1DTBCON(1)                LAPACK routine (version 3.2)                DTBCON(1)
2
3
4

NAME

6       DTBCON - estimates the reciprocal of the condition number of a triangu‐
7       lar band matrix A, in either the 1-norm or the infinity-norm
8

SYNOPSIS

10       SUBROUTINE DTBCON( NORM, UPLO, DIAG, N,  KD,  AB,  LDAB,  RCOND,  WORK,
11                          IWORK, INFO )
12
13           CHARACTER      DIAG, NORM, UPLO
14
15           INTEGER        INFO, KD, LDAB, N
16
17           DOUBLE         PRECISION RCOND
18
19           INTEGER        IWORK( * )
20
21           DOUBLE         PRECISION AB( LDAB, * ), WORK( * )
22

PURPOSE

24       DTBCON estimates the reciprocal of the condition number of a triangular
25       band matrix A, in either the 1-norm or the infinity-norm.  The norm  of
26       A  is  computed  and an estimate is obtained for norm(inv(A)), then the
27       reciprocal of the condition number is computed as
28          RCOND = 1 / ( norm(A) * norm(inv(A)) ).
29

ARGUMENTS

31       NORM    (input) CHARACTER*1
32               Specifies whether the 1-norm condition number or the  infinity-
33               norm condition number is required:
34               = '1' or 'O':  1-norm;
35               = 'I':         Infinity-norm.
36
37       UPLO    (input) CHARACTER*1
38               = 'U':  A is upper triangular;
39               = 'L':  A is lower triangular.
40
41       DIAG    (input) CHARACTER*1
42               = 'N':  A is non-unit triangular;
43               = 'U':  A is unit triangular.
44
45       N       (input) INTEGER
46               The order of the matrix A.  N >= 0.
47
48       KD      (input) INTEGER
49               The  number of superdiagonals or subdiagonals of the triangular
50               band matrix A.  KD >= 0.
51
52       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
53               The upper or lower triangular band  matrix  A,  stored  in  the
54               first kd+1 rows of the array. The j-th column of A is stored in
55               the j-th column of the array AB as  follows:  if  UPLO  =  'U',
56               AB(kd+1+i-j,j)  =  A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
57               AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).  If DIAG =  'U',
58               the  diagonal  elements of A are not referenced and are assumed
59               to be 1.
60
61       LDAB    (input) INTEGER
62               The leading dimension of the array AB.  LDAB >= KD+1.
63
64       RCOND   (output) DOUBLE PRECISION
65               The reciprocal of the condition number of the  matrix  A,  com‐
66               puted as RCOND = 1/(norm(A) * norm(inv(A))).
67
68       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
69
70       IWORK   (workspace) INTEGER array, dimension (N)
71
72       INFO    (output) INTEGER
73               = 0:  successful exit
74               < 0:  if INFO = -i, the i-th argument had an illegal value
75
76
77
78 LAPACK routine (version 3.2)    November 2008                       DTBCON(1)
Impressum