 38: *
! 39: *> \param[in] TRANS
! 40: *> \verbatim
! 41: *> TRANS is CHARACTER*1
! 42: *> On entry, TRANS specifies the operation to be performed as
! 43: *> follows:
! 44: *>
! 45: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
! 46: *>
! 47: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
! 48: *>
! 49: *> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] M
! 53: *> \verbatim
! 54: *> M is INTEGER
! 55: *> On entry, M specifies the number of rows of the matrix A.
! 56: *> M must be at least zero.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] N
! 60: *> \verbatim
! 61: *> N is INTEGER
! 62: *> On entry, N specifies the number of columns of the matrix A.
! 63: *> N must be at least zero.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in] KL
! 67: *> \verbatim
! 68: *> KL is INTEGER
! 69: *> On entry, KL specifies the number of sub-diagonals of the
! 70: *> matrix A. KL must satisfy 0 .le. KL.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] KU
! 74: *> \verbatim
! 75: *> KU is INTEGER
! 76: *> On entry, KU specifies the number of super-diagonals of the
! 77: *> matrix A. KU must satisfy 0 .le. KU.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] ALPHA
! 81: *> \verbatim
! 82: *> ALPHA is DOUBLE PRECISION.
! 83: *> On entry, ALPHA specifies the scalar alpha.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] A
! 87: *> \verbatim
! 88: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
! 89: *> Before entry, the leading ( kl + ku + 1 ) by n part of the
! 90: *> array A must contain the matrix of coefficients, supplied
! 91: *> column by column, with the leading diagonal of the matrix in
! 92: *> row ( ku + 1 ) of the array, the first super-diagonal
! 93: *> starting at position 2 in row ku, the first sub-diagonal
! 94: *> starting at position 1 in row ( ku + 2 ), and so on.
! 95: *> Elements in the array A that do not correspond to elements
! 96: *> in the band matrix (such as the top left ku by ku triangle)
! 97: *> are not referenced.
! 98: *> The following program segment will transfer a band matrix
! 99: *> from conventional full matrix storage to band storage:
! 100: *>
! 101: *> DO 20, J = 1, N
! 102: *> K = KU + 1 - J
! 103: *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
! 104: *> A( K + I, J ) = matrix( I, J )
! 105: *> 10 CONTINUE
! 106: *> 20 CONTINUE
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] LDA
! 110: *> \verbatim
! 111: *> LDA is INTEGER
! 112: *> On entry, LDA specifies the first dimension of A as declared
! 113: *> in the calling (sub) program. LDA must be at least
! 114: *> ( kl + ku + 1 ).
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] X
! 118: *> \verbatim
! 119: *> X is DOUBLE PRECISION array of DIMENSION at least
! 120: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
! 121: *> and at least
! 122: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
! 123: *> Before entry, the incremented array X must contain the
! 124: *> vector x.
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[in] INCX
! 128: *> \verbatim
! 129: *> INCX is INTEGER
! 130: *> On entry, INCX specifies the increment for the elements of
! 131: *> X. INCX must not be zero.
! 132: *> \endverbatim
! 133: *>
! 134: *> \param[in] BETA
! 135: *> \verbatim
! 136: *> BETA is DOUBLE PRECISION.
! 137: *> On entry, BETA specifies the scalar beta. When BETA is
! 138: *> supplied as zero then Y need not be set on input.
! 139: *> \endverbatim
! 140: *>
! 141: *> \param[in,out] Y
! 142: *> \verbatim
! 143: *> Y is DOUBLE PRECISION array of DIMENSION at least
! 144: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
! 145: *> and at least
! 146: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
! 147: *> Before entry, the incremented array Y must contain the
! 148: *> vector y. On exit, Y is overwritten by the updated vector y.
! 149: *> \endverbatim
! 150: *>
! 151: *> \param[in] INCY
! 152: *> \verbatim
! 153: *> INCY is INTEGER
! 154: *> On entry, INCY specifies the increment for the elements of
! 155: *> Y. INCY must not be zero.
! 156: *> \endverbatim
! 157: *
! 158: * Authors:
! 159: * ========
! 160: *
! 161: *> \author Univ. of Tennessee
! 162: *> \author Univ. of California Berkeley
! 163: *> \author Univ. of Colorado Denver
! 164: *> \author NAG Ltd.
! 165: *
! 166: *> \date November 2011
! 167: *
! 168: *> \ingroup double_blas_level2
! 169: *
! 170: *> \par Further Details:
! 171: * =====================
! 172: *>
! 173: *> \verbatim
! 174: *>
! 175: *> Level 2 Blas routine.
! 176: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
! 177: *>
! 178: *> -- Written on 22-October-1986.
! 179: *> Jack Dongarra, Argonne National Lab.
! 180: *> Jeremy Du Croz, Nag Central Office.
! 181: *> Sven Hammarling, Nag Central Office.
! 182: *> Richard Hanson, Sandia National Labs.
! 183: *> \endverbatim
! 184: *>
! 185: * =====================================================================
1.1 bertrand 186: SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
1.8 ! bertrand 187: *
! 188: * -- Reference BLAS level2 routine (version 3.4.0) --
! 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: * November 2011
! 192: *
1.1 bertrand 193: * .. Scalar Arguments ..
194: DOUBLE PRECISION ALPHA,BETA
195: INTEGER INCX,INCY,KL,KU,LDA,M,N
196: CHARACTER TRANS
197: * ..
198: * .. Array Arguments ..
