Annotation of rpl/lapack/blas/dgemm.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DGEMM
! 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 DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * DOUBLE PRECISION ALPHA,BETA
! 15: * INTEGER K,LDA,LDB,LDC,M,N
! 16: * CHARACTER TRANSA,TRANSB
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> DGEMM performs one of the matrix-matrix operations
! 29: *>
! 30: *> C := alpha*op( A )*op( B ) + beta*C,
! 31: *>
! 32: *> where op( X ) is one of
! 33: *>
! 34: *> op( X ) = X or op( X ) = X**T,
! 35: *>
! 36: *> alpha and beta are scalars, and A, B and C are matrices, with op( A )
! 37: *> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] TRANSA
! 44: *> \verbatim
! 45: *> TRANSA is CHARACTER*1
! 46: *> On entry, TRANSA specifies the form of op( A ) to be used in
! 47: *> the matrix multiplication as follows:
! 48: *>
! 49: *> TRANSA = 'N' or 'n', op( A ) = A.
! 50: *>
! 51: *> TRANSA = 'T' or 't', op( A ) = A**T.
! 52: *>
! 53: *> TRANSA = 'C' or 'c', op( A ) = A**T.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] TRANSB
! 57: *> \verbatim
! 58: *> TRANSB is CHARACTER*1
! 59: *> On entry, TRANSB specifies the form of op( B ) to be used in
! 60: *> the matrix multiplication as follows:
! 61: *>
! 62: *> TRANSB = 'N' or 'n', op( B ) = B.
! 63: *>
! 64: *> TRANSB = 'T' or 't', op( B ) = B**T.
! 65: *>
! 66: *> TRANSB = 'C' or 'c', op( B ) = B**T.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] M
! 70: *> \verbatim
! 71: *> M is INTEGER
! 72: *> On entry, M specifies the number of rows of the matrix
! 73: *> op( A ) and of the matrix C. M must be at least zero.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] N
! 77: *> \verbatim
! 78: *> N is INTEGER
! 79: *> On entry, N specifies the number of columns of the matrix
! 80: *> op( B ) and the number of columns of the matrix C. N must be
! 81: *> at least zero.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] K
! 85: *> \verbatim
! 86: *> K is INTEGER
! 87: *> On entry, K specifies the number of columns of the matrix
! 88: *> op( A ) and the number of rows of the matrix op( B ). K must
! 89: *> be at least zero.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] ALPHA
! 93: *> \verbatim
! 94: *> ALPHA is DOUBLE PRECISION.
! 95: *> On entry, ALPHA specifies the scalar alpha.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] A
! 99: *> \verbatim
! 100: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
! 101: *> k when TRANSA = 'N' or 'n', and is m otherwise.
! 102: *> Before entry with TRANSA = 'N' or 'n', the leading m by k
! 103: *> part of the array A must contain the matrix A, otherwise
! 104: *> the leading k by m part of the array A must contain the
! 105: *> matrix A.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] LDA
! 109: *> \verbatim
! 110: *> LDA is INTEGER
! 111: *> On entry, LDA specifies the first dimension of A as declared
! 112: *> in the calling (sub) program. When TRANSA = 'N' or 'n' then
! 113: *> LDA must be at least max( 1, m ), otherwise LDA must be at
! 114: *> least max( 1, k ).
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] B
! 118: *> \verbatim
! 119: *> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
! 120: *> n when TRANSB = 'N' or 'n', and is k otherwise.
! 121: *> Before entry with TRANSB = 'N' or 'n', the leading k by n
! 122: *> part of the array B must contain the matrix B, otherwise
! 123: *> the leading n by k part of the array B must contain the
! 124: *> matrix B.
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[in] LDB
! 128: *> \verbatim
! 129: *> LDB is INTEGER
! 130: *> On entry, LDB specifies the first dimension of B as declared
! 131: *> in the calling (sub) program. When TRANSB = 'N' or 'n' then
! 132: *> LDB must be at least max( 1, k ), otherwise LDB must be at
! 133: *> least max( 1, n ).
