 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ slantr()

 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.

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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.```

Definition at line 139 of file slantr.f.

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  REAL A( LDA, * ), WORK( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  REAL ONE, ZERO
158  parameter( one = 1.0e+0, zero = 0.0e+0 )
159 * ..
160 * .. Local Scalars ..
161  LOGICAL UDIAG
162  INTEGER I, J
163  REAL SCALE, SUM, VALUE
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL slassq
167 * ..
168 * .. External Functions ..
169  LOGICAL LSAME, SISNAN
170  EXTERNAL lsame, sisnan
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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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. sisnan( 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 slassq( 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 slassq( 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 slassq( 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 slassq( 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  slantr = VALUE
346  RETURN
347 *
348 * End of SLANTR
349 *
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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,...
Definition: slantr.f:141
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