1 SUBROUTINE DTPTRI( 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 DOUBLE PRECISION AP( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DTPTRI computes the inverse of a real 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) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
72 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL NOUNIT, UPPER
76 INTEGER J, JC, JCLAST, JJ
77 DOUBLE PRECISION AJJ
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 EXTERNAL LSAME
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DSCAL, DTPMV, XERBLA
85 * ..
86 * .. Executable Statements ..
87 *
88 * Test the input parameters.
89 *
90 INFO = 0
91 UPPER = LSAME( UPLO, 'U' )
92 NOUNIT = LSAME( DIAG, 'N' )
93 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
94 INFO = -1
95 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
96 INFO = -2
97 ELSE IF( N.LT.0 ) THEN
98 INFO = -3
99 END IF
100 IF( INFO.NE.0 ) THEN
101 CALL XERBLA( 'DTPTRI', -INFO )
102 RETURN
103 END IF
104 *
105 * Check for singularity if non-unit.
106 *
107 IF( NOUNIT ) THEN
108 IF( UPPER ) THEN
109 JJ = 0
110 DO 10 INFO = 1, N
111 JJ = JJ + INFO
112 IF( AP( JJ ).EQ.ZERO )
113 $ RETURN
114 10 CONTINUE
115 ELSE
116 JJ = 1
117 DO 20 INFO = 1, N
118 IF( AP( JJ ).EQ.ZERO )
119 $ RETURN
120 JJ = JJ + N - INFO + 1
121 20 CONTINUE
122 END IF
123 INFO = 0
124 END IF
125 *
126 IF( UPPER ) THEN
127 *
128 * Compute inverse of upper triangular matrix.
129 *
130 JC = 1
131 DO 30 J = 1, N
132 IF( NOUNIT ) THEN
133 AP( JC+J-1 ) = ONE / AP( JC+J-1 )
134 AJJ = -AP( JC+J-1 )
135 ELSE
136 AJJ = -ONE
137 END IF
138 *
139 * Compute elements 1:j-1 of j-th column.
140 *
141 CALL DTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
142 $ AP( JC ), 1 )
143 CALL DSCAL( J-1, AJJ, AP( JC ), 1 )
144 JC = JC + J
145 30 CONTINUE
146 *
147 ELSE
148 *
149 * Compute inverse of lower triangular matrix.
150 *
151 JC = N*( N+1 ) / 2
152 DO 40 J = N, 1, -1
153 IF( NOUNIT ) THEN
154 AP( JC ) = ONE / AP( JC )
155 AJJ = -AP( JC )
156 ELSE
157 AJJ = -ONE
158 END IF
159 IF( J.LT.N ) THEN
160 *
161 * Compute elements j+1:n of j-th column.
162 *
163 CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J,
164 $ AP( JCLAST ), AP( JC+1 ), 1 )
165 CALL DSCAL( N-J, AJJ, AP( JC+1 ), 1 )
166 END IF
167 JCLAST = JC
168 JC = JC - N + J - 2
169 40 CONTINUE
170 END IF
171 *
172 RETURN
173 *
174 * End of DTPTRI
175 *
176 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 DOUBLE PRECISION AP( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DTPTRI computes the inverse of a real 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) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO
72 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL NOUNIT, UPPER
76 INTEGER J, JC, JCLAST, JJ
77 DOUBLE PRECISION AJJ
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 EXTERNAL LSAME
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DSCAL, DTPMV, XERBLA
85 * ..
86 * .. Executable Statements ..
87 *
88 * Test the input parameters.
89 *
90 INFO = 0
91 UPPER = LSAME( UPLO, 'U' )
92 NOUNIT = LSAME( DIAG, 'N' )
93 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
94 INFO = -1
95 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
96 INFO = -2
97 ELSE IF( N.LT.0 ) THEN
98 INFO = -3
99 END IF
100 IF( INFO.NE.0 ) THEN
101 CALL XERBLA( 'DTPTRI', -INFO )
102 RETURN
103 END IF
104 *
105 * Check for singularity if non-unit.
106 *
107 IF( NOUNIT ) THEN
108 IF( UPPER ) THEN
109 JJ = 0
110 DO 10 INFO = 1, N
111 JJ = JJ + INFO
112 IF( AP( JJ ).EQ.ZERO )
113 $ RETURN
114 10 CONTINUE
115 ELSE
116 JJ = 1
117 DO 20 INFO = 1, N
118 IF( AP( JJ ).EQ.ZERO )
119 $ RETURN
120 JJ = JJ + N - INFO + 1
121 20 CONTINUE
122 END IF
123 INFO = 0
124 END IF
125 *
126 IF( UPPER ) THEN
127 *
128 * Compute inverse of upper triangular matrix.
129 *
130 JC = 1
131 DO 30 J = 1, N
132 IF( NOUNIT ) THEN
133 AP( JC+J-1 ) = ONE / AP( JC+J-1 )
134 AJJ = -AP( JC+J-1 )
135 ELSE
136 AJJ = -ONE
137 END IF
138 *
139 * Compute elements 1:j-1 of j-th column.
140 *
141 CALL DTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
142 $ AP( JC ), 1 )
143 CALL DSCAL( J-1, AJJ, AP( JC ), 1 )
144 JC = JC + J
145 30 CONTINUE
146 *
147 ELSE
148 *
149 * Compute inverse of lower triangular matrix.
150 *
151 JC = N*( N+1 ) / 2
152 DO 40 J = N, 1, -1
153 IF( NOUNIT ) THEN
154 AP( JC ) = ONE / AP( JC )
155 AJJ = -AP( JC )
156 ELSE
157 AJJ = -ONE
158 END IF
159 IF( J.LT.N ) THEN
160 *
161 * Compute elements j+1:n of j-th column.
162 *
163 CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J,
164 $ AP( JCLAST ), AP( JC+1 ), 1 )
165 CALL DSCAL( N-J, AJJ, AP( JC+1 ), 1 )
166 END IF
167 JCLAST = JC
168 JC = JC - N + J - 2
169 40 CONTINUE
170 END IF
171 *
172 RETURN
173 *
174 * End of DTPTRI
175 *
176 END