Annotation of rpl/lapack/blas/dsymm.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b DSYMM
! 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 DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * DOUBLE PRECISION ALPHA,BETA
! 15: * INTEGER LDA,LDB,LDC,M,N
! 16: * CHARACTER SIDE,UPLO
! 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: *> DSYMM performs one of the matrix-matrix operations
! 29: *>
! 30: *> C := alpha*A*B + beta*C,
! 31: *>
! 32: *> or
! 33: *>
! 34: *> C := alpha*B*A + beta*C,
! 35: *>
! 36: *> where alpha and beta are scalars, A is a symmetric matrix and B and
! 37: *> C are m by n matrices.
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] SIDE
! 44: *> \verbatim
! 45: *> SIDE is CHARACTER*1
! 46: *> On entry, SIDE specifies whether the symmetric matrix A
! 47: *> appears on the left or right in the operation as follows:
! 48: *>
! 49: *> SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
! 50: *>
! 51: *> SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] UPLO
! 55: *> \verbatim
! 56: *> UPLO is CHARACTER*1
! 57: *> On entry, UPLO specifies whether the upper or lower
! 58: *> triangular part of the symmetric matrix A is to be
! 59: *> referenced as follows:
! 60: *>
! 61: *> UPLO = 'U' or 'u' Only the upper triangular part of the
! 62: *> symmetric matrix is to be referenced.
! 63: *>
! 64: *> UPLO = 'L' or 'l' Only the lower triangular part of the
! 65: *> symmetric matrix is to be referenced.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] M
! 69: *> \verbatim
! 70: *> M is INTEGER
! 71: *> On entry, M specifies the number of rows of the matrix C.
! 72: *> M must be at least zero.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] N
! 76: *> \verbatim
! 77: *> N is INTEGER
! 78: *> On entry, N specifies the number of columns of the matrix C.
! 79: *> N must be at least zero.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] ALPHA
! 83: *> \verbatim
! 84: *> ALPHA is DOUBLE PRECISION.
! 85: *> On entry, ALPHA specifies the scalar alpha.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] A
! 89: *> \verbatim
! 90: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
! 91: *> m when SIDE = 'L' or 'l' and is n otherwise.
! 92: *> Before entry with SIDE = 'L' or 'l', the m by m part of
! 93: *> the array A must contain the symmetric matrix, such that
! 94: *> when UPLO = 'U' or 'u', the leading m by m upper triangular
! 95: *> part of the array A must contain the upper triangular part
! 96: *> of the symmetric matrix and the strictly lower triangular
! 97: *> part of A is not referenced, and when UPLO = 'L' or 'l',
! 98: *> the leading m by m lower triangular part of the array A
! 99: *> must contain the lower triangular part of the symmetric
! 100: *> matrix and the strictly upper triangular part of A is not
! 101: *> referenced.
! 102: *> Before entry with SIDE = 'R' or 'r', the n by n part of
! 103: *> the array A must contain the symmetric matrix, such that
! 104: *> when UPLO = 'U' or 'u', the leading n by n upper triangular
! 105: *> part of the array A must contain the upper triangular part
! 106: *> of the symmetric matrix and the strictly lower triangular
! 107: *> part of A is not referenced, and when UPLO = 'L' or 'l',
! 108: *> the leading n by n lower triangular part of the array A
! 109: *> must contain the lower triangular part of the symmetric
! 110: *> matrix and the strictly upper triangular part of A is not
! 111: *> referenced.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in] LDA
! 115: *> \verbatim
! 116: *> LDA is INTEGER
! 117: *> On entry, LDA specifies the first dimension of A as declared
! 118: *> in the calling (sub) program. When SIDE = 'L' or 'l' then
! 119: *> LDA must be at least max( 1, m ), otherwise LDA must be at
! 120: *> least max( 1, n ).
