1: *> \brief \b ZLANTP
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLANTP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlantp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlantp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlantp.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, NORM, UPLO
25: * INTEGER N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION WORK( * )
29: * COMPLEX*16 AP( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLANTP returns the value of the one norm, or the Frobenius norm, or
39: *> the infinity norm, or the element of largest absolute value of a
40: *> triangular matrix A, supplied in packed form.
41: *> \endverbatim
42: *>
43: *> \return ZLANTP
44: *> \verbatim
45: *>
46: *> ZLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47: *> (
48: *> ( norm1(A), NORM = '1', 'O' or 'o'
49: *> (
50: *> ( normI(A), NORM = 'I' or 'i'
51: *> (
52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53: *>
54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58: *> \endverbatim
59: *
60: * Arguments:
61: * ==========
62: *
63: *> \param[in] NORM
64: *> \verbatim
65: *> NORM is CHARACTER*1
66: *> Specifies the value to be returned in ZLANTP as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] UPLO
71: *> \verbatim
72: *> UPLO is CHARACTER*1
73: *> Specifies whether the matrix A is upper or lower triangular.
74: *> = 'U': Upper triangular
75: *> = 'L': Lower triangular
76: *> \endverbatim
77: *>
78: *> \param[in] DIAG
79: *> \verbatim
80: *> DIAG is CHARACTER*1
81: *> Specifies whether or not the matrix A is unit triangular.
82: *> = 'N': Non-unit triangular
83: *> = 'U': Unit triangular
84: *> \endverbatim
85: *>
86: *> \param[in] N
87: *> \verbatim
88: *> N is INTEGER
89: *> The order of the matrix A. N >= 0. When N = 0, ZLANTP is
90: *> set to zero.
91: *> \endverbatim
92: *>
93: *> \param[in] AP
94: *> \verbatim
95: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
96: *> The upper or lower triangular matrix A, packed columnwise in
97: *> a linear array. The j-th column of A is stored in the array
98: *> AP as follows:
99: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
100: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
101: *> Note that when DIAG = 'U', the elements of the array AP
102: *> corresponding to the diagonal elements of the matrix A are
103: *> not referenced, but are assumed to be one.
104: *> \endverbatim
105: *>
106: *> \param[out] WORK
107: *> \verbatim
108: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
109: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
110: *> referenced.
111: *> \endverbatim
112: *
113: * Authors:
114: * ========
115: *
116: *> \author Univ. of Tennessee
117: *> \author Univ. of California Berkeley
118: *> \author Univ. of Colorado Denver
119: *> \author NAG Ltd.
120: *
121: *> \date November 2011
122: *
123: *> \ingroup complex16OTHERauxiliary
124: *
125: * =====================================================================
126: DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
127: *
128: * -- LAPACK auxiliary routine (version 3.4.0) --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: * November 2011
132: *
133: * .. Scalar Arguments ..
134: CHARACTER DIAG, NORM, UPLO
135: INTEGER N
136: * ..
137: * .. Array Arguments ..
138: DOUBLE PRECISION WORK( * )
139: COMPLEX*16 AP( * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Parameters ..
145: DOUBLE PRECISION ONE, ZERO
146: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
147: * ..
148: * .. Local Scalars ..
149: LOGICAL UDIAG
150: INTEGER I, J, K
151: DOUBLE PRECISION SCALE, SUM, VALUE
152: * ..
153: * .. External Functions ..
154: LOGICAL LSAME
155: EXTERNAL LSAME
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL ZLASSQ
159: * ..
160: * .. Intrinsic Functions ..
161: INTRINSIC ABS, MAX, SQRT
162: * ..
163: * .. Executable Statements ..
164: *
165: IF( N.EQ.0 ) THEN
166: VALUE = ZERO
167: ELSE IF( LSAME( NORM, 'M' ) ) THEN
168: *
169: * Find max(abs(A(i,j))).
170: *
171: K = 1
172: IF( LSAME( DIAG, 'U' ) ) THEN
173: VALUE = ONE
174: IF( LSAME( UPLO, 'U' ) ) THEN
175: DO 20 J = 1, N
176: DO 10 I = K, K + J - 2
177: VALUE = MAX( VALUE, ABS( AP( I ) ) )
178: 10 CONTINUE
179: K = K + J
180: 20 CONTINUE
181: ELSE
182: DO 40 J = 1, N
183: DO 30 I = K + 1, K + N - J
184: VALUE = MAX( VALUE, ABS( AP( I ) ) )
185: 30 CONTINUE
186: K = K + N - J + 1
187: 40 CONTINUE
188: END IF
189: ELSE
190: VALUE = ZERO
191: IF( LSAME( UPLO, 'U' ) ) THEN
192: DO 60 J = 1, N
193: DO 50 I = K, K + J - 1
194: VALUE = MAX( VALUE, ABS( AP( I ) ) )
195: 50 CONTINUE
196: K = K + J
197: 60 CONTINUE
198: ELSE
199: DO 80 J = 1, N
200: DO 70 I = K, K + N - J
201: VALUE = MAX( VALUE, ABS( AP( I ) ) )
202: 70 CONTINUE
203: K = K + N - J + 1
204: 80 CONTINUE
205: END IF
206: END IF
207: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
208: *
209: * Find norm1(A).
