Annotation of rpl/lapack/blas/zgbmv.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZGBMV
! 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 ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * COMPLEX*16 ALPHA,BETA
! 15: * INTEGER INCX,INCY,KL,KU,LDA,M,N
! 16: * CHARACTER TRANS
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> ZGBMV performs one of the matrix-vector operations
! 29: *>
! 30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
! 31: *>
! 32: *> y := alpha*A**H*x + beta*y,
! 33: *>
! 34: *> where alpha and beta are scalars, x and y are vectors and A is an
! 35: *> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
! 36: *> \endverbatim
! 37: *
! 38: * Arguments:
! 39: * ==========
! 40: *
! 41: *> \param[in] TRANS
! 42: *> \verbatim
! 43: *> TRANS is CHARACTER*1
! 44: *> On entry, TRANS specifies the operation to be performed as
! 45: *> follows:
! 46: *>
! 47: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
! 48: *>
! 49: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
! 50: *>
! 51: *> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] M
! 55: *> \verbatim
! 56: *> M is INTEGER
! 57: *> On entry, M specifies the number of rows of the matrix A.
! 58: *> M must be at least zero.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> On entry, N specifies the number of columns of the matrix A.
! 65: *> N must be at least zero.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] KL
! 69: *> \verbatim
! 70: *> KL is INTEGER
! 71: *> On entry, KL specifies the number of sub-diagonals of the
! 72: *> matrix A. KL must satisfy 0 .le. KL.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] KU
! 76: *> \verbatim
! 77: *> KU is INTEGER
! 78: *> On entry, KU specifies the number of super-diagonals of the
! 79: *> matrix A. KU must satisfy 0 .le. KU.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] ALPHA
! 83: *> \verbatim
! 84: *> ALPHA is COMPLEX*16
! 85: *> On entry, ALPHA specifies the scalar alpha.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] A
! 89: *> \verbatim
! 90: *> A is COMPLEX*16 array of DIMENSION ( LDA, n ).
! 91: *> Before entry, the leading ( kl + ku + 1 ) by n part of the
! 92: *> array A must contain the matrix of coefficients, supplied
! 93: *> column by column, with the leading diagonal of the matrix in
! 94: *> row ( ku + 1 ) of the array, the first super-diagonal
! 95: *> starting at position 2 in row ku, the first sub-diagonal
! 96: *> starting at position 1 in row ( ku + 2 ), and so on.
! 97: *> Elements in the array A that do not correspond to elements
! 98: *> in the band matrix (such as the top left ku by ku triangle)
! 99: *> are not referenced.
! 100: *> The following program segment will transfer a band matrix
! 101: *> from conventional full matrix storage to band storage:
! 102: *>
! 103: *> DO 20, J = 1, N
! 104: *> K = KU + 1 - J
! 105: *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
! 106: *> A( K + I, J ) = matrix( I, J )
! 107: *> 10 CONTINUE
! 108: *> 20 CONTINUE
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] LDA
! 112: *> \verbatim
! 113: *> LDA is INTEGER
! 114: *> On entry, LDA specifies the first dimension of A as declared
! 115: *> in the calling (sub) program. LDA must be at least
! 116: *> ( kl + ku + 1 ).
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[in] X
! 120: *> \verbatim
! 121: *> X is COMPLEX*16 array of DIMENSION at least
! 122: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
! 123: *> and at least
! 124: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
! 125: *> Before entry, the incremented array X must contain the
! 126: *> vector x.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] INCX
! 130: *> \verbatim
! 131: *> INCX is INTEGER
! 132: *> On entry, INCX specifies the increment for the elements of
! 133: *> X. INCX must not be zero.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[in] BETA
! 137: *> \verbatim
! 138: *> BETA is COMPLEX*16
! 139: *> On entry, BETA specifies the scalar beta. When BETA is
! 140: *> supplied as zero then Y need not be set on input.
! 141: *> \endverbatim
! 142: *>
! 143: *> \param[in,out] Y
! 144: *> \verbatim
! 145: *> Y is COMPLEX*16 array of DIMENSION at least
! 146: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
! 147: *> and at least
! 148: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
! 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 ZGBMV(TRANS,M,N,KL,KU,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,KL,KU,LDA,M,N
198: CHARACTER TRANS
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 TEMP
1.1 bertrand 214: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
215: LOGICAL NOCONJ
216: * ..
217: * .. External Functions ..
218: LOGICAL LSAME
219: EXTERNAL LSAME
220: * ..
221: * .. External Subroutines ..
222: EXTERNAL XERBLA
223: * ..
224: * .. Intrinsic Functions ..
225: INTRINSIC DCONJG,MAX,MIN
226: * ..
227: *
228: * Test the input parameters.
