1 SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, 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, N
11 * ..
12 * .. Array Arguments ..
13 COMPLEX*16 AP( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZTPTRI computes the inverse of a complex upper or lower triangular
20 * matrix A stored in packed format.
21 *
22 * Arguments
23 * =========
24 *
25 * UPLO (input) CHARACTER*1
26 * = 'U': A is upper triangular;
27 * = 'L': A is lower triangular.
28 *
29 * DIAG (input) CHARACTER*1
30 * = 'N': A is non-unit triangular;
31 * = 'U': A is unit triangular.
32 *
33 * N (input) INTEGER
34 * The order of the matrix A. N >= 0.
35 *
36 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
37 * On entry, the upper or lower triangular matrix A, stored
38 * columnwise in a linear array. The j-th column of A is stored
39 * in the array AP as follows:
40 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
41 * if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
42 * See below for further details.
43 * On exit, the (triangular) inverse of the original matrix, in
44 * the same packed storage format.
45 *
46 * INFO (output) INTEGER
47 * = 0: successful exit
48 * < 0: if INFO = -i, the i-th argument had an illegal value
49 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
50 * matrix is singular and its inverse can not be computed.
51 *
52 * Further Details
53 * ===============
54 *
55 * A triangular matrix A can be transferred to packed storage using one
56 * of the following program segments:
57 *
58 * UPLO = 'U': UPLO = 'L':
59 *
60 * JC = 1 JC = 1
61 * DO 2 J = 1, N DO 2 J = 1, N
62 * DO 1 I = 1, J DO 1 I = J, N
63 * AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
64 * 1 CONTINUE 1 CONTINUE
65 * JC = JC + J JC = JC + N - J + 1
66 * 2 CONTINUE 2 CONTINUE
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 COMPLEX*16 ONE, ZERO
72 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
73 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL NOUNIT, UPPER
77 INTEGER J, JC, JCLAST, JJ
78 COMPLEX*16 AJJ
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 EXTERNAL LSAME
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL XERBLA, ZSCAL, ZTPMV
86 * ..
87 * .. Executable Statements ..
88 *
89 * Test the input parameters.
90 *
91 INFO = 0
92 UPPER = LSAME( UPLO, 'U' )
93 NOUNIT = LSAME( DIAG, 'N' )
94 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
95 INFO = -1
96 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
97 INFO = -2
98 ELSE IF( N.LT.0 ) THEN
99 INFO = -3
100 END IF
101 IF( INFO.NE.0 ) THEN
102 CALL XERBLA( 'ZTPTRI', -INFO )
103 RETURN
104 END IF
105 *
106 * Check for singularity if non-unit.
107 *
108 IF( NOUNIT ) THEN
109 IF( UPPER ) THEN
110 JJ = 0
111 DO 10 INFO = 1, N
112 JJ = JJ + INFO
113 IF( AP( JJ ).EQ.ZERO )
114 $ RETURN
115 10 CONTINUE
116 ELSE
117 JJ = 1
118 DO 20 INFO = 1, N
119 IF( AP( JJ ).EQ.ZERO )
120 $ RETURN
121 JJ = JJ + N - INFO + 1
122 20 CONTINUE
123 END IF
124 INFO = 0
125 END IF
126 *
127 IF( UPPER ) THEN
128 *
129 * Compute inverse of upper triangular matrix.
130 *
131 JC = 1
132 DO 30 J = 1, N
133 IF( NOUNIT ) THEN
134 AP( JC+J-1 ) = ONE / AP( JC+J-1 )
135 AJJ = -AP( JC+J-1 )
136 ELSE
137 AJJ = -ONE
138 END IF
139 *
140 * Compute elements 1:j-1 of j-th column.
141 *
142 CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
143 $ AP( JC ), 1 )
144 CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
145 JC = JC + J
146 30 CONTINUE
147 *
148 ELSE
149 *
150 * Compute inverse of lower triangular matrix.
151 *
152 JC = N*( N+1 ) / 2
153 DO 40 J = N, 1, -1
154 IF( NOUNIT ) THEN
155 AP( JC ) = ONE / AP( JC )
156 AJJ = -AP( JC )
157 ELSE
158 AJJ = -ONE
159 END IF
160 IF( J.LT.N ) THEN
161 *
162 * Compute elements j+1:n of j-th column.
163 *
164 CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
165 $ AP( JCLAST ), AP( JC+1 ), 1 )
166 CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
167 END IF
168 JCLAST = JC
169 JC = JC - N + J - 2
170 40 CONTINUE
171 END IF
172 *
173 RETURN
174 *
175 * End of ZTPTRI
176 *
177 END
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, N
11 * ..