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[in] B
! 124: *> \verbatim
! 125: *> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
! 126: *> Before entry, the leading m by n part of the array B must
! 127: *> contain the matrix B.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] LDB
! 131: *> \verbatim
! 132: *> LDB is INTEGER
! 133: *> On entry, LDB specifies the first dimension of B as declared
! 134: *> in the calling (sub) program. LDB must be at least
! 135: *> max( 1, m ).
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[in] BETA
! 139: *> \verbatim
! 140: *> BETA is DOUBLE PRECISION.
! 141: *> On entry, BETA specifies the scalar beta. When BETA is
! 142: *> supplied as zero then C need not be set on input.
! 143: *> \endverbatim
! 144: *>
! 145: *> \param[in,out] C
! 146: *> \verbatim
! 147: *> C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
! 148: *> Before entry, the leading m by n part of the array C must
! 149: *> contain the matrix C, except when beta is zero, in which
! 150: *> case C need not be set on entry.
! 151: *> On exit, the array C is overwritten by the m by n updated
! 152: *> matrix.
! 153: *> \endverbatim
! 154: *>
! 155: *> \param[in] LDC
! 156: *> \verbatim
! 157: *> LDC is INTEGER
! 158: *> On entry, LDC specifies the first dimension of C as declared
! 159: *> in the calling (sub) program. LDC must be at least
! 160: *> max( 1, m ).
! 161: *> \endverbatim
! 162: *
! 163: * Authors:
! 164: * ========
! 165: *
! 166: *> \author Univ. of Tennessee
! 167: *> \author Univ. of California Berkeley
! 168: *> \author Univ. of Colorado Denver
! 169: *> \author NAG Ltd.
! 170: *
! 171: *> \date November 2011
! 172: *
! 173: *> \ingroup double_blas_level3
! 174: *
! 175: *> \par Further Details:
! 176: * =====================
! 177: *>
! 178: *> \verbatim
! 179: *>
! 180: *> Level 3 Blas routine.
! 181: *>
! 182: *> -- Written on 8-February-1989.
! 183: *> Jack Dongarra, Argonne National Laboratory.
! 184: *> Iain Duff, AERE Harwell.
! 185: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 186: *> Sven Hammarling, Numerical Algorithms Group Ltd.
! 187: *> \endverbatim
! 188: *>
! 189: * =====================================================================
1.1 bertrand 190: SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
1.7 ! bertrand 191: *
! 192: * -- Reference BLAS level3 routine (version 3.4.0) --
! 193: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 194: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 195: * November 2011
! 196: *
1.1 bertrand 197: * .. Scalar Arguments ..
198: DOUBLE PRECISION ALPHA,BETA
199: INTEGER LDA,LDB,LDC,M,N
200: CHARACTER SIDE,UPLO
201: * ..
202: * .. Array Arguments ..
203: DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
204: * ..
205: *
206: * =====================================================================
207: *
208: * .. External Functions ..
209: LOGICAL LSAME
210: EXTERNAL LSAME
211: * ..
212: * .. External Subroutines ..
213: EXTERNAL XERBLA
214: * ..
215: * .. Intrinsic Functions ..
216: INTRINSIC MAX
217: * ..
218: * .. Local Scalars ..
219: DOUBLE PRECISION TEMP1,TEMP2
220: INTEGER I,INFO,J,K,NROWA
221: LOGICAL UPPER
222: * ..
223: * .. Parameters ..
224: DOUBLE PRECISION ONE,ZERO
225: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
226: * ..
227: *
228: * Set NROWA as the number of rows of A.
229: *
230: IF (LSAME(SIDE,'L')) THEN
231: NROWA = M
232: ELSE
233: NROWA = N
234: END IF
235: UPPER = LSAME(UPLO,'U')
236: *
237: * Test the input parameters.
