Annotation of rpl/lapack/lapack/dsytrf_rook.f, revision 1.2
1.1 bertrand 1: *> \brief \b DSYTRF_ROOK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYTRF_ROOK + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrf_rook.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrf_rook.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrf_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, LWORK, N
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * DOUBLE PRECISION A( LDA, * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DSYTRF_ROOK computes the factorization of a real symmetric matrix A
39: *> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
40: *> The form of the factorization is
41: *>
42: *> A = U*D*U**T or A = L*D*L**T
43: *>
44: *> where U (or L) is a product of permutation and unit upper (lower)
45: *> triangular matrices, and D is symmetric and block diagonal with
46: *> 1-by-1 and 2-by-2 diagonal blocks.
47: *>
48: *> This is the blocked version of the algorithm, calling Level 3 BLAS.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] UPLO
55: *> \verbatim
56: *> UPLO is CHARACTER*1
57: *> = 'U': Upper triangle of A is stored;
58: *> = 'L': Lower triangle of A is stored.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The order of the matrix A. N >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is DOUBLE PRECISION array, dimension (LDA,N)
70: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
71: *> N-by-N upper triangular part of A contains the upper
72: *> triangular part of the matrix A, and the strictly lower
73: *> triangular part of A is not referenced. If UPLO = 'L', the
74: *> leading N-by-N lower triangular part of A contains the lower
75: *> triangular part of the matrix A, and the strictly upper
76: *> triangular part of A is not referenced.
77: *>
78: *> On exit, the block diagonal matrix D and the multipliers used
79: *> to obtain the factor U or L (see below for further details).
80: *> \endverbatim
81: *>
82: *> \param[in] LDA
83: *> \verbatim
84: *> LDA is INTEGER
85: *> The leading dimension of the array A. LDA >= max(1,N).
86: *> \endverbatim
87: *>
88: *> \param[out] IPIV
89: *> \verbatim
90: *> IPIV is INTEGER array, dimension (N)
91: *> Details of the interchanges and the block structure of D.
92: *>
93: *> If UPLO = 'U':
94: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
95: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
96: *>
97: *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
98: *> columns k and -IPIV(k) were interchanged and rows and
99: *> columns k-1 and -IPIV(k-1) were inerchaged,
100: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
101: *>
102: *> If UPLO = 'L':
103: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
104: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
105: *>
106: *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
107: *> columns k and -IPIV(k) were interchanged and rows and
108: *> columns k+1 and -IPIV(k+1) were inerchaged,
109: *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
110: *> \endverbatim
111: *>
112: *> \param[out] WORK
113: *> \verbatim
114: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
115: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
116: *> \endverbatim
117: *>
118: *> \param[in] LWORK
119: *> \verbatim
120: *> LWORK is INTEGER
121: *> The length of WORK. LWORK >=1. For best performance
122: *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
123: *>
124: *> If LWORK = -1, then a workspace query is assumed; the routine
125: *> only calculates the optimal size of the WORK array, returns
126: *> this value as the first entry of the WORK array, and no error
127: *> message related to LWORK is issued by XERBLA.
128: *> \endverbatim
129: *>
130: *> \param[out] INFO
131: *> \verbatim
132: *> INFO is INTEGER
133: *> = 0: successful exit
134: *> < 0: if INFO = -i, the i-th argument had an illegal value
135: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
136: *> has been completed, but the block diagonal matrix D is
137: *> exactly singular, and division by zero will occur if it
138: *> is used to solve a system of equations.
139: *> \endverbatim
140: *
141: * Authors:
142: * ========
143: *
144: *> \author Univ. of Tennessee
145: *> \author Univ. of California Berkeley
146: *> \author Univ. of Colorado Denver
147: *> \author NAG Ltd.
148: *
149: *> \date April 2012
150: *
151: *> \ingroup doubleSYcomputational
152: *
153: *> \par Further Details:
154: * =====================
155: *>
156: *> \verbatim
157: *>
158: *> If UPLO = 'U', then A = U*D*U**T, where
159: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
160: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
161: *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
162: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
163: *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
164: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
165: *>
166: *> ( I v 0 ) k-s
167: *> U(k) = ( 0 I 0 ) s
168: *> ( 0 0 I ) n-k
169: *> k-s s n-k
170: *>
171: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
172: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
173: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
174: *>
175: *> If UPLO = 'L', then A = L*D*L**T, where
176: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
177: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
178: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
179: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
180: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
181: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
182: *>
183: *> ( I 0 0 ) k-1
184: *> L(k) = ( 0 I 0 ) s
185: *> ( 0 v I ) n-k-s+1
186: *> k-1 s n-k-s+1
187: *>
188: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
189: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
190: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
191: *> \endverbatim
192: *
193: *> \par Contributors:
194: * ==================
195: *>
196: *> \verbatim
197: *>
198: *> April 2012, Igor Kozachenko,
199: *> Computer Science Division,
200: *> University of California, Berkeley
201: *>
202: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
203: *> School of Mathematics,
204: *> University of Manchester
205: *>
206: *> \endverbatim
207: *
208: * =====================================================================
209: SUBROUTINE DSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
210: *
211: * -- LAPACK computational routine (version 3.4.1) --
212: * -- LAPACK is a software package provided by Univ. of Tennessee, --
213: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
214: * April 2012
215: *
216: * .. Scalar Arguments ..
