Annotation of rpl/lapack/lapack/dtrtri.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, 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 DIAG, UPLO
10: INTEGER INFO, LDA, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DTRTRI computes the inverse of a real upper or lower triangular
20: * matrix A.
21: *
22: * This is the Level 3 BLAS version of the algorithm.
23: *
24: * Arguments
25: * =========
26: *
27: * UPLO (input) CHARACTER*1
28: * = 'U': A is upper triangular;
29: * = 'L': A is lower triangular.
30: *
31: * DIAG (input) CHARACTER*1
32: * = 'N': A is non-unit triangular;
33: * = 'U': A is unit triangular.
34: *
35: * N (input) INTEGER
36: * The order of the matrix A. N >= 0.
37: *
38: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
39: * On entry, the triangular matrix A. If UPLO = 'U', the
40: * leading N-by-N upper triangular part of the array A contains
41: * the upper triangular matrix, and the strictly lower
42: * triangular part of A is not referenced. If UPLO = 'L', the
43: * leading N-by-N lower triangular part of the array A contains
44: * the lower triangular matrix, and the strictly upper
45: * triangular part of A is not referenced. If DIAG = 'U', the
46: * diagonal elements of A are also not referenced and are
47: * assumed to be 1.
48: * On exit, the (triangular) inverse of the original matrix, in
49: * the same storage format.
50: *
51: * LDA (input) INTEGER
52: * The leading dimension of the array A. LDA >= max(1,N).
53: *
54: * INFO (output) INTEGER
55: * = 0: successful exit
56: * < 0: if INFO = -i, the i-th argument had an illegal value
57: * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
58: * matrix is singular and its inverse can not be computed.
59: *
60: * =====================================================================
61: *
62: * .. Parameters ..
63: DOUBLE PRECISION ONE, ZERO
64: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
65: * ..
66: * .. Local Scalars ..
67: LOGICAL NOUNIT, UPPER
68: INTEGER J, JB, NB, NN
69: * ..
70: * .. External Functions ..
71: LOGICAL LSAME
72: INTEGER ILAENV
73: EXTERNAL LSAME, ILAENV
74: * ..
75: * .. External Subroutines ..
76: EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA
77: * ..
78: * .. Intrinsic Functions ..
79: INTRINSIC MAX, MIN
80: * ..
81: * .. Executable Statements ..
82: *
83: * Test the input parameters.
84: *
85: INFO = 0
86: UPPER = LSAME( UPLO, 'U' )
87: NOUNIT = LSAME( DIAG, 'N' )
88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
89: INFO = -1
90: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
91: INFO = -2
92: ELSE IF( N.LT.0 ) THEN
93: INFO = -3
94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
95: INFO = -5
96: END IF
97: IF( INFO.NE.0 ) THEN
98: CALL XERBLA( 'DTRTRI', -INFO )
99: RETURN
100: END IF
101: *
102: * Quick return if possible
103: *
104: IF( N.EQ.0 )
105: $ RETURN
106: *
107: * Check for singularity if non-unit.
108: *
109: IF( NOUNIT ) THEN
110: DO 10 INFO = 1, N
111: IF( A( INFO, INFO ).EQ.ZERO )
112: $ RETURN
113: 10 CONTINUE
114: INFO = 0
115: END IF
116: *
117: * Determine the block size for this environment.
118: *
119: NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 )
120: IF( NB.LE.1 .OR. NB.GE.N ) THEN
121: *
122: * Use unblocked code
123: *
124: CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
125: ELSE
126: *
127: * Use blocked code
128: *
129: IF( UPPER ) THEN
130: *
131: * Compute inverse of upper triangular matrix
132: *
133: DO 20 J = 1, N, NB
134: JB = MIN( NB, N-J+1 )
135: *
136: * Compute rows 1:j-1 of current block column
137: *
138: CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
139: $ JB, ONE, A, LDA, A( 1, J ), LDA )
140: CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
141: $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
142: *
143: * Compute inverse of current diagonal block
144: *
145: CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
146: 20 CONTINUE
147: ELSE
148: *
149: * Compute inverse of lower triangular matrix
150: *
151: NN = ( ( N-1 ) / NB )*NB + 1
152: DO 30 J = NN, 1, -NB
153: JB = MIN( NB, N-J+1 )
154: IF( J+JB.LE.N ) THEN
155: *
156: * Compute rows j+jb:n of current block column
157: *
158: CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG,
159: $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
160: $ A( J+JB, J ), LDA )
161: CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG,
162: $ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
163: $ A( J+JB, J ), LDA )
164: END IF
165: *
166: * Compute inverse of current diagonal block
167: *
168: CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
169: 30 CONTINUE
170: END IF
171: END IF
172: *
173: RETURN
174: *
175: * End of DTRTRI
176: *
177: END
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