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[in] BETA
! 137: *> \verbatim
! 138: *> BETA is DOUBLE PRECISION.
! 139: *> On entry, BETA specifies the scalar beta. When BETA is
! 140: *> supplied as zero then C need not be set on input.
! 141: *> \endverbatim
! 142: *>
! 143: *> \param[in,out] C
! 144: *> \verbatim
! 145: *> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
! 146: *> Before entry, the leading m by n part of the array C must
! 147: *> contain the matrix C, except when beta is zero, in which
! 148: *> case C need not be set on entry.
! 149: *> On exit, the array C is overwritten by the m by n matrix
! 150: *> ( alpha*op( A )*op( B ) + beta*C ).
! 151: *> \endverbatim
! 152: *>
! 153: *> \param[in] LDC
! 154: *> \verbatim
! 155: *> LDC is INTEGER
! 156: *> On entry, LDC specifies the first dimension of C as declared
! 157: *> in the calling (sub) program. LDC must be at least
! 158: *> max( 1, m ).
! 159: *> \endverbatim
! 160: *
! 161: * Authors:
! 162: * ========
! 163: *
! 164: *> \author Univ. of Tennessee
! 165: *> \author Univ. of California Berkeley
! 166: *> \author Univ. of Colorado Denver
! 167: *> \author NAG Ltd.
! 168: *
! 169: *> \date November 2011
! 170: *
! 171: *> \ingroup double_blas_level3
! 172: *
! 173: *> \par Further Details:
! 174: * =====================
! 175: *>
! 176: *> \verbatim
! 177: *>
! 178: *> Level 3 Blas routine.
! 179: *>
! 180: *> -- Written on 8-February-1989.
! 181: *> Jack Dongarra, Argonne National Laboratory.
! 182: *> Iain Duff, AERE Harwell.
! 183: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 184: *> Sven Hammarling, Numerical Algorithms Group Ltd.
! 185: *> \endverbatim
! 186: *>
! 187: * =====================================================================
1.1 bertrand 188: SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
1.8 ! bertrand 189: *
! 190: * -- Reference BLAS level3 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 ..
196: DOUBLE PRECISION ALPHA,BETA
197: INTEGER K,LDA,LDB,LDC,M,N
198: CHARACTER TRANSA,TRANSB
199: * ..
200: * .. Array Arguments ..
201: DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
202: * ..
203: *
204: * =====================================================================
205: *
206: * .. External Functions ..
207: LOGICAL LSAME
208: EXTERNAL LSAME
209: * ..
210: * .. External Subroutines ..
211: EXTERNAL XERBLA
212: * ..
213: * .. Intrinsic Functions ..
214: INTRINSIC MAX
215: * ..
216: * .. Local Scalars ..
217: DOUBLE PRECISION TEMP
218: INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
219: LOGICAL NOTA,NOTB
220: * ..
221: * .. Parameters ..
222: DOUBLE PRECISION ONE,ZERO
223: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
224: * ..
225: *
226: * Set NOTA and NOTB as true if A and B respectively are not
227: * transposed and set NROWA, NCOLA and NROWB as the number of rows
228: * and columns of A and the number of rows of B respectively.
229: *
230: NOTA = LSAME(TRANSA,'N')
231: NOTB = LSAME(TRANSB,'N')
232: IF (NOTA) THEN
233: NROWA = M
234: NCOLA = K
235: ELSE
236: NROWA = K
237: NCOLA = M
238: END IF
239: IF (NOTB) THEN
240: NROWB = K
241: ELSE
242: NROWB = N
243: END IF
244: *
245: * Test the input parameters.
246: *
247: INFO = 0
248: IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND.
249: + (.NOT.LSAME(TRANSA,'T'))) THEN
250: INFO = 1
251: ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND.
252: + (.NOT.LSAME(TRANSB,'T'))) THEN
253: INFO = 2
254: ELSE IF (M.LT.0) THEN
255: INFO = 3
256: ELSE IF (N.LT.0) THEN
257: INFO = 4
258: ELSE IF (K.LT.0) THEN
259: INFO = 5
260: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
261: INFO = 8
262: ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
263: INFO = 10
264: ELSE IF (LDC.LT.MAX(1,M)) THEN
265: INFO = 13
266: END IF
267: IF (INFO.NE.0) THEN
268: CALL XERBLA('DGEMM ',INFO)
269: RETURN
270: END IF
271: *
272: * Quick return if possible.