217: CHARACTER UPLO
218: INTEGER INFO, LDA, LWORK, N
219: * ..
220: * .. Array Arguments ..
221: INTEGER IPIV( * )
222: DOUBLE PRECISION A( LDA, * ), WORK( * )
223: * ..
224: *
225: * =====================================================================
226: *
227: * .. Local Scalars ..
228: LOGICAL LQUERY, UPPER
229: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
230: * ..
231: * .. External Functions ..
232: LOGICAL LSAME
233: INTEGER ILAENV
234: EXTERNAL LSAME, ILAENV
235: * ..
236: * .. External Subroutines ..
237: EXTERNAL DLASYF_ROOK, DSYTF2_ROOK, XERBLA
238: * ..
239: * .. Intrinsic Functions ..
240: INTRINSIC MAX
241: * ..
242: * .. Executable Statements ..
243: *
244: * Test the input parameters.
245: *
246: INFO = 0
247: UPPER = LSAME( UPLO, 'U' )
248: LQUERY = ( LWORK.EQ.-1 )
249: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
250: INFO = -1
251: ELSE IF( N.LT.0 ) THEN
252: INFO = -2
253: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
254: INFO = -4
255: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
256: INFO = -7
257: END IF
258: *
259: IF( INFO.EQ.0 ) THEN
260: *
261: * Determine the block size
262: *
263: NB = ILAENV( 1, 'DSYTRF_ROOK', UPLO, N, -1, -1, -1 )
264: LWKOPT = N*NB
265: WORK( 1 ) = LWKOPT
266: END IF
267: *
268: IF( INFO.NE.0 ) THEN
269: CALL XERBLA( 'DSYTRF_ROOK', -INFO )
270: RETURN
271: ELSE IF( LQUERY ) THEN
272: RETURN
273: END IF
274: *
275: NBMIN = 2
276: LDWORK = N
277: IF( NB.GT.1 .AND. NB.LT.N ) THEN
278: IWS = LDWORK*NB
279: IF( LWORK.LT.IWS ) THEN
280: NB = MAX( LWORK / LDWORK, 1 )
281: NBMIN = MAX( 2, ILAENV( 2, 'DSYTRF_ROOK',
282: $ UPLO, N, -1, -1, -1 ) )
283: END IF
284: ELSE
285: IWS = 1
286: END IF
287: IF( NB.LT.NBMIN )
288: $ NB = N
289: *
290: IF( UPPER ) THEN
291: *
292: * Factorize A as U*D*U**T using the upper triangle of A
293: *
294: * K is the main loop index, decreasing from N to 1 in steps of
295: * KB, where KB is the number of columns factorized by DLASYF_ROOK;
296: * KB is either NB or NB-1, or K for the last block
297: *
298: K = N
299: 10 CONTINUE
300: *
301: * If K < 1, exit from loop
302: *
303: IF( K.LT.1 )
304: $ GO TO 40
305: *
306: IF( K.GT.NB ) THEN
307: *
308: * Factorize columns k-kb+1:k of A and use blocked code to
309: * update columns 1:k-kb
310: *
311: CALL DLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
312: $ IPIV, WORK, LDWORK, IINFO )
313: ELSE
314: *
315: * Use unblocked code to factorize columns 1:k of A
316: *
317: CALL DSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
318: KB = K
319: END IF
320: *
321: * Set INFO on the first occurrence of a zero pivot
322: *
323: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
324: $ INFO = IINFO
325: *
326: * No need to adjust IPIV
327: *
328: * Decrease K and return to the start of the main loop
329: *
330: K = K - KB
331: GO TO 10
332: *
333: ELSE
334: *
335: * Factorize A as L*D*L**T using the lower triangle of A
336: *
337: * K is the main loop index, increasing from 1 to N in steps of
338: * KB, where KB is the number of columns factorized by DLASYF_ROOK;
339: * KB is either NB or NB-1, or N-K+1 for the last block
340: *
341: K = 1
342: 20 CONTINUE
343: *
344: * If K > N, exit from loop
345: *
346: IF( K.GT.N )
347: $ GO TO 40
348: *
349: IF( K.LE.N-NB ) THEN
350: *
351: * Factorize columns k:k+kb-1 of A and use blocked code to
352: * update columns k+kb:n
353: *
354: CALL DLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
355: $ IPIV( K ), WORK, LDWORK, IINFO )
356: ELSE
357: *
358: * Use unblocked code to factorize columns k:n of A
359: *
360: CALL DSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
361: $ IINFO )
362: KB = N - K + 1
363: END IF
364: *
365: * Set INFO on the first occurrence of a zero pivot
366: *
367: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
368: $ INFO = IINFO + K - 1
369: *
370: * Adjust IPIV
371: *
372: DO 30 J = K, K + KB - 1
373: IF( IPIV( J ).GT.0 ) THEN
374: IPIV( J ) = IPIV( J ) + K - 1
375: ELSE
376: IPIV( J ) = IPIV( J ) - K + 1
377: END IF
378: 30 CONTINUE
379: *
380: * Increase K and return to the start of the main loop
381: *
382: K = K + KB
383: GO TO 20
384: *
385: END IF
386: *
387: 40 CONTINUE
388: WORK( 1 ) = LWKOPT
389: RETURN
390: *
391: * End of DSYTRF_ROOK
392: *
393: END
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