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1.1 bertrand 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