LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zlangt.f
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1 *> \brief \b ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZLANGT + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangt.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 D( * ), DL( * ), DU( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZLANGT returns the value of the one norm, or the Frobenius norm, or
38 *> the infinity norm, or the element of largest absolute value of a
39 *> complex tridiagonal matrix A.
40 *> \endverbatim
41 *>
42 *> \return ZLANGT
43 *> \verbatim
44 *>
45 *> ZLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
46 *> (
47 *> ( norm1(A), NORM = '1', 'O' or 'o'
48 *> (
49 *> ( normI(A), NORM = 'I' or 'i'
50 *> (
51 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
52 *>
53 *> where norm1 denotes the one norm of a matrix (maximum column sum),
54 *> normI denotes the infinity norm of a matrix (maximum row sum) and
55 *> normF denotes the Frobenius norm of a matrix (square root of sum of
56 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
57 *> \endverbatim
58 *
59 * Arguments:
60 * ==========
61 *
62 *> \param[in] NORM
63 *> \verbatim
64 *> NORM is CHARACTER*1
65 *> Specifies the value to be returned in ZLANGT as described
66 *> above.
67 *> \endverbatim
68 *>
69 *> \param[in] N
70 *> \verbatim
71 *> N is INTEGER
72 *> The order of the matrix A. N >= 0. When N = 0, ZLANGT is
73 *> set to zero.
74 *> \endverbatim
75 *>
76 *> \param[in] DL
77 *> \verbatim
78 *> DL is COMPLEX*16 array, dimension (N-1)
79 *> The (n-1) sub-diagonal elements of A.
80 *> \endverbatim
81 *>
82 *> \param[in] D
83 *> \verbatim
84 *> D is COMPLEX*16 array, dimension (N)
85 *> The diagonal elements of A.
86 *> \endverbatim
87 *>
88 *> \param[in] DU
89 *> \verbatim
90 *> DU is COMPLEX*16 array, dimension (N-1)
91 *> The (n-1) super-diagonal elements of A.
92 *> \endverbatim
93 *
94 * Authors:
95 * ========
96 *
97 *> \author Univ. of Tennessee
98 *> \author Univ. of California Berkeley
99 *> \author Univ. of Colorado Denver
100 *> \author NAG Ltd.
101 *
102 *> \ingroup complex16OTHERauxiliary
103 *
104 * =====================================================================
105  DOUBLE PRECISION FUNCTION zlangt( NORM, N, DL, D, DU )
106 *
107 * -- LAPACK auxiliary routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER norm
113  INTEGER n
114 * ..
115 * .. Array Arguments ..
116  COMPLEX*16 d( * ), dl( * ), du( * )
117 * ..
118 *
119 * =====================================================================
120 *
121 * .. Parameters ..
122  DOUBLE PRECISION one, zero
123  parameter( one = 1.0d+0, zero = 0.0d+0 )
124 * ..
125 * .. Local Scalars ..
126  INTEGER i
127  DOUBLE PRECISION anorm, scale, sum, temp
128 * ..
129 * .. External Functions ..
130  LOGICAL lsame, disnan
131  EXTERNAL lsame, disnan
132 * ..
133 * .. External Subroutines ..
134  EXTERNAL zlassq
135 * ..
136 * .. Intrinsic Functions ..
137  INTRINSIC abs, sqrt
138 * ..
139 * .. Executable Statements ..
140 *
141  IF( n.LE.0 ) THEN
142  anorm = zero
143  ELSE IF( lsame( norm, 'M' ) ) THEN
144 *
145 * Find max(abs(A(i,j))).
146 *
147  anorm = abs( d( n ) )
148  DO 10 i = 1, n - 1
149  IF( anorm.LT.abs( dl( i ) ) .OR. disnan( abs( dl( i ) ) ) )
150  $ anorm = abs(dl(i))
151  IF( anorm.LT.abs( d( i ) ) .OR. disnan( abs( d( i ) ) ) )
152  $ anorm = abs(d(i))
153  IF( anorm.LT.abs( du( i ) ) .OR. disnan(abs( du( i ) ) ) )
154  $ anorm = abs(du(i))
155  10 CONTINUE
156  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' ) THEN
157 *
158 * Find norm1(A).
159 *
160  IF( n.EQ.1 ) THEN
161  anorm = abs( d( 1 ) )
162  ELSE
163  anorm = abs( d( 1 ) )+abs( dl( 1 ) )
164  temp = abs( d( n ) )+abs( du( n-1 ) )
165  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
166  DO 20 i = 2, n - 1
167  temp = abs( d( i ) )+abs( dl( i ) )+abs( du( i-1 ) )
168  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
169  20 CONTINUE
170  END IF
171  ELSE IF( lsame( norm, 'I' ) ) THEN
172 *
173 * Find normI(A).
174 *
175  IF( n.EQ.1 ) THEN
176  anorm = abs( d( 1 ) )
177  ELSE
178  anorm = abs( d( 1 ) )+abs( du( 1 ) )
179  temp = abs( d( n ) )+abs( dl( n-1 ) )
180  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
181  DO 30 i = 2, n - 1
182  temp = abs( d( i ) )+abs( du( i ) )+abs( dl( i-1 ) )
183  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
184  30 CONTINUE
185  END IF
186  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
187 *
188 * Find normF(A).
189 *
190  scale = zero
191  sum = one
192  CALL zlassq( n, d, 1, scale, sum )
193  IF( n.GT.1 ) THEN
194  CALL zlassq( n-1, dl, 1, scale, sum )
195  CALL zlassq( n-1, du, 1, scale, sum )
196  END IF
197  anorm = scale*sqrt( sum )
198  END IF
199 *
200  zlangt = anorm
201  RETURN
202 *
203 * End of ZLANGT
204 *
205  END
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f90:126
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zlangt(NORM, N, DL, D, DU)
ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlangt.f:106