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1.8 bertrand 1: *> \brief \b DSYRK
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
1.13 bertrand 12: *
1.8 bertrand 13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA,BETA
15: * INTEGER K,LDA,LDC,N
16: * CHARACTER TRANS,UPLO
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),C(LDC,*)
20: * ..
1.13 bertrand 21: *
1.8 bertrand 22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DSYRK performs one of the symmetric rank k operations
29: *>
30: *> C := alpha*A*A**T + beta*C,
31: *>
32: *> or
33: *>
34: *> C := alpha*A**T*A + beta*C,
35: *>
36: *> where alpha and beta are scalars, C is an n by n symmetric matrix
37: *> and A is an n by k matrix in the first case and a k by n matrix
38: *> in the second case.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] UPLO
45: *> \verbatim
46: *> UPLO is CHARACTER*1
47: *> On entry, UPLO specifies whether the upper or lower
48: *> triangular part of the array C is to be referenced as
49: *> follows:
50: *>
51: *> UPLO = 'U' or 'u' Only the upper triangular part of C
52: *> is to be referenced.
53: *>
54: *> UPLO = 'L' or 'l' Only the lower triangular part of C
55: *> is to be referenced.
56: *> \endverbatim
57: *>
58: *> \param[in] TRANS
59: *> \verbatim
60: *> TRANS is CHARACTER*1
61: *> On entry, TRANS specifies the operation to be performed as
62: *> follows:
63: *>
64: *> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
65: *>
66: *> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
67: *>
68: *> TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> On entry, N specifies the order of the matrix C. N must be
75: *> at least zero.
76: *> \endverbatim
77: *>
78: *> \param[in] K
79: *> \verbatim
80: *> K is INTEGER
81: *> On entry with TRANS = 'N' or 'n', K specifies the number
82: *> of columns of the matrix A, and on entry with
83: *> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
84: *> of rows of the matrix A. K must be at least zero.
85: *> \endverbatim
86: *>
87: *> \param[in] ALPHA
88: *> \verbatim
89: *> ALPHA is DOUBLE PRECISION.
90: *> On entry, ALPHA specifies the scalar alpha.
91: *> \endverbatim
92: *>
93: *> \param[in] A
94: *> \verbatim
1.14 bertrand 95: *> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
1.8 bertrand 96: *> k when TRANS = 'N' or 'n', and is n otherwise.
97: *> Before entry with TRANS = 'N' or 'n', the leading n by k
98: *> part of the array A must contain the matrix A, otherwise
99: *> the leading k by n part of the array A must contain the
100: *> matrix A.
101: *> \endverbatim
102: *>
103: *> \param[in] LDA
104: *> \verbatim
105: *> LDA is INTEGER
106: *> On entry, LDA specifies the first dimension of A as declared
107: *> in the calling (sub) program. When TRANS = 'N' or 'n'
108: *> then LDA must be at least max( 1, n ), otherwise LDA must
109: *> be at least max( 1, k ).
110: *> \endverbatim
111: *>
112: *> \param[in] BETA
113: *> \verbatim
114: *> BETA is DOUBLE PRECISION.
115: *> On entry, BETA specifies the scalar beta.
116: *> \endverbatim
117: *>
118: *> \param[in,out] C
119: *> \verbatim
1.14 bertrand 120: *> C is DOUBLE PRECISION array, dimension ( LDC, N )
1.8 bertrand 121: *> Before entry with UPLO = 'U' or 'u', the leading n by n
122: *> upper triangular part of the array C must contain the upper
123: *> triangular part of the symmetric matrix and the strictly
124: *> lower triangular part of C is not referenced. On exit, the
125: *> upper triangular part of the array C is overwritten by the
126: *> upper triangular part of the updated matrix.
127: *> Before entry with UPLO = 'L' or 'l', the leading n by n
128: *> lower triangular part of the array C must contain the lower
129: *> triangular part of the symmetric matrix and the strictly
130: *> upper triangular part of C is not referenced. On exit, the
131: *> lower triangular part of the array C is overwritten by the
132: *> lower triangular part of the updated matrix.
133: *> \endverbatim
134: *>
135: *> \param[in] LDC
136: *> \verbatim
137: *> LDC is INTEGER
138: *> On entry, LDC specifies the first dimension of C as declared
139: *> in the calling (sub) program. LDC must be at least
140: *> max( 1, n ).
141: *> \endverbatim
142: *
143: * Authors:
144: * ========
145: *
1.13 bertrand 146: *> \author Univ. of Tennessee
147: *> \author Univ. of California Berkeley
148: *> \author Univ. of Colorado Denver
149: *> \author NAG Ltd.
1.8 bertrand 150: *
151: *> \ingroup double_blas_level3
152: *
153: *> \par Further Details:
154: * =====================
155: *>
156: *> \verbatim
157: *>
158: *> Level 3 Blas routine.
159: *>
160: *> -- Written on 8-February-1989.
161: *> Jack Dongarra, Argonne National Laboratory.
162: *> Iain Duff, AERE Harwell.
163: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
164: *> Sven Hammarling, Numerical Algorithms Group Ltd.
165: *> \endverbatim
166: *>
167: * =====================================================================
1.1 bertrand 168: SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
1.8 bertrand 169: *
1.16 ! bertrand 170: * -- Reference BLAS level3 routine --
1.8 bertrand 171: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
172: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173: *
1.1 bertrand 174: * .. Scalar Arguments ..
175: DOUBLE PRECISION ALPHA,BETA
176: INTEGER K,LDA,LDC,N
177: CHARACTER TRANS,UPLO
178: * ..
179: * .. Array Arguments ..