238: *
239: INFO = 0
240: IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
241: INFO = 1
242: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
243: INFO = 2
244: ELSE IF (M.LT.0) THEN
245: INFO = 3
246: ELSE IF (N.LT.0) THEN
247: INFO = 4
248: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
249: INFO = 7
250: ELSE IF (LDB.LT.MAX(1,M)) THEN
251: INFO = 9
252: ELSE IF (LDC.LT.MAX(1,M)) THEN
253: INFO = 12
254: END IF
255: IF (INFO.NE.0) THEN
256: CALL XERBLA('DSYMM ',INFO)
257: RETURN
258: END IF
259: *
260: * Quick return if possible.
261: *
262: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
263: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
264: *
265: * And when alpha.eq.zero.
266: *
267: IF (ALPHA.EQ.ZERO) THEN
268: IF (BETA.EQ.ZERO) THEN
269: DO 20 J = 1,N
270: DO 10 I = 1,M
271: C(I,J) = ZERO
272: 10 CONTINUE
273: 20 CONTINUE
274: ELSE
275: DO 40 J = 1,N
276: DO 30 I = 1,M
277: C(I,J) = BETA*C(I,J)
278: 30 CONTINUE
279: 40 CONTINUE
280: END IF
281: RETURN
282: END IF
283: *
284: * Start the operations.
285: *
286: IF (LSAME(SIDE,'L')) THEN
287: *
288: * Form C := alpha*A*B + beta*C.
289: *
290: IF (UPPER) THEN
291: DO 70 J = 1,N
292: DO 60 I = 1,M
293: TEMP1 = ALPHA*B(I,J)
294: TEMP2 = ZERO
295: DO 50 K = 1,I - 1
296: C(K,J) = C(K,J) + TEMP1*A(K,I)
297: TEMP2 = TEMP2 + B(K,J)*A(K,I)
298: 50 CONTINUE
299: IF (BETA.EQ.ZERO) THEN
300: C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
301: ELSE
302: C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
303: + ALPHA*TEMP2
304: END IF
305: 60 CONTINUE
306: 70 CONTINUE
307: ELSE
308: DO 100 J = 1,N
309: DO 90 I = M,1,-1
310: TEMP1 = ALPHA*B(I,J)
311: TEMP2 = ZERO
312: DO 80 K = I + 1,M
313: C(K,J) = C(K,J) + TEMP1*A(K,I)
314: TEMP2 = TEMP2 + B(K,J)*A(K,I)
315: 80 CONTINUE
316: IF (BETA.EQ.ZERO) THEN
317: C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
318: ELSE
319: C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
320: + ALPHA*TEMP2
321: END IF
322: 90 CONTINUE
323: 100 CONTINUE
324: END IF
325: ELSE
326: *
327: * Form C := alpha*B*A + beta*C.
328: *
329: DO 170 J = 1,N
330: TEMP1 = ALPHA*A(J,J)
331: IF (BETA.EQ.ZERO) THEN
332: DO 110 I = 1,M
333: C(I,J) = TEMP1*B(I,J)
334: 110 CONTINUE
335: ELSE
336: DO 120 I = 1,M
337: C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
338: 120 CONTINUE
339: END IF
340: DO 140 K = 1,J - 1
341: IF (UPPER) THEN
342: TEMP1 = ALPHA*A(K,J)
343: ELSE
344: TEMP1 = ALPHA*A(J,K)
345: END IF
346: DO 130 I = 1,M
347: C(I,J) = C(I,J) + TEMP1*B(I,K)
348: 130 CONTINUE
349: 140 CONTINUE
350: DO 160 K = J + 1,N
351: IF (UPPER) THEN
352: TEMP1 = ALPHA*A(J,K)
353: ELSE
354: TEMP1 = ALPHA*A(K,J)
355: END IF
356: DO 150 I = 1,M
357: C(I,J) = C(I,J) + TEMP1*B(I,K)
358: 150 CONTINUE
359: 160 CONTINUE
360: 170 CONTINUE
361: END IF
362: *
363: RETURN
364: *
365: * End of DSYMM .
366: *
367: END
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