Annotation of rpl/lapack/lapack/zlangt.f, revision 1.17
1.11 bertrand 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.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 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">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER NORM
25: * INTEGER N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 D( * ), DL( * ), DU( * )
29: * ..
1.15 bertrand 30: *
1.8 bertrand 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: *
1.15 bertrand 97: *> \author Univ. of Tennessee
98: *> \author Univ. of California Berkeley
99: *> \author Univ. of Colorado Denver
100: *> \author NAG Ltd.
1.8 bertrand 101: *
1.15 bertrand 102: *> \date December 2016
1.8 bertrand 103: *
104: *> \ingroup complex16OTHERauxiliary
105: *
106: * =====================================================================
1.1 bertrand 107: DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
108: *
1.15 bertrand 109: * -- LAPACK auxiliary routine (version 3.7.0) --
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..--
1.15 bertrand 112: * December 2016
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
1.11 bertrand 130: DOUBLE PRECISION ANORM, SCALE, SUM, TEMP
1.1 bertrand 131: * ..
132: * .. External Functions ..
1.11 bertrand 133: LOGICAL LSAME, DISNAN
134: EXTERNAL LSAME, DISNAN
1.1 bertrand 135: * ..
136: * .. External Subroutines ..
137: EXTERNAL ZLASSQ
138: * ..
139: * .. Intrinsic Functions ..
1.11 bertrand 140: INTRINSIC ABS, SQRT
1.1 bertrand 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
1.15 bertrand 152: IF( ANORM.LT.ABS( DL( I ) ) .OR. DISNAN( ABS( DL( I ) ) ) )
1.11 bertrand 153: $ ANORM = ABS(DL(I))
1.15 bertrand 154: IF( ANORM.LT.ABS( D( I ) ) .OR. DISNAN( ABS( D( I ) ) ) )
1.11 bertrand 155: $ ANORM = ABS(D(I))
1.15 bertrand 156: IF( ANORM.LT.ABS( DU( I ) ) .OR. DISNAN (ABS( DU( I ) ) ) )
1.11 bertrand 157: $ ANORM = ABS(DU(I))
1.1 bertrand 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
1.11 bertrand 166: ANORM = ABS( D( 1 ) )+ABS( DL( 1 ) )
1.15 bertrand 167: TEMP = ABS( D( N ) )+ABS( DU( N-1 ) )
1.11 bertrand 168: IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
1.1 bertrand 169: DO 20 I = 2, N - 1
1.11 bertrand 170: TEMP = ABS( D( I ) )+ABS( DL( I ) )+ABS( DU( I-1 ) )
171: IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
1.1 bertrand 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
1.11 bertrand 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
1.1 bertrand 184: DO 30 I = 2, N - 1
1.11 bertrand 185: TEMP = ABS( D( I ) )+ABS( DU( I ) )+ABS( DL( I-1 ) )
186: IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
1.1 bertrand 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
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