Annotation of rpl/lapack/lapack/zgetrf2.f, revision 1.7
1.1 bertrand 1: *> \brief \b ZGETRF2
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.4 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
8: * Definition:
9: * ===========
10: *
11: * RECURSIVE SUBROUTINE ZGETRF2( M, N, A, LDA, IPIV, INFO )
1.4 bertrand 12: *
1.1 bertrand 13: * .. Scalar Arguments ..
14: * INTEGER INFO, LDA, M, N
15: * ..
16: * .. Array Arguments ..
17: * INTEGER IPIV( * )
18: * COMPLEX*16 A( LDA, * )
19: * ..
1.4 bertrand 20: *
1.1 bertrand 21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> ZGETRF2 computes an LU factorization of a general M-by-N matrix A
28: *> using partial pivoting with row interchanges.
29: *>
30: *> The factorization has the form
31: *> A = P * L * U
32: *> where P is a permutation matrix, L is lower triangular with unit
33: *> diagonal elements (lower trapezoidal if m > n), and U is upper
34: *> triangular (upper trapezoidal if m < n).
35: *>
36: *> This is the recursive version of the algorithm. It divides
37: *> the matrix into four submatrices:
1.4 bertrand 38: *>
1.1 bertrand 39: *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
1.2 bertrand 40: *> A = [ -----|----- ] with n1 = min(m,n)/2
1.1 bertrand 41: *> [ A21 | A22 ] n2 = n-n1
1.4 bertrand 42: *>
1.1 bertrand 43: *> [ A11 ]
44: *> The subroutine calls itself to factor [ --- ],
45: *> [ A12 ]
46: *> [ A12 ]
47: *> do the swaps on [ --- ], solve A12, update A22,
48: *> [ A22 ]
49: *>
50: *> then calls itself to factor A22 and do the swaps on A21.
51: *>
52: *> \endverbatim
53: *
54: * Arguments:
55: * ==========
56: *
57: *> \param[in] M
58: *> \verbatim
59: *> M is INTEGER
60: *> The number of rows of the matrix A. M >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] N
64: *> \verbatim
65: *> N is INTEGER
66: *> The number of columns of the matrix A. N >= 0.
67: *> \endverbatim
68: *>
69: *> \param[in,out] A
70: *> \verbatim
71: *> A is COMPLEX*16 array, dimension (LDA,N)
72: *> On entry, the M-by-N matrix to be factored.
73: *> On exit, the factors L and U from the factorization
74: *> A = P*L*U; the unit diagonal elements of L are not stored.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The leading dimension of the array A. LDA >= max(1,M).
81: *> \endverbatim
82: *>
83: *> \param[out] IPIV
84: *> \verbatim
85: *> IPIV is INTEGER array, dimension (min(M,N))
86: *> The pivot indices; for 1 <= i <= min(M,N), row i of the
87: *> matrix was interchanged with row IPIV(i).
88: *> \endverbatim
89: *>
90: *> \param[out] INFO
91: *> \verbatim
92: *> INFO is INTEGER
93: *> = 0: successful exit
94: *> < 0: if INFO = -i, the i-th argument had an illegal value
95: *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
96: *> has been completed, but the factor U is exactly
97: *> singular, and division by zero will occur if it is used
98: *> to solve a system of equations.
99: *> \endverbatim
100: *
101: * Authors:
102: * ========
103: *
1.4 bertrand 104: *> \author Univ. of Tennessee
105: *> \author Univ. of California Berkeley
106: *> \author Univ. of Colorado Denver
107: *> \author NAG Ltd.
1.1 bertrand 108: *
109: *> \ingroup complex16GEcomputational
110: *
111: * =====================================================================
112: RECURSIVE SUBROUTINE ZGETRF2( M, N, A, LDA, IPIV, INFO )
113: *
1.7 ! bertrand 114: * -- LAPACK computational routine --
1.1 bertrand 115: * -- LAPACK is a software package provided by Univ. of Tennessee, --
116: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117: *
118: * .. Scalar Arguments ..
119: INTEGER INFO, LDA, M, N
120: * ..
121: * .. Array Arguments ..
