Annotation of rpl/lapack/lapack/dgetri.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DGETRI( 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: INTEGER INFO, LDA, LWORK, N
10: * ..
11: * .. Array Arguments ..
12: INTEGER IPIV( * )
13: DOUBLE PRECISION A( LDA, * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DGETRI computes the inverse of a matrix using the LU factorization
20: * computed by DGETRF.
21: *
22: * This method inverts U and then computes inv(A) by solving the system
23: * inv(A)*L = inv(U) for inv(A).
24: *
25: * Arguments
26: * =========
27: *
28: * N (input) INTEGER
29: * The order of the matrix A. N >= 0.
30: *
31: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
32: * On entry, the factors L and U from the factorization
33: * A = P*L*U as computed by DGETRF.
34: * On exit, if INFO = 0, the inverse of the original matrix A.
35: *
36: * LDA (input) INTEGER
37: * The leading dimension of the array A. LDA >= max(1,N).
38: *
39: * IPIV (input) INTEGER array, dimension (N)
40: * The pivot indices from DGETRF; for 1<=i<=N, row i of the
41: * matrix was interchanged with row IPIV(i).
42: *
43: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
44: * On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
45: *
46: * LWORK (input) INTEGER
47: * The dimension of the array WORK. LWORK >= max(1,N).
48: * For optimal performance LWORK >= N*NB, where NB is
49: * the optimal blocksize returned by ILAENV.
50: *
51: * If LWORK = -1, then a workspace query is assumed; the routine
52: * only calculates the optimal size of the WORK array, returns
53: * this value as the first entry of the WORK array, and no error
54: * message related to LWORK is issued by XERBLA.
55: *
56: * INFO (output) INTEGER
57: * = 0: successful exit
58: * < 0: if INFO = -i, the i-th argument had an illegal value
59: * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
60: * singular and its inverse could not be computed.
61: *
62: * =====================================================================
63: *
64: * .. Parameters ..
65: DOUBLE PRECISION ZERO, ONE
66: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
67: * ..
68: * .. Local Scalars ..
69: LOGICAL LQUERY
70: INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
71: $ NBMIN, NN
72: * ..
73: * .. External Functions ..
74: INTEGER ILAENV
75: EXTERNAL ILAENV
76: * ..
77: * .. External Subroutines ..
78: EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA
79: * ..
80: * .. Intrinsic Functions ..
81: INTRINSIC MAX, MIN
82: * ..
83: * .. Executable Statements ..
84: *
85: * Test the input parameters.
86: *
87: INFO = 0
88: NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 )
89: LWKOPT = N*NB
90: WORK( 1 ) = LWKOPT
91: LQUERY = ( LWORK.EQ.-1 )
92: IF( N.LT.0 ) THEN
93: INFO = -1
94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
95: INFO = -3
96: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
97: INFO = -6
98: END IF
99: IF( INFO.NE.0 ) THEN
100: CALL XERBLA( 'DGETRI', -INFO )
101: RETURN
102: ELSE IF( LQUERY ) THEN
103: RETURN
104: END IF
105: *
106: * Quick return if possible
107: *
108: IF( N.EQ.0 )
109: $ RETURN
110: *
111: * Form inv(U). If INFO > 0 from DTRTRI, then U is singular,
112: * and the inverse is not computed.
113: *
114: CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
115: IF( INFO.GT.0 )
116: $ RETURN
117: *
118: NBMIN = 2
119: LDWORK = N
120: IF( NB.GT.1 .AND. NB.LT.N ) THEN
121: IWS = MAX( LDWORK*NB, 1 )
122: IF( LWORK.LT.IWS ) THEN
123: NB = LWORK / LDWORK
124: NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) )
125: END IF
126: ELSE
127: IWS = N
128: END IF
129: *
130: * Solve the equation inv(A)*L = inv(U) for inv(A).
131: *
132: IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
133: *
134: * Use unblocked code.
135: *
136: DO 20 J = N, 1, -1
137: *
138: * Copy current column of L to WORK and replace with zeros.
139: *
140: DO 10 I = J + 1, N
141: WORK( I ) = A( I, J )
142: A( I, J ) = ZERO
143: 10 CONTINUE
144: *
145: * Compute current column of inv(A).
146: *
147: IF( J.LT.N )
148: $ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
149: $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
150: 20 CONTINUE
151: ELSE
152: *
153: * Use blocked code.
154: *
155: NN = ( ( N-1 ) / NB )*NB + 1
156: DO 50 J = NN, 1, -NB
157: JB = MIN( NB, N-J+1 )
158: *
159: * Copy current block column of L to WORK and replace with
160: * zeros.
161: *
162: DO 40 JJ = J, J + JB - 1
163: DO 30 I = JJ + 1, N
164: WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
165: A( I, JJ ) = ZERO
166: 30 CONTINUE
167: 40 CONTINUE
168: *
169: * Compute current block column of inv(A).
170: *
171: IF( J+JB.LE.N )
172: $ CALL DGEMM( 'No transpose', 'No transpose', N, JB,
173: $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
174: $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
175: CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
176: $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
177: 50 CONTINUE
178: END IF
179: *
180: * Apply column interchanges.
181: *
182: DO 60 J = N - 1, 1, -1
183: JP = IPIV( J )
184: IF( JP.NE.J )
185: $ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
186: 60 CONTINUE
187: *
188: WORK( 1 ) = IWS
189: RETURN
190: *
191: * End of DGETRI
192: *
193: END
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