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1.11 bertrand 1: *> \brief \b ZLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
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 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">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, NORM, UPLO
25: * INTEGER N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION WORK( * )
29: * COMPLEX*16 AP( * )
30: * ..
1.15 bertrand 31: *
1.8 bertrand 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: *
1.15 bertrand 116: *> \author Univ. of Tennessee
117: *> \author Univ. of California Berkeley
118: *> \author Univ. of Colorado Denver
119: *> \author NAG Ltd.
1.8 bertrand 120: *
1.15 bertrand 121: *> \date December 2016
1.8 bertrand 122: *
123: *> \ingroup complex16OTHERauxiliary
124: *
125: * =====================================================================
1.1 bertrand 126: DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
127: *
1.15 bertrand 128: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 131: * December 2016
1.1 bertrand 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 ..
1.11 bertrand 154: LOGICAL LSAME, DISNAN
155: EXTERNAL LSAME, DISNAN
1.1 bertrand 156: * ..
157: * .. External Subroutines ..
158: EXTERNAL ZLASSQ
159: * ..
160: * .. Intrinsic Functions ..
1.11 bertrand 161: INTRINSIC ABS, SQRT
1.1 bertrand 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
1.11 bertrand 177: SUM = ABS( AP( I ) )
178: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 179: 10 CONTINUE
180: K = K + J
181: 20 CONTINUE
182: ELSE
183: DO 40 J = 1, N
184: DO 30 I = K + 1, K + N - J
1.11 bertrand 185: SUM = ABS( AP( I ) )
186: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 187: 30 CONTINUE
188: K = K + N - J + 1
189: 40 CONTINUE
190: END IF
191: ELSE
192: VALUE = ZERO
193: IF( LSAME( UPLO, 'U' ) ) THEN
194: DO 60 J = 1, N
195: DO 50 I = K, K + J - 1
1.11 bertrand 196: SUM = ABS( AP( I ) )
197: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 198: 50 CONTINUE
199: K = K + J
200: 60 CONTINUE
201: ELSE
202: DO 80 J = 1, N
203: DO 70 I = K, K + N - J
1.11 bertrand 204: SUM = ABS( AP( I ) )
205: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 206: 70 CONTINUE
207: K = K + N - J + 1
208: 80 CONTINUE
209: END IF
210: END IF
211: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
212: *
213: * Find norm1(A).
214: *
215: VALUE = ZERO
216: K = 1
217: UDIAG = LSAME( DIAG, 'U' )
218: IF( LSAME( UPLO, 'U' ) ) THEN
219: DO 110 J = 1, N
220: IF( UDIAG ) THEN
221: SUM = ONE
222: DO 90 I = K, K + J - 2
223: SUM = SUM + ABS( AP( I ) )
224: 90 CONTINUE
225: ELSE
226: SUM = ZERO
227: DO 100 I = K, K + J - 1
228: SUM = SUM + ABS( AP( I ) )
229: 100 CONTINUE
230: END IF
231: K = K + J
1.11 bertrand 232: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 233: 110 CONTINUE
234: ELSE
235: DO 140 J = 1, N
236: IF( UDIAG ) THEN
237: SUM = ONE
238: DO 120 I = K + 1, K + N - J
239: SUM = SUM + ABS( AP( I ) )
240: 120 CONTINUE
241: ELSE
242: SUM = ZERO
243: DO 130 I = K, K + N - J
244: SUM = SUM + ABS( AP( I ) )
245: 130 CONTINUE
246: END IF
247: K = K + N - J + 1
1.11 bertrand 248: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 249: 140 CONTINUE
250: END IF
251: ELSE IF( LSAME( NORM, 'I' ) ) THEN
252: *
253: * Find normI(A).
254: *
255: K = 1
256: IF( LSAME( UPLO, 'U' ) ) THEN
257: IF( LSAME( DIAG, 'U' ) ) THEN
258: DO 150 I = 1, N
259: WORK( I ) = ONE
260: 150 CONTINUE
261: DO 170 J = 1, N
262: DO 160 I = 1, J - 1
263: WORK( I ) = WORK( I ) + ABS( AP( K ) )
264: K = K + 1
265: 160 CONTINUE
266: K = K + 1
267: 170 CONTINUE
268: ELSE
269: DO 180 I = 1, N
270: WORK( I ) = ZERO
271: 180 CONTINUE
272: DO 200 J = 1, N
273: DO 190 I = 1, J
274: WORK( I ) = WORK( I ) + ABS( AP( K ) )
275: K = K + 1
276: 190 CONTINUE
277: 200 CONTINUE
278: END IF
279: ELSE
280: IF( LSAME( DIAG, 'U' ) ) THEN
281: DO 210 I = 1, N
282: WORK( I ) = ONE
283: 210 CONTINUE
284: DO 230 J = 1, N
285: K = K + 1
286: DO 220 I = J + 1, N
287: WORK( I ) = WORK( I ) + ABS( AP( K ) )
288: K = K + 1
289: 220 CONTINUE
290: 230 CONTINUE
291: ELSE
292: DO 240 I = 1, N
293: WORK( I ) = ZERO
294: 240 CONTINUE
295: DO 260 J = 1, N
296: DO 250 I = J, N
297: WORK( I ) = WORK( I ) + ABS( AP( K ) )
298: K = K + 1
299: 250 CONTINUE
300: 260 CONTINUE
301: END IF
302: END IF
303: VALUE = ZERO
304: DO 270 I = 1, N
1.11 bertrand 305: SUM = WORK( I )
306: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 307: 270 CONTINUE
308: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
309: *
310: * Find normF(A).
311: *
312: IF( LSAME( UPLO, 'U' ) ) THEN
313: IF( LSAME( DIAG, 'U' ) ) THEN
314: SCALE = ONE
315: SUM = N
316: K = 2
317: DO 280 J = 2, N
318: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
319: K = K + J
320: 280 CONTINUE
321: ELSE
322: SCALE = ZERO
323: SUM = ONE
324: K = 1
325: DO 290 J = 1, N
326: CALL ZLASSQ( J, AP( K ), 1, SCALE, SUM )
327: K = K + J
328: 290 CONTINUE
329: END IF
330: ELSE
331: IF( LSAME( DIAG, 'U' ) ) THEN
332: SCALE = ONE
333: SUM = N
334: K = 2
335: DO 300 J = 1, N - 1
336: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
337: K = K + N - J + 1
338: 300 CONTINUE
339: ELSE
340: SCALE = ZERO
341: SUM = ONE
342: K = 1
343: DO 310 J = 1, N
344: CALL ZLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
345: K = K + N - J + 1
346: 310 CONTINUE
347: END IF
348: END IF
349: VALUE = SCALE*SQRT( SUM )
350: END IF
351: *
352: ZLANTP = VALUE
353: RETURN
354: *
355: * End of ZLANTP
356: *
357: END