273: *
274: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
275: + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
276: *
277: * And if alpha.eq.zero.
278: *
279: IF (ALPHA.EQ.ZERO) THEN
280: IF (BETA.EQ.ZERO) THEN
281: DO 20 J = 1,N
282: DO 10 I = 1,M
283: C(I,J) = ZERO
284: 10 CONTINUE
285: 20 CONTINUE
286: ELSE
287: DO 40 J = 1,N
288: DO 30 I = 1,M
289: C(I,J) = BETA*C(I,J)
290: 30 CONTINUE
291: 40 CONTINUE
292: END IF
293: RETURN
294: END IF
295: *
296: * Start the operations.
297: *
298: IF (NOTB) THEN
299: IF (NOTA) THEN
300: *
301: * Form C := alpha*A*B + beta*C.
302: *
303: DO 90 J = 1,N
304: IF (BETA.EQ.ZERO) THEN
305: DO 50 I = 1,M
306: C(I,J) = ZERO
307: 50 CONTINUE
308: ELSE IF (BETA.NE.ONE) THEN
309: DO 60 I = 1,M
310: C(I,J) = BETA*C(I,J)
311: 60 CONTINUE
312: END IF
313: DO 80 L = 1,K
314: IF (B(L,J).NE.ZERO) THEN
315: TEMP = ALPHA*B(L,J)
316: DO 70 I = 1,M
317: C(I,J) = C(I,J) + TEMP*A(I,L)
318: 70 CONTINUE
319: END IF
320: 80 CONTINUE
321: 90 CONTINUE
322: ELSE
323: *
1.7 bertrand 324: * Form C := alpha*A**T*B + beta*C
1.1 bertrand 325: *
326: DO 120 J = 1,N
327: DO 110 I = 1,M
328: TEMP = ZERO
329: DO 100 L = 1,K
330: TEMP = TEMP + A(L,I)*B(L,J)
331: 100 CONTINUE
332: IF (BETA.EQ.ZERO) THEN
333: C(I,J) = ALPHA*TEMP
334: ELSE
335: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
336: END IF
337: 110 CONTINUE
338: 120 CONTINUE
339: END IF
340: ELSE
341: IF (NOTA) THEN
342: *
1.7 bertrand 343: * Form C := alpha*A*B**T + beta*C
1.1 bertrand 344: *
345: DO 170 J = 1,N
346: IF (BETA.EQ.ZERO) THEN
347: DO 130 I = 1,M
348: C(I,J) = ZERO
349: 130 CONTINUE
350: ELSE IF (BETA.NE.ONE) THEN
351: DO 140 I = 1,M
352: C(I,J) = BETA*C(I,J)
353: 140 CONTINUE
354: END IF
355: DO 160 L = 1,K
356: IF (B(J,L).NE.ZERO) THEN
357: TEMP = ALPHA*B(J,L)
358: DO 150 I = 1,M
359: C(I,J) = C(I,J) + TEMP*A(I,L)
360: 150 CONTINUE
361: END IF
362: 160 CONTINUE
363: 170 CONTINUE
364: ELSE
365: *
1.7 bertrand 366: * Form C := alpha*A**T*B**T + beta*C
1.1 bertrand 367: *
368: DO 200 J = 1,N
369: DO 190 I = 1,M
370: TEMP = ZERO
371: DO 180 L = 1,K
372: TEMP = TEMP + A(L,I)*B(J,L)
373: 180 CONTINUE
374: IF (BETA.EQ.ZERO) THEN
375: C(I,J) = ALPHA*TEMP
376: ELSE
377: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
378: END IF
379: 190 CONTINUE
380: 200 CONTINUE
381: END IF
382: END IF
383: *
384: RETURN
385: *
386: * End of DGEMM .
387: *
388: END
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