![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dtptri.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack|
Return to dtptri.f CVS log | Up to [local] / rpl / lapack / lapack |
1.1 bertrand 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