Annotation of rpl/lapack/lapack/ztrtri.f, revision 1.3
1.1 bertrand 1: SUBROUTINE ZTRTRI( 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: COMPLEX*16 A( LDA, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZTRTRI computes the inverse of a complex 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) COMPLEX*16 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: COMPLEX*16 ONE, ZERO
64: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
65: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
66: * ..
67: * .. Local Scalars ..
68: LOGICAL NOUNIT, UPPER
69: INTEGER J, JB, NB, NN
70: * ..
71: * .. External Functions ..
72: LOGICAL LSAME
73: INTEGER ILAENV
74: EXTERNAL LSAME, ILAENV
75: * ..
76: * .. External Subroutines ..
77: EXTERNAL XERBLA, ZTRMM, ZTRSM, ZTRTI2
78: * ..
79: * .. Intrinsic Functions ..
80: INTRINSIC MAX, MIN
81: * ..
82: * .. Executable Statements ..
83: *
84: * Test the input parameters.
85: *
86: INFO = 0
87: UPPER = LSAME( UPLO, 'U' )
88: NOUNIT = LSAME( DIAG, 'N' )
89: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
90: INFO = -1
91: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
92: INFO = -2
93: ELSE IF( N.LT.0 ) THEN
94: INFO = -3
95: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
96: INFO = -5
97: END IF
98: IF( INFO.NE.0 ) THEN
99: CALL XERBLA( 'ZTRTRI', -INFO )
100: RETURN
101: END IF
102: *
103: * Quick return if possible
104: *
105: IF( N.EQ.0 )
106: $ RETURN
107: *
108: * Check for singularity if non-unit.
109: *
110: IF( NOUNIT ) THEN
111: DO 10 INFO = 1, N
112: IF( A( INFO, INFO ).EQ.ZERO )
113: $ RETURN
114: 10 CONTINUE
115: INFO = 0
116: END IF
117: *
118: * Determine the block size for this environment.
119: *
120: NB = ILAENV( 1, 'ZTRTRI', UPLO // DIAG, N, -1, -1, -1 )
121: IF( NB.LE.1 .OR. NB.GE.N ) THEN
122: *
123: * Use unblocked code
124: *
125: CALL ZTRTI2( UPLO, DIAG, N, A, LDA, INFO )
126: ELSE
127: *
128: * Use blocked code
129: *
130: IF( UPPER ) THEN
131: *
132: * Compute inverse of upper triangular matrix
133: *
134: DO 20 J = 1, N, NB
135: JB = MIN( NB, N-J+1 )
136: *
137: * Compute rows 1:j-1 of current block column
138: *
139: CALL ZTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
140: $ JB, ONE, A, LDA, A( 1, J ), LDA )
141: CALL ZTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
142: $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
143: *
144: * Compute inverse of current diagonal block
145: *
146: CALL ZTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
147: 20 CONTINUE
148: ELSE
149: *
150: * Compute inverse of lower triangular matrix
151: *
152: NN = ( ( N-1 ) / NB )*NB + 1
153: DO 30 J = NN, 1, -NB
154: JB = MIN( NB, N-J+1 )
155: IF( J+JB.LE.N ) THEN
156: *
157: * Compute rows j+jb:n of current block column
158: *
159: CALL ZTRMM( 'Left', 'Lower', 'No transpose', DIAG,
160: $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
161: $ A( J+JB, J ), LDA )
162: CALL ZTRSM( 'Right', 'Lower', 'No transpose', DIAG,
163: $ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
164: $ A( J+JB, J ), LDA )
165: END IF
166: *
167: * Compute inverse of current diagonal block
168: *
169: CALL ZTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
170: 30 CONTINUE
171: END IF
172: END IF
173: *
174: RETURN
175: *
176: * End of ZTRTRI
177: *
178: END
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