122: INTEGER IPIV( * )
123: COMPLEX*16 A( LDA, * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: COMPLEX*16 ONE, ZERO
130: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
131: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
132: * ..
133: * .. Local Scalars ..
134: DOUBLE PRECISION SFMIN
135: COMPLEX*16 TEMP
136: INTEGER I, IINFO, N1, N2
137: * ..
138: * .. External Functions ..
139: DOUBLE PRECISION DLAMCH
140: INTEGER IZAMAX
141: EXTERNAL DLAMCH, IZAMAX
142: * ..
143: * .. External Subroutines ..
1.2 bertrand 144: EXTERNAL ZGEMM, ZSCAL, ZLASWP, ZTRSM, XERBLA
1.1 bertrand 145: * ..
146: * .. Intrinsic Functions ..
147: INTRINSIC MAX, MIN
148: * ..
149: * .. Executable Statements ..
150: *
151: * Test the input parameters
152: *
153: INFO = 0
154: IF( M.LT.0 ) THEN
155: INFO = -1
156: ELSE IF( N.LT.0 ) THEN
157: INFO = -2
158: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
159: INFO = -4
160: END IF
161: IF( INFO.NE.0 ) THEN
162: CALL XERBLA( 'ZGETRF2', -INFO )
163: RETURN
164: END IF
165: *
166: * Quick return if possible
167: *
168: IF( M.EQ.0 .OR. N.EQ.0 )
169: $ RETURN
170:
171: IF ( M.EQ.1 ) THEN
172: *
173: * Use unblocked code for one row case
174: * Just need to handle IPIV and INFO
175: *
176: IPIV( 1 ) = 1
177: IF ( A(1,1).EQ.ZERO )
178: $ INFO = 1
179: *
180: ELSE IF( N.EQ.1 ) THEN
181: *
182: * Use unblocked code for one column case
183: *
184: *
185: * Compute machine safe minimum
186: *
187: SFMIN = DLAMCH('S')
188: *
189: * Find pivot and test for singularity
190: *
191: I = IZAMAX( M, A( 1, 1 ), 1 )
192: IPIV( 1 ) = I
193: IF( A( I, 1 ).NE.ZERO ) THEN
194: *
195: * Apply the interchange
196: *
197: IF( I.NE.1 ) THEN
198: TEMP = A( 1, 1 )
199: A( 1, 1 ) = A( I, 1 )
200: A( I, 1 ) = TEMP
201: END IF
202: *
203: * Compute elements 2:M of the column
204: *
205: IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN
206: CALL ZSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 )
207: ELSE
208: DO 10 I = 1, M-1
209: A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 )
210: 10 CONTINUE
211: END IF
212: *
213: ELSE
214: INFO = 1
215: END IF
216:
217: ELSE
218: *
219: * Use recursive code
220: *
221: N1 = MIN( M, N ) / 2
222: N2 = N-N1
223: *
224: * [ A11 ]
225: * Factor [ --- ]
226: * [ A21 ]
227: *
228: CALL ZGETRF2( M, N1, A, LDA, IPIV, IINFO )
229:
230: IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
231: $ INFO = IINFO
232: *
233: * [ A12 ]
234: * Apply interchanges to [ --- ]
235: * [ A22 ]
236: *
237: CALL ZLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 )
238: *
239: * Solve A12
240: *
1.4 bertrand 241: CALL ZTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA,
1.1 bertrand 242: $ A( 1, N1+1 ), LDA )
243: *
244: * Update A22
245: *
1.4 bertrand 246: CALL ZGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA,
1.1 bertrand 247: $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA )
248: *
249: * Factor A22
250: *
251: CALL ZGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ),
252: $ IINFO )
253: *
254: * Adjust INFO and the pivot indices
255: *
256: IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
257: $ INFO = IINFO + N1
258: DO 20 I = N1+1, MIN( M, N )
259: IPIV( I ) = IPIV( I ) + N1
260: 20 CONTINUE
261: *
262: * Apply interchanges to A21
263: *
264: CALL ZLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 )
265: *
266: END IF
267: RETURN
268: *
269: * End of ZGETRF2
270: *
271: END
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