1: *> \brief \b ZSYTRF_ROOK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYTRF_ROOK + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYTRF_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: * COMPLEX*16 A( LDA, * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSYTRF_ROOK computes the factorization of a complex 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 COMPLEX*16 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 COMPLEX*16 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: *> \ingroup complex16SYcomputational
150: *
151: *> \par Further Details:
152: * =====================
153: *>
154: *> \verbatim
155: *>
156: *> If UPLO = 'U', then A = U*D*U**T, where
157: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
158: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
159: *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
160: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
161: *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
162: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
163: *>
164: *> ( I v 0 ) k-s
165: *> U(k) = ( 0 I 0 ) s
166: *> ( 0 0 I ) n-k
167: *> k-s s n-k
168: *>
169: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
170: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
171: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
172: *>
173: *> If UPLO = 'L', then A = L*D*L**T, where
174: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
175: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
176: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
177: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
178: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
179: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
180: *>
181: *> ( I 0 0 ) k-1
182: *> L(k) = ( 0 I 0 ) s
183: *> ( 0 v I ) n-k-s+1
184: *> k-1 s n-k-s+1
185: *>
186: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
187: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
188: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
189: *> \endverbatim
190: *
191: *> \par Contributors:
192: * ==================
193: *>
194: *> \verbatim
195: *>
196: *> June 2016, Igor Kozachenko,
197: *> Computer Science Division,
198: *> University of California, Berkeley
199: *>
200: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
201: *> School of Mathematics,
202: *> University of Manchester
203: *>
204: *> \endverbatim
205: *
206: * =====================================================================
207: SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
208: *
209: * -- LAPACK computational routine --
210: * -- LAPACK is a software package provided by Univ. of Tennessee, --
211: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
212: *
213: * .. Scalar Arguments ..
214: CHARACTER UPLO
215: INTEGER INFO, LDA, LWORK, N
216: * ..
217: * .. Array Arguments ..
218: INTEGER IPIV( * )
219: COMPLEX*16 A( LDA, * ), WORK( * )
220: * ..
221: *
222: * =====================================================================
223: *
224: * .. Local Scalars ..
225: LOGICAL LQUERY, UPPER
226: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
227: * ..
228: * .. External Functions ..
229: LOGICAL LSAME
230: INTEGER ILAENV
231: EXTERNAL LSAME, ILAENV
232: * ..
233: * .. External Subroutines ..
234: EXTERNAL ZLASYF_ROOK, ZSYTF2_ROOK, XERBLA
235: * ..
236: * .. Intrinsic Functions ..
237: INTRINSIC MAX
238: * ..
239: * .. Executable Statements ..
240: *
241: * Test the input parameters.
242: *
243: INFO = 0
244: UPPER = LSAME( UPLO, 'U' )
245: LQUERY = ( LWORK.EQ.-1 )
246: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
247: INFO = -1
248: ELSE IF( N.LT.0 ) THEN
249: INFO = -2
250: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
251: INFO = -4
252: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
253: INFO = -7
254: END IF
255: *
256: IF( INFO.EQ.0 ) THEN
257: *
258: * Determine the block size
259: *
260: NB = ILAENV( 1, 'ZSYTRF_ROOK', UPLO, N, -1, -1, -1 )
261: LWKOPT = MAX( 1, N*NB )
262: WORK( 1 ) = LWKOPT
263: END IF
264: *
265: IF( INFO.NE.0 ) THEN
266: CALL XERBLA( 'ZSYTRF_ROOK', -INFO )
267: RETURN
268: ELSE IF( LQUERY ) THEN
269: RETURN
270: END IF
271: *
272: NBMIN = 2
273: LDWORK = N
274: IF( NB.GT.1 .AND. NB.LT.N ) THEN
275: IWS = LDWORK*NB
276: IF( LWORK.LT.IWS ) THEN
277: NB = MAX( LWORK / LDWORK, 1 )
278: NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF_ROOK',
279: $ UPLO, N, -1, -1, -1 ) )
280: END IF
281: ELSE
282: IWS = 1
283: END IF
284: IF( NB.LT.NBMIN )
285: $ NB = N
286: *
287: IF( UPPER ) THEN
288: *
289: * Factorize A as U*D*U**T using the upper triangle of A
290: *
291: * K is the main loop index, decreasing from N to 1 in steps of
292: * KB, where KB is the number of columns factorized by ZLASYF_ROOK;
293: * KB is either NB or NB-1, or K for the last block
294: *
295: K = N
296: 10 CONTINUE
297: *
298: * If K < 1, exit from loop
299: *
300: IF( K.LT.1 )
301: $ GO TO 40
302: *
303: IF( K.GT.NB ) THEN
304: *
305: * Factorize columns k-kb+1:k of A and use blocked code to
306: * update columns 1:k-kb
307: *
308: CALL ZLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
309: $ IPIV, WORK, LDWORK, IINFO )
310: ELSE
311: *
312: * Use unblocked code to factorize columns 1:k of A
313: *
314: CALL ZSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
315: KB = K
316: END IF
317: *
318: * Set INFO on the first occurrence of a zero pivot
319: *
320: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
321: $ INFO = IINFO
322: *
323: * No need to adjust IPIV
324: *
325: * Decrease K and return to the start of the main loop
326: *
327: K = K - KB
328: GO TO 10
329: *
330: ELSE
331: *
332: * Factorize A as L*D*L**T using the lower triangle of A
333: *
334: * K is the main loop index, increasing from 1 to N in steps of
335: * KB, where KB is the number of columns factorized by ZLASYF_ROOK;
336: * KB is either NB or NB-1, or N-K+1 for the last block
337: *
338: K = 1
339: 20 CONTINUE
340: *
341: * If K > N, exit from loop
342: *
343: IF( K.GT.N )
344: $ GO TO 40
345: *
346: IF( K.LE.N-NB ) THEN
347: *
348: * Factorize columns k:k+kb-1 of A and use blocked code to
349: * update columns k+kb:n
350: *
351: CALL ZLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
352: $ IPIV( K ), WORK, LDWORK, IINFO )
353: ELSE
354: *
355: * Use unblocked code to factorize columns k:n of A
356: *
357: CALL ZSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
358: $ IINFO )
359: KB = N - K + 1
360: END IF
361: *
362: * Set INFO on the first occurrence of a zero pivot
363: *
364: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
365: $ INFO = IINFO + K - 1
366: *
367: * Adjust IPIV
368: *
369: DO 30 J = K, K + KB - 1
370: IF( IPIV( J ).GT.0 ) THEN
371: IPIV( J ) = IPIV( J ) + K - 1
372: ELSE
373: IPIV( J ) = IPIV( J ) - K + 1
374: END IF
375: 30 CONTINUE
376: *
377: * Increase K and return to the start of the main loop
378: *
379: K = K + KB
380: GO TO 20
381: *
382: END IF
383: *
384: 40 CONTINUE
385: WORK( 1 ) = LWKOPT
386: RETURN
387: *
388: * End of ZSYTRF_ROOK
389: *
390: END
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