12 * .. Array Arguments ..
13 COMPLEX*16 AP( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZTPTRI computes the inverse of a complex upper or lower triangular
20 * matrix A stored in packed format.
21 *
22 * Arguments
23 * =========
24 *
25 * UPLO (input) CHARACTER*1
26 * = 'U': A is upper triangular;
27 * = 'L': A is lower triangular.
28 *
29 * DIAG (input) CHARACTER*1
30 * = 'N': A is non-unit triangular;
31 * = 'U': A is unit triangular.
32 *
33 * N (input) INTEGER
34 * The order of the matrix A. N >= 0.
35 *
36 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
37 * On entry, the upper or lower triangular matrix A, stored
38 * columnwise in a linear array. The j-th column of A is stored
39 * in the array AP as follows:
40 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
41 * if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
42 * See below for further details.
43 * On exit, the (triangular) inverse of the original matrix, in
44 * the same packed storage format.
45 *
46 * INFO (output) INTEGER
47 * = 0: successful exit
48 * < 0: if INFO = -i, the i-th argument had an illegal value
49 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
50 * matrix is singular and its inverse can not be computed.
51 *
52 * Further Details
53 * ===============
54 *
55 * A triangular matrix A can be transferred to packed storage using one
56 * of the following program segments:
57 *
58 * UPLO = 'U': UPLO = 'L':
59 *
60 * JC = 1 JC = 1
61 * DO 2 J = 1, N DO 2 J = 1, N
62 * DO 1 I = 1, J DO 1 I = J, N
63 * AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
64 * 1 CONTINUE 1 CONTINUE
65 * JC = JC + J JC = JC + N - J + 1
66 * 2 CONTINUE 2 CONTINUE
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 COMPLEX*16 ONE, ZERO
72 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
73 $ ZERO = ( 0.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL NOUNIT, UPPER
77 INTEGER J, JC, JCLAST, JJ
78 COMPLEX*16 AJJ
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 EXTERNAL LSAME
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL XERBLA, ZSCAL, ZTPMV
86 * ..
87 * .. Executable Statements ..
88 *
89 * Test the input parameters.
90 *
91 INFO = 0
92 UPPER = LSAME( UPLO, 'U' )
93 NOUNIT = LSAME( DIAG, 'N' )
94 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
95 INFO = -1
96 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
97 INFO = -2
98 ELSE IF( N.LT.0 ) THEN
99 INFO = -3
100 END IF
101 IF( INFO.NE.0 ) THEN
102 CALL XERBLA( 'ZTPTRI', -INFO )
103 RETURN
104 END IF
105 *
106 * Check for singularity if non-unit.
107 *
108 IF( NOUNIT ) THEN
109 IF( UPPER ) THEN
110 JJ = 0
111 DO 10 INFO = 1, N
112 JJ = JJ + INFO
113 IF( AP( JJ ).EQ.ZERO )
114 $ RETURN
115 10 CONTINUE
116 ELSE
117 JJ = 1
118 DO 20 INFO = 1, N
119 IF( AP( JJ ).EQ.ZERO )
120 $ RETURN
121 JJ = JJ + N - INFO + 1
122 20 CONTINUE
123 END IF
124 INFO = 0
125 END IF
126 *
127 IF( UPPER ) THEN
128 *
129 * Compute inverse of upper triangular matrix.
130 *
131 JC = 1
132 DO 30 J = 1, N
133 IF( NOUNIT ) THEN
134 AP( JC+J-1 ) = ONE / AP( JC+J-1 )
135 AJJ = -AP( JC+J-1 )
136 ELSE
137 AJJ = -ONE
138 END IF
139 *
140 * Compute elements 1:j-1 of j-th column.
141 *
142 CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
143 $ AP( JC ), 1 )
144 CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
145 JC = JC + J
146 30 CONTINUE
147 *
148 ELSE
149 *
150 * Compute inverse of lower triangular matrix.
151 *
152 JC = N*( N+1 ) / 2
153 DO 40 J = N, 1, -1
154 IF( NOUNIT ) THEN
155 AP( JC ) = ONE / AP( JC )
156 AJJ = -AP( JC )
157 ELSE
158 AJJ = -ONE
159 END IF
160 IF( J.LT.N ) THEN
161 *
162 * Compute elements j+1:n of j-th column.
163 *
164 CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
165 $ AP( JCLAST ), AP( JC+1 ), 1 )
166 CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
167 END IF
168 JCLAST = JC
169 JC = JC - N + J - 2
170 40 CONTINUE
171 END IF
172 *
173 RETURN
174 *
175 * End of ZTPTRI
176 *
177 END