 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 real function slantr ( character NORM, character UPLO, character DIAG, integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) WORK )

SLANTR 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.

Purpose:
``` SLANTR  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
trapezoidal or triangular matrix A.```
Returns
SLANTR
```    SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A),         NORM = '1', 'O' or 'o'
(
( normI(A),         NORM = 'I' or 'i'
(
( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies the value to be returned in SLANTR as described above.``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower trapezoidal. = 'U': Upper trapezoidal = 'L': Lower trapezoidal Note that A is triangular instead of trapezoidal if M = N.``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal. = 'N': Non-unit diagonal = 'U': Unit diagonal``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, SLANTR is set to zero.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, SLANTR is set to zero.``` [in] A ``` A is REAL array, dimension (LDA,N) The trapezoidal matrix A (A is triangular if M = N). If UPLO = 'U', the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(M,1).``` [out] WORK ``` WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.```
Date
September 2012

Definition at line 143 of file slantr.f.

143 *
144 * -- LAPACK auxiliary routine (version 3.4.2) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * September 2012
148 *
149 * .. Scalar Arguments ..
150  CHARACTER diag, norm, uplo
151  INTEGER lda, m, n
152 * ..
153 * .. Array Arguments ..
154  REAL a( lda, * ), work( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  REAL one, zero
161  parameter ( one = 1.0e+0, zero = 0.0e+0 )
162 * ..
163 * .. Local Scalars ..
164  LOGICAL udiag
165  INTEGER i, j
166  REAL scale, sum, value
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL slassq
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame, sisnan
173  EXTERNAL lsame, sisnan
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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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 slassq( 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 slassq( 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 slassq( 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 slassq( 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  slantr = VALUE
349  RETURN
350 *
351 * End of SLANTR
352 *
subroutine slassq(N, X, INCX, SCALE, SUMSQ)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f:105
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
real function slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR 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.
Definition: slantr.f:143
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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