199: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
200: * ..
201: *
202: * =====================================================================
203: *
204: * .. Parameters ..
205: DOUBLE PRECISION ONE,ZERO
206: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
207: * ..
208: * .. Local Scalars ..
209: DOUBLE PRECISION TEMP
210: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
211: * ..
212: * .. External Functions ..
213: LOGICAL LSAME
214: EXTERNAL LSAME
215: * ..
216: * .. External Subroutines ..
217: EXTERNAL XERBLA
218: * ..
219: * .. Intrinsic Functions ..
220: INTRINSIC MAX,MIN
221: * ..
222: *
223: * Test the input parameters.
224: *
225: INFO = 0
226: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
227: + .NOT.LSAME(TRANS,'C')) THEN
228: INFO = 1
229: ELSE IF (M.LT.0) THEN
230: INFO = 2
231: ELSE IF (N.LT.0) THEN
232: INFO = 3
233: ELSE IF (KL.LT.0) THEN
234: INFO = 4
235: ELSE IF (KU.LT.0) THEN
236: INFO = 5
237: ELSE IF (LDA.LT. (KL+KU+1)) THEN
238: INFO = 8
239: ELSE IF (INCX.EQ.0) THEN
240: INFO = 10
241: ELSE IF (INCY.EQ.0) THEN
242: INFO = 13
243: END IF
244: IF (INFO.NE.0) THEN
245: CALL XERBLA('DGBMV ',INFO)
246: RETURN
247: END IF
248: *
249: * Quick return if possible.
250: *
251: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
252: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
253: *
254: * Set LENX and LENY, the lengths of the vectors x and y, and set
255: * up the start points in X and Y.
256: *
257: IF (LSAME(TRANS,'N')) THEN
258: LENX = N
259: LENY = M
260: ELSE
261: LENX = M
262: LENY = N
263: END IF
264: IF (INCX.GT.0) THEN
265: KX = 1
266: ELSE
267: KX = 1 - (LENX-1)*INCX
268: END IF
269: IF (INCY.GT.0) THEN
270: KY = 1
271: ELSE
272: KY = 1 - (LENY-1)*INCY
273: END IF
274: *
275: * Start the operations. In this version the elements of A are
276: * accessed sequentially with one pass through the band part of A.
277: *
278: * First form y := beta*y.
279: *
280: IF (BETA.NE.ONE) THEN
281: IF (INCY.EQ.1) THEN
282: IF (BETA.EQ.ZERO) THEN
283: DO 10 I = 1,LENY
284: Y(I) = ZERO
285: 10 CONTINUE
286: ELSE
287: DO 20 I = 1,LENY
288: Y(I) = BETA*Y(I)
289: 20 CONTINUE
290: END IF
291: ELSE
292: IY = KY
293: IF (BETA.EQ.ZERO) THEN
294: DO 30 I = 1,LENY
295: Y(IY) = ZERO
296: IY = IY + INCY
297: 30 CONTINUE
298: ELSE
299: DO 40 I = 1,LENY
300: Y(IY) = BETA*Y(IY)
301: IY = IY + INCY
302: 40 CONTINUE
303: END IF
304: END IF
305: END IF
306: IF (ALPHA.EQ.ZERO) RETURN
307: KUP1 = KU + 1
308: IF (LSAME(TRANS,'N')) THEN
309: *
310: * Form y := alpha*A*x + y.
311: *
312: JX = KX
313: IF (INCY.EQ.1) THEN
314: DO 60 J = 1,N
315: IF (X(JX).NE.ZERO) THEN
316: TEMP = ALPHA*X(JX)
317: K = KUP1 - J
318: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
319: Y(I) = Y(I) + TEMP*A(K+I,J)
320: 50 CONTINUE
321: END IF
322: JX = JX + INCX
323: 60 CONTINUE
324: ELSE
325: DO 80 J = 1,N
326: IF (X(JX).NE.ZERO) THEN
327: TEMP = ALPHA*X(JX)
328: IY = KY
329: K = KUP1 - J
330: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
331: Y(IY) = Y(IY) + TEMP*A(K+I,J)
332: IY = IY + INCY
333: 70 CONTINUE
334: END IF
335: JX = JX + INCX
336: IF (J.GT.KU) KY = KY + INCY
337: 80 CONTINUE
338: END IF
339: ELSE
340: *
1.7 bertrand 341: * Form y := alpha*A**T*x + y.
1.1 bertrand 342: *
343: JY = KY
344: IF (INCX.EQ.1) THEN
345: DO 100 J = 1,N
346: TEMP = ZERO
347: K = KUP1 - J
348: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
349: TEMP = TEMP + A(K+I,J)*X(I)
350: 90 CONTINUE
351: Y(JY) = Y(JY) + ALPHA*TEMP
352: JY = JY + INCY
353: 100 CONTINUE
354: ELSE
355: DO 120 J = 1,N
356: TEMP = ZERO
357: IX = KX
358: K = KUP1 - J
359: DO 110 I = MAX(1,J-KU),MIN(M,J+KL)
360: TEMP = TEMP + A(K+I,J)*X(IX)
361: IX = IX + INCX
362: 110 CONTINUE
363: Y(JY) = Y(JY) + ALPHA*TEMP
364: JY = JY + INCY
365: IF (J.GT.KU) KX = KX + INCX
366: 120 CONTINUE
367: END IF
368: END IF
369: *
370: RETURN
371: *
372: * End of DGBMV .
373: *
374: END
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