Annotation of rpl/lapack/lapack/zlangt.f, revision 1.9
1.8 bertrand 1: *> \brief \b ZLANGT
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
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangt.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangt.f">
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: *> \date November 2011
103: *
104: *> \ingroup complex16OTHERauxiliary
105: *
106: * =====================================================================
1.1 bertrand 107: DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
108: *
1.8 bertrand 109: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 110: * -- LAPACK is a software package provided by Univ. of Tennessee, --
111: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 112: * November 2011
1.1 bertrand 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
131: * ..
132: * .. External Functions ..
133: LOGICAL LSAME
134: EXTERNAL LSAME
135: * ..
136: * .. External Subroutines ..
137: EXTERNAL ZLASSQ
138: * ..
139: * .. Intrinsic Functions ..
140: INTRINSIC ABS, MAX, 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: ANORM = MAX( ANORM, ABS( DL( I ) ) )
153: ANORM = MAX( ANORM, ABS( D( I ) ) )
154: ANORM = MAX( 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 = MAX( ABS( D( 1 ) )+ABS( DL( 1 ) ),
164: $ ABS( D( N ) )+ABS( DU( N-1 ) ) )
165: DO 20 I = 2, N - 1
166: ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DL( I ) )+
167: $ ABS( DU( I-1 ) ) )
168: 20 CONTINUE
169: END IF
170: ELSE IF( LSAME( NORM, 'I' ) ) THEN
171: *
172: * Find normI(A).
173: *
174: IF( N.EQ.1 ) THEN
175: ANORM = ABS( D( 1 ) )
176: ELSE
177: ANORM = MAX( ABS( D( 1 ) )+ABS( DU( 1 ) ),
178: $ ABS( D( N ) )+ABS( DL( N-1 ) ) )
179: DO 30 I = 2, N - 1
180: ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DU( I ) )+
181: $ ABS( DL( I-1 ) ) )
182: 30 CONTINUE
183: END IF
184: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
185: *
186: * Find normF(A).
187: *
188: SCALE = ZERO
189: SUM = ONE
190: CALL ZLASSQ( N, D, 1, SCALE, SUM )
191: IF( N.GT.1 ) THEN
192: CALL ZLASSQ( N-1, DL, 1, SCALE, SUM )
193: CALL ZLASSQ( N-1, DU, 1, SCALE, SUM )
194: END IF
195: ANORM = SCALE*SQRT( SUM )
196: END IF
197: *
198: ZLANGT = ANORM
199: RETURN
200: *
201: * End of ZLANGT
202: *
203: END
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