210: *
211: VALUE = ZERO
212: K = 1
213: UDIAG = LSAME( DIAG, 'U' )
214: IF( LSAME( UPLO, 'U' ) ) THEN
215: DO 110 J = 1, N
216: IF( UDIAG ) THEN
217: SUM = ONE
218: DO 90 I = K, K + J - 2
219: SUM = SUM + ABS( AP( I ) )
220: 90 CONTINUE
221: ELSE
222: SUM = ZERO
223: DO 100 I = K, K + J - 1
224: SUM = SUM + ABS( AP( I ) )
225: 100 CONTINUE
226: END IF
227: K = K + J
228: VALUE = MAX( VALUE, SUM )
229: 110 CONTINUE
230: ELSE
231: DO 140 J = 1, N
232: IF( UDIAG ) THEN
233: SUM = ONE
234: DO 120 I = K + 1, K + N - J
235: SUM = SUM + ABS( AP( I ) )
236: 120 CONTINUE
237: ELSE
238: SUM = ZERO
239: DO 130 I = K, K + N - J
240: SUM = SUM + ABS( AP( I ) )
241: 130 CONTINUE
242: END IF
243: K = K + N - J + 1
244: VALUE = MAX( VALUE, SUM )
245: 140 CONTINUE
246: END IF
247: ELSE IF( LSAME( NORM, 'I' ) ) THEN
248: *
249: * Find normI(A).
250: *
251: K = 1
252: IF( LSAME( UPLO, 'U' ) ) THEN
253: IF( LSAME( DIAG, 'U' ) ) THEN
254: DO 150 I = 1, N
255: WORK( I ) = ONE
256: 150 CONTINUE
257: DO 170 J = 1, N
258: DO 160 I = 1, J - 1
259: WORK( I ) = WORK( I ) + ABS( AP( K ) )
260: K = K + 1
261: 160 CONTINUE
262: K = K + 1
263: 170 CONTINUE
264: ELSE
265: DO 180 I = 1, N
266: WORK( I ) = ZERO
267: 180 CONTINUE
268: DO 200 J = 1, N
269: DO 190 I = 1, J
270: WORK( I ) = WORK( I ) + ABS( AP( K ) )
271: K = K + 1
272: 190 CONTINUE
273: 200 CONTINUE
274: END IF
275: ELSE
276: IF( LSAME( DIAG, 'U' ) ) THEN
277: DO 210 I = 1, N
278: WORK( I ) = ONE
279: 210 CONTINUE
280: DO 230 J = 1, N
281: K = K + 1
282: DO 220 I = J + 1, N
283: WORK( I ) = WORK( I ) + ABS( AP( K ) )
284: K = K + 1
285: 220 CONTINUE
286: 230 CONTINUE
287: ELSE
288: DO 240 I = 1, N
289: WORK( I ) = ZERO
290: 240 CONTINUE
291: DO 260 J = 1, N
292: DO 250 I = J, N
293: WORK( I ) = WORK( I ) + ABS( AP( K ) )
294: K = K + 1
295: 250 CONTINUE
296: 260 CONTINUE
297: END IF
298: END IF
299: VALUE = ZERO
300: DO 270 I = 1, N
301: VALUE = MAX( VALUE, WORK( I ) )
302: 270 CONTINUE
303: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
304: *
305: * Find normF(A).
306: *
307: IF( LSAME( UPLO, 'U' ) ) THEN
308: IF( LSAME( DIAG, 'U' ) ) THEN
309: SCALE = ONE
310: SUM = N
311: K = 2
312: DO 280 J = 2, N
313: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
314: K = K + J
315: 280 CONTINUE
316: ELSE
317: SCALE = ZERO
318: SUM = ONE
319: K = 1
320: DO 290 J = 1, N
321: CALL ZLASSQ( J, AP( K ), 1, SCALE, SUM )
322: K = K + J
323: 290 CONTINUE
324: END IF
325: ELSE
326: IF( LSAME( DIAG, 'U' ) ) THEN
327: SCALE = ONE
328: SUM = N
329: K = 2
330: DO 300 J = 1, N - 1
331: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
332: K = K + N - J + 1
333: 300 CONTINUE
334: ELSE
335: SCALE = ZERO
336: SUM = ONE
337: K = 1
338: DO 310 J = 1, N
339: CALL ZLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
340: K = K + N - J + 1
341: 310 CONTINUE
342: END IF
343: END IF
344: VALUE = SCALE*SQRT( SUM )
345: END IF
346: *
347: ZLANTP = VALUE
348: RETURN
349: *
350: * End of ZLANTP
351: *
352: END
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