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