229: *
230: INFO = 0
231: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
232: + .NOT.LSAME(TRANS,'C')) THEN
233: INFO = 1
234: ELSE IF (M.LT.0) THEN
235: INFO = 2
236: ELSE IF (N.LT.0) THEN
237: INFO = 3
238: ELSE IF (KL.LT.0) THEN
239: INFO = 4
240: ELSE IF (KU.LT.0) THEN
241: INFO = 5
242: ELSE IF (LDA.LT. (KL+KU+1)) THEN
243: INFO = 8
244: ELSE IF (INCX.EQ.0) THEN
245: INFO = 10
246: ELSE IF (INCY.EQ.0) THEN
247: INFO = 13
248: END IF
249: IF (INFO.NE.0) THEN
250: CALL XERBLA('ZGBMV ',INFO)
251: RETURN
252: END IF
253: *
254: * Quick return if possible.
255: *
256: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
257: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
258: *
259: NOCONJ = LSAME(TRANS,'T')
260: *
261: * Set LENX and LENY, the lengths of the vectors x and y, and set
262: * up the start points in X and Y.
263: *
264: IF (LSAME(TRANS,'N')) THEN
265: LENX = N
266: LENY = M
267: ELSE
268: LENX = M
269: LENY = N
270: END IF
271: IF (INCX.GT.0) THEN
272: KX = 1
273: ELSE
274: KX = 1 - (LENX-1)*INCX
275: END IF
276: IF (INCY.GT.0) THEN
277: KY = 1
278: ELSE
279: KY = 1 - (LENY-1)*INCY
280: END IF
281: *
282: * Start the operations. In this version the elements of A are
283: * accessed sequentially with one pass through the band part of A.
284: *
285: * First form y := beta*y.
286: *
287: IF (BETA.NE.ONE) THEN
288: IF (INCY.EQ.1) THEN
289: IF (BETA.EQ.ZERO) THEN
290: DO 10 I = 1,LENY
291: Y(I) = ZERO
292: 10 CONTINUE
293: ELSE
294: DO 20 I = 1,LENY
295: Y(I) = BETA*Y(I)
296: 20 CONTINUE
297: END IF
298: ELSE
299: IY = KY
300: IF (BETA.EQ.ZERO) THEN
301: DO 30 I = 1,LENY
302: Y(IY) = ZERO
303: IY = IY + INCY
304: 30 CONTINUE
305: ELSE
306: DO 40 I = 1,LENY
307: Y(IY) = BETA*Y(IY)
308: IY = IY + INCY
309: 40 CONTINUE
310: END IF
311: END IF
312: END IF
313: IF (ALPHA.EQ.ZERO) RETURN
314: KUP1 = KU + 1
315: IF (LSAME(TRANS,'N')) THEN
316: *
317: * Form y := alpha*A*x + y.
318: *
319: JX = KX
320: IF (INCY.EQ.1) THEN
321: DO 60 J = 1,N
322: IF (X(JX).NE.ZERO) THEN
323: TEMP = ALPHA*X(JX)
324: K = KUP1 - J
325: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
326: Y(I) = Y(I) + TEMP*A(K+I,J)
327: 50 CONTINUE
328: END IF
329: JX = JX + INCX
330: 60 CONTINUE
331: ELSE
332: DO 80 J = 1,N
333: IF (X(JX).NE.ZERO) THEN
334: TEMP = ALPHA*X(JX)
335: IY = KY
336: K = KUP1 - J
337: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
338: Y(IY) = Y(IY) + TEMP*A(K+I,J)
339: IY = IY + INCY
340: 70 CONTINUE
341: END IF
342: JX = JX + INCX
343: IF (J.GT.KU) KY = KY + INCY
344: 80 CONTINUE
345: END IF
346: ELSE
347: *
1.7 bertrand 348: * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
1.1 bertrand 349: *
350: JY = KY
351: IF (INCX.EQ.1) THEN
352: DO 110 J = 1,N
353: TEMP = ZERO
354: K = KUP1 - J
355: IF (NOCONJ) THEN
356: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
357: TEMP = TEMP + A(K+I,J)*X(I)
358: 90 CONTINUE
359: ELSE
360: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
361: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
362: 100 CONTINUE
363: END IF
364: Y(JY) = Y(JY) + ALPHA*TEMP
365: JY = JY + INCY
366: 110 CONTINUE
367: ELSE
368: DO 140 J = 1,N
369: TEMP = ZERO
370: IX = KX
371: K = KUP1 - J
372: IF (NOCONJ) THEN
373: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
374: TEMP = TEMP + A(K+I,J)*X(IX)
375: IX = IX + INCX
376: 120 CONTINUE
377: ELSE
378: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
379: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
380: IX = IX + INCX
381: 130 CONTINUE
382: END IF
383: Y(JY) = Y(JY) + ALPHA*TEMP
384: JY = JY + INCY
385: IF (J.GT.KU) KX = KX + INCX
386: 140 CONTINUE
387: END IF
388: END IF
389: *
390: RETURN
391: *
392: * End of ZGBMV .
393: *
394: END
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