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: *> \date December 2016
137: *
138: *> \ingroup doubleOTHERauxiliary
139: *
140: * =====================================================================
141: DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
142: $ WORK )
143: *
144: * -- LAPACK auxiliary routine (version 3.7.0) --
145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147: * December 2016
148: *
149: * .. Scalar Arguments ..
150: CHARACTER DIAG, NORM, UPLO
151: INTEGER LDA, M, N
152: * ..
153: * .. Array Arguments ..
154: DOUBLE PRECISION A( LDA, * ), WORK( * )
155: * ..
156: *
157: * =====================================================================
158: *
159: * .. Parameters ..
160: DOUBLE PRECISION ONE, ZERO
161: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
162: * ..
163: * .. Local Scalars ..
164: LOGICAL UDIAG
165: INTEGER I, J
166: DOUBLE PRECISION SCALE, SUM, VALUE
167: * ..
168: * .. External Subroutines ..
169: EXTERNAL DLASSQ
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME, DISNAN
173: EXTERNAL LSAME, DISNAN
174: * ..
175: * .. Intrinsic Functions ..
176: INTRINSIC ABS, MIN, SQRT
177: * ..
178: * .. Executable Statements ..
179: *
180: IF( MIN( M, N ).EQ.0 ) THEN
181: VALUE = ZERO
182: ELSE IF( LSAME( NORM, 'M' ) ) THEN
183: *
184: * Find max(abs(A(i,j))).
185: *
186: IF( LSAME( DIAG, 'U' ) ) THEN
187: VALUE = ONE
188: IF( LSAME( UPLO, 'U' ) ) THEN
189: DO 20 J = 1, N
190: DO 10 I = 1, MIN( M, J-1 )
191: SUM = ABS( A( I, J ) )
192: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
193: 10 CONTINUE
194: 20 CONTINUE
195: ELSE
196: DO 40 J = 1, N
197: DO 30 I = J + 1, M
198: SUM = ABS( A( I, J ) )
199: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
200: 30 CONTINUE
201: 40 CONTINUE
202: END IF
203: ELSE
204: VALUE = ZERO
205: IF( LSAME( UPLO, 'U' ) ) THEN
206: DO 60 J = 1, N
207: DO 50 I = 1, MIN( M, J )
208: SUM = ABS( A( I, J ) )
209: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
210: 50 CONTINUE
211: 60 CONTINUE
212: ELSE
213: DO 80 J = 1, N
214: DO 70 I = J, M
215: SUM = ABS( A( I, J ) )
216: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
217: 70 CONTINUE
218: 80 CONTINUE
219: END IF
220: END IF
221: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
222: *
223: * Find norm1(A).
224: *
225: VALUE = ZERO
226: UDIAG = LSAME( DIAG, 'U' )
227: IF( LSAME( UPLO, 'U' ) ) THEN
228: DO 110 J = 1, N
229: IF( ( UDIAG ) .AND. ( J.LE.M ) ) THEN
230: SUM = ONE
231: DO 90 I = 1, J - 1
232: SUM = SUM + ABS( A( I, J ) )
233: 90 CONTINUE
234: ELSE
235: SUM = ZERO
236: DO 100 I = 1, MIN( M, J )
237: SUM = SUM + ABS( A( I, J ) )
238: 100 CONTINUE
239: END IF
240: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
241: 110 CONTINUE
242: ELSE
243: DO 140 J = 1, N
244: IF( UDIAG ) THEN
245: SUM = ONE
246: DO 120 I = J + 1, M
247: SUM = SUM + ABS( A( I, J ) )
248: 120 CONTINUE
249: ELSE
250: SUM = ZERO
251: DO 130 I = J, M
252: SUM = SUM + ABS( A( I, J ) )
253: 130 CONTINUE
254: END IF
255: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
256: 140 CONTINUE
257: END IF
258: ELSE IF( LSAME( NORM, 'I' ) ) THEN
259: *
260: * Find normI(A).
261: *
262: IF( LSAME( UPLO, 'U' ) ) THEN
263: IF( LSAME( DIAG, 'U' ) ) THEN
264: DO 150 I = 1, M
265: WORK( I ) = ONE
266: 150 CONTINUE
267: DO 170 J = 1, N
268: DO 160 I = 1, MIN( M, J-1 )
269: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
270: 160 CONTINUE
271: 170 CONTINUE
272: ELSE
273: DO 180 I = 1, M
274: WORK( I ) = ZERO
275: 180 CONTINUE
276: DO 200 J = 1, N
277: DO 190 I = 1, MIN( M, J )
278: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
279: 190 CONTINUE
280: 200 CONTINUE
281: END IF
282: ELSE
283: IF( LSAME( DIAG, 'U' ) ) THEN
284: DO 210 I = 1, N
285: WORK( I ) = ONE
286: 210 CONTINUE
287: DO 220 I = N + 1, M
288: WORK( I ) = ZERO
289: 220 CONTINUE
290: DO 240 J = 1, N
291: DO 230 I = J + 1, M
292: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
293: 230 CONTINUE
294: 240 CONTINUE
295: ELSE
296: DO 250 I = 1, M
297: WORK( I ) = ZERO
298: 250 CONTINUE
299: DO 270 J = 1, N
300: DO 260 I = J, M
301: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
302: 260 CONTINUE
303: 270 CONTINUE
304: END IF
305: END IF
306: VALUE = ZERO
307: DO 280 I = 1, M
308: SUM = WORK( I )
309: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
310: 280 CONTINUE
311: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
312: *
313: * Find normF(A).
314: *
315: IF( LSAME( UPLO, 'U' ) ) THEN
316: IF( LSAME( DIAG, 'U' ) ) THEN
317: SCALE = ONE
318: SUM = MIN( M, N )
319: DO 290 J = 2, N
320: CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
321: 290 CONTINUE
322: ELSE
323: SCALE = ZERO
324: SUM = ONE
325: DO 300 J = 1, N
326: CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
327: 300 CONTINUE
328: END IF
329: ELSE
330: IF( LSAME( DIAG, 'U' ) ) THEN
331: SCALE = ONE
332: SUM = MIN( M, N )
333: DO 310 J = 1, N
334: CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
335: $ SUM )
336: 310 CONTINUE
337: ELSE
338: SCALE = ZERO
339: SUM = ONE
340: DO 320 J = 1, N
341: CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
342: 320 CONTINUE
343: END IF
344: END IF
345: VALUE = SCALE*SQRT( SUM )
346: END IF
347: *
348: DLANTR = VALUE
349: RETURN
350: *
351: * End of DLANTR
352: *
353: END
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