LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dlantb()

double precision function dlantb ( character  NORM,
character  UPLO,
character  DIAG,
integer  N,
integer  K,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  WORK 
)

DLANTB 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 band matrix.

Download DLANTB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLANTB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n triangular band matrix A,  with ( k + 1 ) diagonals.
Returns
DLANTB
    DLANTB = ( 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 DLANTB as described
          above.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANTB is
          set to zero.
[in]K
          K is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
          K >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first k+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
          Note that when DIAG = 'U', the elements of the array AB
          corresponding to the diagonal elements of the matrix A are
          not referenced, but are assumed to be one.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= K+1.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
          referenced.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 138 of file dlantb.f.

140 *
141 * -- LAPACK auxiliary routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  CHARACTER DIAG, NORM, UPLO
147  INTEGER K, LDAB, N
148 * ..
149 * .. Array Arguments ..
150  DOUBLE PRECISION AB( LDAB, * ), WORK( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  DOUBLE PRECISION ONE, ZERO
157  parameter( one = 1.0d+0, zero = 0.0d+0 )
158 * ..
159 * .. Local Scalars ..
160  LOGICAL UDIAG
161  INTEGER I, J, L
162  DOUBLE PRECISION SCALE, SUM, VALUE
163 * ..
164 * .. External Subroutines ..
165  EXTERNAL dlassq
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME, DISNAN
169  EXTERNAL lsame, disnan
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC abs, max, min, sqrt
173 * ..
174 * .. Executable Statements ..
175 *
176  IF( n.EQ.0 ) THEN
177  VALUE = zero
178  ELSE IF( lsame( norm, 'M' ) ) THEN
179 *
180 * Find max(abs(A(i,j))).
181 *
182  IF( lsame( diag, 'U' ) ) THEN
183  VALUE = one
184  IF( lsame( uplo, 'U' ) ) THEN
185  DO 20 j = 1, n
186  DO 10 i = max( k+2-j, 1 ), k
187  sum = abs( ab( i, j ) )
188  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
189  10 CONTINUE
190  20 CONTINUE
191  ELSE
192  DO 40 j = 1, n
193  DO 30 i = 2, min( n+1-j, k+1 )
194  sum = abs( ab( i, j ) )
195  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
196  30 CONTINUE
197  40 CONTINUE
198  END IF
199  ELSE
200  VALUE = zero
201  IF( lsame( uplo, 'U' ) ) THEN
202  DO 60 j = 1, n
203  DO 50 i = max( k+2-j, 1 ), k + 1
204  sum = abs( ab( i, j ) )
205  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
206  50 CONTINUE
207  60 CONTINUE
208  ELSE
209  DO 80 j = 1, n
210  DO 70 i = 1, min( n+1-j, k+1 )
211  sum = abs( ab( i, j ) )
212  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
213  70 CONTINUE
214  80 CONTINUE
215  END IF
216  END IF
217  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
218 *
219 * Find norm1(A).
220 *
221  VALUE = zero
222  udiag = lsame( diag, 'U' )
223  IF( lsame( uplo, 'U' ) ) THEN
224  DO 110 j = 1, n
225  IF( udiag ) THEN
226  sum = one
227  DO 90 i = max( k+2-j, 1 ), k
228  sum = sum + abs( ab( i, j ) )
229  90 CONTINUE
230  ELSE
231  sum = zero
232  DO 100 i = max( k+2-j, 1 ), k + 1
233  sum = sum + abs( ab( i, j ) )
234  100 CONTINUE
235  END IF
236  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
237  110 CONTINUE
238  ELSE
239  DO 140 j = 1, n
240  IF( udiag ) THEN
241  sum = one
242  DO 120 i = 2, min( n+1-j, k+1 )
243  sum = sum + abs( ab( i, j ) )
244  120 CONTINUE
245  ELSE
246  sum = zero
247  DO 130 i = 1, min( n+1-j, k+1 )
248  sum = sum + abs( ab( i, j ) )
249  130 CONTINUE
250  END IF
251  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
252  140 CONTINUE
253  END IF
254  ELSE IF( lsame( norm, 'I' ) ) THEN
255 *
256 * Find normI(A).
257 *
258  VALUE = zero
259  IF( lsame( uplo, 'U' ) ) THEN
260  IF( lsame( diag, 'U' ) ) THEN
261  DO 150 i = 1, n
262  work( i ) = one
263  150 CONTINUE
264  DO 170 j = 1, n
265  l = k + 1 - j
266  DO 160 i = max( 1, j-k ), j - 1
267  work( i ) = work( i ) + abs( ab( l+i, j ) )
268  160 CONTINUE
269  170 CONTINUE
270  ELSE
271  DO 180 i = 1, n
272  work( i ) = zero
273  180 CONTINUE
274  DO 200 j = 1, n
275  l = k + 1 - j
276  DO 190 i = max( 1, j-k ), j
277  work( i ) = work( i ) + abs( ab( l+i, j ) )
278  190 CONTINUE
279  200 CONTINUE
280  END IF
281  ELSE
282  IF( lsame( diag, 'U' ) ) THEN
283  DO 210 i = 1, n
284  work( i ) = one
285  210 CONTINUE
286  DO 230 j = 1, n
287  l = 1 - j
288  DO 220 i = j + 1, min( n, j+k )
289  work( i ) = work( i ) + abs( ab( l+i, j ) )
290  220 CONTINUE
291  230 CONTINUE
292  ELSE
293  DO 240 i = 1, n
294  work( i ) = zero
295  240 CONTINUE
296  DO 260 j = 1, n
297  l = 1 - j
298  DO 250 i = j, min( n, j+k )
299  work( i ) = work( i ) + abs( ab( l+i, j ) )
300  250 CONTINUE
301  260 CONTINUE
302  END IF
303  END IF
304  DO 270 i = 1, n
305  sum = work( i )
306  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
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  IF( k.GT.0 ) THEN
317  DO 280 j = 2, n
318  CALL dlassq( min( j-1, k ),
319  $ ab( max( k+2-j, 1 ), j ), 1, scale,
320  $ sum )
321  280 CONTINUE
322  END IF
323  ELSE
324  scale = zero
325  sum = one
326  DO 290 j = 1, n
327  CALL dlassq( min( j, k+1 ), ab( max( k+2-j, 1 ), j ),
328  $ 1, scale, sum )
329  290 CONTINUE
330  END IF
331  ELSE
332  IF( lsame( diag, 'U' ) ) THEN
333  scale = one
334  sum = n
335  IF( k.GT.0 ) THEN
336  DO 300 j = 1, n - 1
337  CALL dlassq( min( n-j, k ), ab( 2, j ), 1, scale,
338  $ sum )
339  300 CONTINUE
340  END IF
341  ELSE
342  scale = zero
343  sum = one
344  DO 310 j = 1, n
345  CALL dlassq( min( n-j+1, k+1 ), ab( 1, j ), 1, scale,
346  $ sum )
347  310 CONTINUE
348  END IF
349  END IF
350  VALUE = scale*sqrt( sum )
351  END IF
352 *
353  dlantb = VALUE
354  RETURN
355 *
356 * End of DLANTB
357 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantb.f:140
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