180: DOUBLE PRECISION A(LDA,*),C(LDC,*)
181: * ..
182: *
183: * =====================================================================
184: *
185: * .. External Functions ..
186: LOGICAL LSAME
187: EXTERNAL LSAME
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL XERBLA
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC MAX
194: * ..
195: * .. Local Scalars ..
196: DOUBLE PRECISION TEMP
197: INTEGER I,INFO,J,L,NROWA
198: LOGICAL UPPER
199: * ..
200: * .. Parameters ..
201: DOUBLE PRECISION ONE,ZERO
202: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
203: * ..
204: *
205: * Test the input parameters.
206: *
207: IF (LSAME(TRANS,'N')) THEN
208: NROWA = N
209: ELSE
210: NROWA = K
211: END IF
212: UPPER = LSAME(UPLO,'U')
213: *
214: INFO = 0
215: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
216: INFO = 1
217: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
218: + (.NOT.LSAME(TRANS,'T')) .AND.
219: + (.NOT.LSAME(TRANS,'C'))) THEN
220: INFO = 2
221: ELSE IF (N.LT.0) THEN
222: INFO = 3
223: ELSE IF (K.LT.0) THEN
224: INFO = 4
225: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
226: INFO = 7
227: ELSE IF (LDC.LT.MAX(1,N)) THEN
228: INFO = 10
229: END IF
230: IF (INFO.NE.0) THEN
231: CALL XERBLA('DSYRK ',INFO)
232: RETURN
233: END IF
234: *
235: * Quick return if possible.
236: *
237: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
238: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
239: *
240: * And when alpha.eq.zero.
241: *
242: IF (ALPHA.EQ.ZERO) THEN
243: IF (UPPER) THEN
244: IF (BETA.EQ.ZERO) THEN
245: DO 20 J = 1,N
246: DO 10 I = 1,J
247: C(I,J) = ZERO
248: 10 CONTINUE
249: 20 CONTINUE
250: ELSE
251: DO 40 J = 1,N
252: DO 30 I = 1,J
253: C(I,J) = BETA*C(I,J)
254: 30 CONTINUE
255: 40 CONTINUE
256: END IF
257: ELSE
258: IF (BETA.EQ.ZERO) THEN
259: DO 60 J = 1,N
260: DO 50 I = J,N
261: C(I,J) = ZERO
262: 50 CONTINUE
263: 60 CONTINUE
264: ELSE
265: DO 80 J = 1,N
266: DO 70 I = J,N
267: C(I,J) = BETA*C(I,J)
268: 70 CONTINUE
269: 80 CONTINUE
270: END IF
271: END IF
272: RETURN
273: END IF
274: *
275: * Start the operations.
276: *
277: IF (LSAME(TRANS,'N')) THEN
278: *
1.7 bertrand 279: * Form C := alpha*A*A**T + beta*C.
1.1 bertrand 280: *
281: IF (UPPER) THEN
282: DO 130 J = 1,N
283: IF (BETA.EQ.ZERO) THEN
284: DO 90 I = 1,J
285: C(I,J) = ZERO
286: 90 CONTINUE
287: ELSE IF (BETA.NE.ONE) THEN
288: DO 100 I = 1,J
289: C(I,J) = BETA*C(I,J)
290: 100 CONTINUE
291: END IF
292: DO 120 L = 1,K
293: IF (A(J,L).NE.ZERO) THEN
294: TEMP = ALPHA*A(J,L)
295: DO 110 I = 1,J
296: C(I,J) = C(I,J) + TEMP*A(I,L)
297: 110 CONTINUE
298: END IF
299: 120 CONTINUE
300: 130 CONTINUE
301: ELSE
302: DO 180 J = 1,N
303: IF (BETA.EQ.ZERO) THEN
304: DO 140 I = J,N
305: C(I,J) = ZERO
306: 140 CONTINUE
307: ELSE IF (BETA.NE.ONE) THEN
308: DO 150 I = J,N
309: C(I,J) = BETA*C(I,J)
310: 150 CONTINUE
311: END IF
312: DO 170 L = 1,K
313: IF (A(J,L).NE.ZERO) THEN
314: TEMP = ALPHA*A(J,L)
315: DO 160 I = J,N
316: C(I,J) = C(I,J) + TEMP*A(I,L)
317: 160 CONTINUE
318: END IF
319: 170 CONTINUE
320: 180 CONTINUE
321: END IF
322: ELSE
323: *
1.7 bertrand 324: * Form C := alpha*A**T*A + beta*C.
1.1 bertrand 325: *
326: IF (UPPER) THEN
327: DO 210 J = 1,N
328: DO 200 I = 1,J
329: TEMP = ZERO
330: DO 190 L = 1,K
331: TEMP = TEMP + A(L,I)*A(L,J)
332: 190 CONTINUE
333: IF (BETA.EQ.ZERO) THEN
334: C(I,J) = ALPHA*TEMP
335: ELSE
336: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
337: END IF
338: 200 CONTINUE
339: 210 CONTINUE
340: ELSE
341: DO 240 J = 1,N
342: DO 230 I = J,N
343: TEMP = ZERO
344: DO 220 L = 1,K
345: TEMP = TEMP + A(L,I)*A(L,J)
346: 220 CONTINUE
347: IF (BETA.EQ.ZERO) THEN
348: C(I,J) = ALPHA*TEMP
349: ELSE
350: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
351: END IF
352: 230 CONTINUE
353: 240 CONTINUE
354: END IF
355: END IF
356: *
357: RETURN
358: *
1.16 ! bertrand 359: * End of DSYRK
1.1 bertrand 360: *
361: END