LAPACK  3.6.1 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 *
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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 *> \date September 2012
103 *
104 *> \ingroup complex16OTHERauxiliary
105 *
106 * =====================================================================
107  DOUBLE PRECISION FUNCTION zlangt( NORM, N, DL, D, DU )
108 *
109 * -- LAPACK auxiliary routine (version 3.4.2) --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 * September 2012
113 *
114 * .. Scalar Arguments ..
115  CHARACTER NORM
116  INTEGER N
117 * ..
118 * .. Array Arguments ..
119  COMPLEX*16 D( * ), DL( * ), DU( * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  DOUBLE PRECISION ONE, ZERO
126  parameter ( one = 1.0d+0, zero = 0.0d+0 )
127 * ..
128 * .. Local Scalars ..
129  INTEGER I
130  DOUBLE PRECISION ANORM, SCALE, SUM, TEMP
131 * ..
132 * .. External Functions ..
133  LOGICAL LSAME, DISNAN
134  EXTERNAL lsame, disnan
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL zlassq
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC abs, sqrt
141 * ..
142 * .. Executable Statements ..
143 *
144  IF( n.LE.0 ) THEN
145  anorm = zero
146  ELSE IF( lsame( norm, 'M' ) ) THEN
147 *
148 * Find max(abs(A(i,j))).
149 *
150  anorm = abs( d( n ) )
151  DO 10 i = 1, n - 1
152  IF( anorm.LT.abs( dl( i ) ) .OR. disnan( abs( dl( i ) ) ) )
153  \$ anorm = abs(dl(i))
154  IF( anorm.LT.abs( d( i ) ) .OR. disnan( abs( d( i ) ) ) )
155  \$ anorm = abs(d(i))
156  IF( anorm.LT.abs( du( i ) ) .OR. disnan(abs( du( i ) ) ) )
157  \$ anorm = abs(du(i))
158  10 CONTINUE
159  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' ) THEN
160 *
161 * Find norm1(A).
162 *
163  IF( n.EQ.1 ) THEN
164  anorm = abs( d( 1 ) )
165  ELSE
166  anorm = abs( d( 1 ) )+abs( dl( 1 ) )
167  temp = abs( d( n ) )+abs( du( n-1 ) )
168  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
169  DO 20 i = 2, n - 1
170  temp = abs( d( i ) )+abs( dl( i ) )+abs( du( i-1 ) )
171  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
172  20 CONTINUE
173  END IF
174  ELSE IF( lsame( norm, 'I' ) ) THEN
175 *
176 * Find normI(A).
177 *
178  IF( n.EQ.1 ) THEN
179  anorm = abs( d( 1 ) )
180  ELSE
181  anorm = abs( d( 1 ) )+abs( du( 1 ) )
182  temp = abs( d( n ) )+abs( dl( n-1 ) )
183  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
184  DO 30 i = 2, n - 1
185  temp = abs( d( i ) )+abs( du( i ) )+abs( dl( i-1 ) )
186  IF( anorm .LT. temp .OR. disnan( temp ) ) anorm = temp
187  30 CONTINUE
188  END IF
189  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
190 *
191 * Find normF(A).
192 *
193  scale = zero
194  sum = one
195  CALL zlassq( n, d, 1, scale, sum )
196  IF( n.GT.1 ) THEN
197  CALL zlassq( n-1, dl, 1, scale, sum )
198  CALL zlassq( n-1, du, 1, scale, sum )
199  END IF
200  anorm = scale*sqrt( sum )
201  END IF
202 *
203  zlangt = anorm
204  RETURN
205 *
206 * End of ZLANGT
207 *
208  END
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
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:108