LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ssyr2k.f
Go to the documentation of this file.
1 *> \brief \b SSYR2K
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 SSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12 *
13 * .. Scalar Arguments ..
14 * REAL ALPHA,BETA
15 * INTEGER K,LDA,LDB,LDC,N
16 * CHARACTER TRANS,UPLO
17 * ..
18 * .. Array Arguments ..
19 * REAL A(LDA,*),B(LDB,*),C(LDC,*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> SSYR2K performs one of the symmetric rank 2k operations
29 *>
30 *> C := alpha*A*B**T + alpha*B*A**T + beta*C,
31 *>
32 *> or
33 *>
34 *> C := alpha*A**T*B + alpha*B**T*A + beta*C,
35 *>
36 *> where alpha and beta are scalars, C is an n by n symmetric matrix
37 *> and A and B are n by k matrices in the first case and k by n
38 *> matrices 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*B**T + alpha*B*A**T +
65 *> beta*C.
66 *>
67 *> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
68 *> beta*C.
69 *>
70 *> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A +
71 *> beta*C.
72 *> \endverbatim
73 *>
74 *> \param[in] N
75 *> \verbatim
76 *> N is INTEGER
77 *> On entry, N specifies the order of the matrix C. N must be
78 *> at least zero.
79 *> \endverbatim
80 *>
81 *> \param[in] K
82 *> \verbatim
83 *> K is INTEGER
84 *> On entry with TRANS = 'N' or 'n', K specifies the number
85 *> of columns of the matrices A and B, and on entry with
86 *> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
87 *> of rows of the matrices A and B. K must be at least zero.
88 *> \endverbatim
89 *>
90 *> \param[in] ALPHA
91 *> \verbatim
92 *> ALPHA is REAL
93 *> On entry, ALPHA specifies the scalar alpha.
94 *> \endverbatim
95 *>
96 *> \param[in] A
97 *> \verbatim
98 *> A is REAL array, dimension ( LDA, ka ), where ka is
99 *> k when TRANS = 'N' or 'n', and is n otherwise.
100 *> Before entry with TRANS = 'N' or 'n', the leading n by k
101 *> part of the array A must contain the matrix A, otherwise
102 *> the leading k by n part of the array A must contain the
103 *> matrix A.
104 *> \endverbatim
105 *>
106 *> \param[in] LDA
107 *> \verbatim
108 *> LDA is INTEGER
109 *> On entry, LDA specifies the first dimension of A as declared
110 *> in the calling (sub) program. When TRANS = 'N' or 'n'
111 *> then LDA must be at least max( 1, n ), otherwise LDA must
112 *> be at least max( 1, k ).
113 *> \endverbatim
114 *>
115 *> \param[in] B
116 *> \verbatim
117 *> B is REAL array, dimension ( LDB, kb ), where kb is
118 *> k when TRANS = 'N' or 'n', and is n otherwise.
119 *> Before entry with TRANS = 'N' or 'n', the leading n by k
120 *> part of the array B must contain the matrix B, otherwise
121 *> the leading k by n part of the array B must contain the
122 *> matrix B.
123 *> \endverbatim
124 *>
125 *> \param[in] LDB
126 *> \verbatim
127 *> LDB is INTEGER
128 *> On entry, LDB specifies the first dimension of B as declared
129 *> in the calling (sub) program. When TRANS = 'N' or 'n'
130 *> then LDB must be at least max( 1, n ), otherwise LDB must
131 *> be at least max( 1, k ).
132 *> \endverbatim
133 *>
134 *> \param[in] BETA
135 *> \verbatim
136 *> BETA is REAL
137 *> On entry, BETA specifies the scalar beta.
138 *> \endverbatim
139 *>
140 *> \param[in,out] C
141 *> \verbatim
142 *> C is REAL array, dimension ( LDC, N )
143 *> Before entry with UPLO = 'U' or 'u', the leading n by n
144 *> upper triangular part of the array C must contain the upper
145 *> triangular part of the symmetric matrix and the strictly
146 *> lower triangular part of C is not referenced. On exit, the
147 *> upper triangular part of the array C is overwritten by the
148 *> upper triangular part of the updated matrix.
149 *> Before entry with UPLO = 'L' or 'l', the leading n by n
150 *> lower triangular part of the array C must contain the lower
151 *> triangular part of the symmetric matrix and the strictly
152 *> upper triangular part of C is not referenced. On exit, the
153 *> lower triangular part of the array C is overwritten by the
154 *> lower triangular part of the updated matrix.
155 *> \endverbatim
156 *>
157 *> \param[in] LDC
158 *> \verbatim
159 *> LDC is INTEGER
160 *> On entry, LDC specifies the first dimension of C as declared
161 *> in the calling (sub) program. LDC must be at least
162 *> max( 1, n ).
163 *> \endverbatim
164 *
165 * Authors:
166 * ========
167 *
168 *> \author Univ. of Tennessee
169 *> \author Univ. of California Berkeley
170 *> \author Univ. of Colorado Denver
171 *> \author NAG Ltd.
172 *
173 *> \ingroup single_blas_level3
174 *
175 *> \par Further Details:
176 * =====================
177 *>
178 *> \verbatim
179 *>
180 *> Level 3 Blas routine.
181 *>
182 *>
183 *> -- Written on 8-February-1989.
184 *> Jack Dongarra, Argonne National Laboratory.
185 *> Iain Duff, AERE Harwell.
186 *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
187 *> Sven Hammarling, Numerical Algorithms Group Ltd.
188 *> \endverbatim
189 *>
190 * =====================================================================
191  SUBROUTINE ssyr2k(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
192 *
193 * -- Reference BLAS level3 routine --
194 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
195 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
196 *
197 * .. Scalar Arguments ..
