Annotation of rpl/lapack/lapack/zhetrf.f, revision 1.7
1.1 bertrand 1: SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, LDA, LWORK, N
11: * ..
12: * .. Array Arguments ..
13: INTEGER IPIV( * )
14: COMPLEX*16 A( LDA, * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZHETRF computes the factorization of a complex Hermitian matrix A
21: * using the Bunch-Kaufman diagonal pivoting method. The form of the
22: * factorization is
23: *
24: * A = U*D*U**H or A = L*D*L**H
25: *
26: * where U (or L) is a product of permutation and unit upper (lower)
27: * triangular matrices, and D is Hermitian and block diagonal with
28: * 1-by-1 and 2-by-2 diagonal blocks.
29: *
30: * This is the blocked version of the algorithm, calling Level 3 BLAS.
31: *
32: * Arguments
33: * =========
34: *
35: * UPLO (input) CHARACTER*1
36: * = 'U': Upper triangle of A is stored;
37: * = 'L': Lower triangle of A is stored.
38: *
39: * N (input) INTEGER
40: * The order of the matrix A. N >= 0.
41: *
42: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
43: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
44: * N-by-N upper triangular part of A contains the upper
45: * triangular part of the matrix A, and the strictly lower
46: * triangular part of A is not referenced. If UPLO = 'L', the
47: * leading N-by-N lower triangular part of A contains the lower
48: * triangular part of the matrix A, and the strictly upper
49: * triangular part of A is not referenced.
50: *
51: * On exit, the block diagonal matrix D and the multipliers used
52: * to obtain the factor U or L (see below for further details).
53: *
54: * LDA (input) INTEGER
55: * The leading dimension of the array A. LDA >= max(1,N).
56: *
57: * IPIV (output) INTEGER array, dimension (N)
58: * Details of the interchanges and the block structure of D.
59: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were
60: * interchanged and D(k,k) is a 1-by-1 diagonal block.
61: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
62: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
63: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
64: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
65: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
66: *
67: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
68: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
69: *
70: * LWORK (input) INTEGER
71: * The length of WORK. LWORK >=1. For best performance
72: * LWORK >= N*NB, where NB is the block size returned by ILAENV.
73: *
74: * INFO (output) INTEGER
75: * = 0: successful exit
76: * < 0: if INFO = -i, the i-th argument had an illegal value
77: * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
78: * has been completed, but the block diagonal matrix D is
79: * exactly singular, and division by zero will occur if it
80: * is used to solve a system of equations.
81: *
82: * Further Details
83: * ===============
84: *
85: * If UPLO = 'U', then A = U*D*U', where
86: * U = P(n)*U(n)* ... *P(k)U(k)* ...,
87: * i.e., U is a product of terms P(k)*U(k), where k decreases from n to
88: * 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
89: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
90: * defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
91: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
92: *
93: * ( I v 0 ) k-s
94: * U(k) = ( 0 I 0 ) s
95: * ( 0 0 I ) n-k
96: * k-s s n-k
97: *
98: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
99: * If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
100: * and A(k,k), and v overwrites A(1:k-2,k-1:k).
101: *
102: * If UPLO = 'L', then A = L*D*L', where
103: * L = P(1)*L(1)* ... *P(k)*L(k)* ...,
104: * i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
105: * n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
106: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
107: * defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
108: * that if the diagonal block D(k) is of order s (s = 1 or 2), then
109: *
110: * ( I 0 0 ) k-1
111: * L(k) = ( 0 I 0 ) s
112: * ( 0 v I ) n-k-s+1
113: * k-1 s n-k-s+1
114: *
115: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
116: * If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
117: * and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
118: *
119: * =====================================================================
120: *
121: * .. Local Scalars ..
122: LOGICAL LQUERY, UPPER
123: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
124: * ..
125: * .. External Functions ..
126: LOGICAL LSAME
127: INTEGER ILAENV
128: EXTERNAL LSAME, ILAENV
129: * ..
130: * .. External Subroutines ..
131: EXTERNAL XERBLA, ZHETF2, ZLAHEF
132: * ..
133: * .. Intrinsic Functions ..
134: INTRINSIC MAX
135: * ..
136: * .. Executable Statements ..
137: *
138: * Test the input parameters.
139: *
140: INFO = 0
141: UPPER = LSAME( UPLO, 'U' )
142: LQUERY = ( LWORK.EQ.-1 )
143: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
144: INFO = -1
145: ELSE IF( N.LT.0 ) THEN
146: INFO = -2
147: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
148: INFO = -4
149: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
150: INFO = -7
151: END IF
152: *
153: IF( INFO.EQ.0 ) THEN
154: *
155: * Determine the block size
156: *
157: NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
158: LWKOPT = N*NB
159: WORK( 1 ) = LWKOPT
160: END IF
161: *
162: IF( INFO.NE.0 ) THEN
163: CALL XERBLA( 'ZHETRF', -INFO )
164: RETURN
165: ELSE IF( LQUERY ) THEN
166: RETURN
167: END IF
168: *
169: NBMIN = 2
170: LDWORK = N
171: IF( NB.GT.1 .AND. NB.LT.N ) THEN
172: IWS = LDWORK*NB
173: IF( LWORK.LT.IWS ) THEN
174: NB = MAX( LWORK / LDWORK, 1 )
175: NBMIN = MAX( 2, ILAENV( 2, 'ZHETRF', UPLO, N, -1, -1, -1 ) )
176: END IF
177: ELSE
178: IWS = 1
179: END IF
180: IF( NB.LT.NBMIN )
181: $ NB = N
182: *
183: IF( UPPER ) THEN
184: *
185: * Factorize A as U*D*U' using the upper triangle of A
186: *
187: * K is the main loop index, decreasing from N to 1 in steps of
188: * KB, where KB is the number of columns factorized by ZLAHEF;
189: * KB is either NB or NB-1, or K for the last block
190: *
191: K = N
192: 10 CONTINUE
193: *
194: * If K < 1, exit from loop
195: *
196: IF( K.LT.1 )
197: $ GO TO 40
198: *
199: IF( K.GT.NB ) THEN
200: *
201: * Factorize columns k-kb+1:k of A and use blocked code to
202: * update columns 1:k-kb
203: *
204: CALL ZLAHEF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
205: ELSE
206: *
207: * Use unblocked code to factorize columns 1:k of A
208: *
209: CALL ZHETF2( UPLO, K, A, LDA, IPIV, IINFO )
210: KB = K
211: END IF
212: *
213: * Set INFO on the first occurrence of a zero pivot
214: *
215: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
216: $ INFO = IINFO
217: *
218: * Decrease K and return to the start of the main loop
219: *
220: K = K - KB
221: GO TO 10
222: *
223: ELSE
224: *
225: * Factorize A as L*D*L' using the lower triangle of A
226: *
227: * K is the main loop index, increasing from 1 to N in steps of
228: * KB, where KB is the number of columns factorized by ZLAHEF;
229: * KB is either NB or NB-1, or N-K+1 for the last block
230: *
231: K = 1
232: 20 CONTINUE
233: *
234: * If K > N, exit from loop
235: *
236: IF( K.GT.N )
237: $ GO TO 40
238: *
239: IF( K.LE.N-NB ) THEN
240: *
241: * Factorize columns k:k+kb-1 of A and use blocked code to
242: * update columns k+kb:n
243: *
244: CALL ZLAHEF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
245: $ WORK, N, IINFO )
246: ELSE
247: *
248: * Use unblocked code to factorize columns k:n of A
249: *
250: CALL ZHETF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
251: KB = N - K + 1
252: END IF
253: *
254: * Set INFO on the first occurrence of a zero pivot
255: *
256: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
257: $ INFO = IINFO + K - 1
258: *
259: * Adjust IPIV
260: *
261: DO 30 J = K, K + KB - 1
262: IF( IPIV( J ).GT.0 ) THEN
263: IPIV( J ) = IPIV( J ) + K - 1
264: ELSE
265: IPIV( J ) = IPIV( J ) - K + 1
266: END IF
267: 30 CONTINUE
268: *
269: * Increase K and return to the start of the main loop
270: *
271: K = K + KB
272: GO TO 20
273: *
274: END IF
275: *
276: 40 CONTINUE
277: WORK( 1 ) = LWKOPT
278: RETURN
279: *
280: * End of ZHETRF
281: *
282: END
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