198  REAL ALPHA,BETA
199  INTEGER K,LDA,LDB,LDC,N
200  CHARACTER TRANS,UPLO
201 * ..
202 * .. Array Arguments ..
203  REAL 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  REAL TEMP1,TEMP2
220  INTEGER I,INFO,J,L,NROWA
221  LOGICAL UPPER
222 * ..
223 * .. Parameters ..
224  REAL ONE,ZERO
225  parameter(one=1.0e+0,zero=0.0e+0)
226 * ..
227 *
228 * Test the input parameters.
229 *
230  IF (lsame(trans,'N')) THEN
231  nrowa = n
232  ELSE
233  nrowa = k
234  END IF
235  upper = lsame(uplo,'U')
236 *
237  info = 0
238  IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
239  info = 1
240  ELSE IF ((.NOT.lsame(trans,'N')) .AND.
241  + (.NOT.lsame(trans,'T')) .AND.
242  + (.NOT.lsame(trans,'C'))) THEN
243  info = 2
244  ELSE IF (n.LT.0) THEN
245  info = 3
246  ELSE IF (k.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,nrowa)) THEN
251  info = 9
252  ELSE IF (ldc.LT.max(1,n)) THEN
253  info = 12
254  END IF
255  IF (info.NE.0) THEN
256  CALL xerbla('SSYR2K',info)
257  RETURN
258  END IF
259 *
260 * Quick return if possible.
261 *
262  IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
263  + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
264 *
265 * And when alpha.eq.zero.
266 *
267  IF (alpha.EQ.zero) THEN
268  IF (upper) THEN
269  IF (beta.EQ.zero) THEN
270  DO 20 j = 1,n
271  DO 10 i = 1,j
272  c(i,j) = zero
273  10 CONTINUE
274  20 CONTINUE
275  ELSE
276  DO 40 j = 1,n
277  DO 30 i = 1,j
278  c(i,j) = beta*c(i,j)
279  30 CONTINUE
280  40 CONTINUE
281  END IF
282  ELSE
283  IF (beta.EQ.zero) THEN
284  DO 60 j = 1,n
285  DO 50 i = j,n
286  c(i,j) = zero
287  50 CONTINUE
288  60 CONTINUE
289  ELSE
290  DO 80 j = 1,n
291  DO 70 i = j,n
292  c(i,j) = beta*c(i,j)
293  70 CONTINUE
294  80 CONTINUE
295  END IF
296  END IF
297  RETURN
298  END IF
299 *
300 * Start the operations.
301 *
302  IF (lsame(trans,'N')) THEN
303 *
304 * Form C := alpha*A*B**T + alpha*B*A**T + C.
305 *
306  IF (upper) THEN
307  DO 130 j = 1,n
308  IF (beta.EQ.zero) THEN
309  DO 90 i = 1,j
310  c(i,j) = zero
311  90 CONTINUE
312  ELSE IF (beta.NE.one) THEN
313  DO 100 i = 1,j
314  c(i,j) = beta*c(i,j)
315  100 CONTINUE
316  END IF
317  DO 120 l = 1,k
318  IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
319  temp1 = alpha*b(j,l)
320  temp2 = alpha*a(j,l)
321  DO 110 i = 1,j
322  c(i,j) = c(i,j) + a(i,l)*temp1 +
323  + b(i,l)*temp2
324  110 CONTINUE
325  END IF
326  120 CONTINUE
327  130 CONTINUE
328  ELSE
329  DO 180 j = 1,n
330  IF (beta.EQ.zero) THEN
331  DO 140 i = j,n
332  c(i,j) = zero
333  140 CONTINUE
334  ELSE IF (beta.NE.one) THEN
335  DO 150 i = j,n
336  c(i,j) = beta*c(i,j)
337  150 CONTINUE
338  END IF
339  DO 170 l = 1,k
340  IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
341  temp1 = alpha*b(j,l)
342  temp2 = alpha*a(j,l)
343  DO 160 i = j,n
344  c(i,j) = c(i,j) + a(i,l)*temp1 +
345  + b(i,l)*temp2
346  160 CONTINUE
347  END IF
348  170 CONTINUE
349  180 CONTINUE
350  END IF
351  ELSE
352 *
353 * Form C := alpha*A**T*B + alpha*B**T*A + C.
354 *
355  IF (upper) THEN
356  DO 210 j = 1,n
357  DO 200 i = 1,j
358  temp1 = zero
359  temp2 = zero
360  DO 190 l = 1,k
361  temp1 = temp1 + a(l,i)*b(l,j)
362  temp2 = temp2 + b(l,i)*a(l,j)
363  190 CONTINUE
364  IF (beta.EQ.zero) THEN
365  c(i,j) = alpha*temp1 + alpha*temp2
366  ELSE
367  c(i,j) = beta*c(i,j) + alpha*temp1 +
368  + alpha*temp2
369  END IF
370  200 CONTINUE
371  210 CONTINUE
372  ELSE
373  DO 240 j = 1,n
374  DO 230 i = j,n
375  temp1 = zero
376  temp2 = zero
377  DO 220 l = 1,k
378  temp1 = temp1 + a(l,i)*b(l,j)
379  temp2 = temp2 + b(l,i)*a(l,j)
380  220 CONTINUE
381  IF (beta.EQ.zero) THEN
382  c(i,j) = alpha*temp1 + alpha*temp2
383  ELSE
384  c(i,j) = beta*c(i,j) + alpha*temp1 +
385  + alpha*temp2
386  END IF
387  230 CONTINUE
388  240 CONTINUE
389  END IF
390  END IF
391 *
392  RETURN
393 *
394 * End of SSYR2K
395 *
396  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssyr2k(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SSYR2K
Definition: ssyr2k.f:192