LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine dtrmm ( character  SIDE,
character  UPLO,
character  TRANSA,
character  DIAG,
integer  M,
integer  N,
double precision  ALPHA,
double precision, dimension(lda,*)  A,
integer  LDA,
double precision, dimension(ldb,*)  B,
integer  LDB 
)

DTRMM

Purpose: 
 DTRMM  performs one of the matrix-matrix operations

    B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

 where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
 non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

    op( A ) = A   or   op( A ) = A**T.
Parameters
[in]SIDE
          SIDE is CHARACTER*1
           On entry,  SIDE specifies whether  op( A ) multiplies B from
           the left or right as follows:

              SIDE = 'L' or 'l'   B := alpha*op( A )*B.

              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
[in]UPLO
          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the matrix A is an upper or
           lower triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.
[in]TRANSA
          TRANSA is CHARACTER*1
           On entry, TRANSA specifies the form of op( A ) to be used in
           the matrix multiplication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.

              TRANSA = 'T' or 't'   op( A ) = A**T.

              TRANSA = 'C' or 'c'   op( A ) = A**T.
[in]DIAG
          DIAG is CHARACTER*1
           On entry, DIAG specifies whether or not A is unit triangular
           as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular.
[in]M
          M is INTEGER
           On entry, M specifies the number of rows of B. M must be at
           least zero.
[in]N
          N is INTEGER
           On entry, N specifies the number of columns of B.  N must be
           at least zero.
[in]ALPHA
          ALPHA is DOUBLE PRECISION.
           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
           zero then  A is not referenced and  B need not be set before
           entry.
[in]A
           A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
           upper triangular part of the array  A must contain the upper
           triangular matrix  and the strictly lower triangular part of
           A is not referenced.
           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
           lower triangular part of the array  A must contain the lower
           triangular matrix  and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
           A  are not referenced either,  but are assumed to be  unity.
[in]LDA
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
           then LDA must be at least max( 1, n ).
[in,out]B
          B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
           Before entry,  the leading  m by n part of the array  B must
           contain the matrix  B,  and  on exit  is overwritten  by the
           transformed matrix.
[in]LDB
          LDB is INTEGER
           On entry, LDB specifies the first dimension of B as declared
           in  the  calling  (sub)  program.   LDB  must  be  at  least
           max( 1, m ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Further Details: 
  Level 3 Blas routine.

  -- Written on 8-February-1989.
     Jack Dongarra, Argonne National Laboratory.
     Iain Duff, AERE Harwell.
     Jeremy Du Croz, Numerical Algorithms Group Ltd.
     Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 179 of file dtrmm.f.

179 *
180 * -- Reference BLAS level3 routine (version 3.4.0) --
181 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
182 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183 * November 2011
184 *
185 * .. Scalar Arguments ..
186  DOUBLE PRECISION alpha
187  INTEGER lda,ldb,m,n
188  CHARACTER diag,side,transa,uplo
189 * ..
190 * .. Array Arguments ..
191  DOUBLE PRECISION a(lda,*),b(ldb,*)
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. External Functions ..
197  LOGICAL lsame
198  EXTERNAL lsame
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL xerbla
202 * ..
203 * .. Intrinsic Functions ..
204  INTRINSIC max
205 * ..
206 * .. Local Scalars ..
207  DOUBLE PRECISION temp
208  INTEGER i,info,j,k,nrowa
209  LOGICAL lside,nounit,upper
210 * ..
211 * .. Parameters ..
212  DOUBLE PRECISION one,zero
213  parameter(one=1.0d+0,zero=0.0d+0)
214 * ..
215 *
216 * Test the input parameters.
217 *
218  lside = lsame(side,'L')
219  IF (lside) THEN
220  nrowa = m
221  ELSE
222  nrowa = n
223  END IF
224  nounit = lsame(diag,'N')
225  upper = lsame(uplo,'U')
226 *
227  info = 0
228  IF ((.NOT.lside) .AND. (.NOT.lsame(side,'R'))) THEN
229  info = 1
230  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
231  info = 2
232  ELSE IF ((.NOT.lsame(transa,'N')) .AND.
233  + (.NOT.lsame(transa,'T')) .AND.
234  + (.NOT.lsame(transa,'C'))) THEN
235  info = 3
236  ELSE IF ((.NOT.lsame(diag,'U')) .AND. (.NOT.lsame(diag,'N'))) THEN
237  info = 4
238  ELSE IF (m.LT.0) THEN
239  info = 5
240  ELSE IF (n.LT.0) THEN
241  info = 6
242  ELSE IF (lda.LT.max(1,nrowa)) THEN
243  info = 9
244  ELSE IF (ldb.LT.max(1,m)) THEN
245  info = 11
246  END IF
247  IF (info.NE.0) THEN
248  CALL xerbla('DTRMM ',info)
249  RETURN
250  END IF
251 *
252 * Quick return if possible.
253 *
254  IF (m.EQ.0 .OR. n.EQ.0) RETURN
255 *
256 * And when alpha.eq.zero.
257 *
258  IF (alpha.EQ.zero) THEN
259  DO 20 j = 1,n
260  DO 10 i = 1,m
261  b(i,j) = zero
262  10 CONTINUE
263  20 CONTINUE
264  RETURN
265  END IF
266 *
267 * Start the operations.
268 *
269  IF (lside) THEN
270  IF (lsame(transa,'N')) THEN
271 *
272 * Form B := alpha*A*B.
273 *
274  IF (upper) THEN
275  DO 50 j = 1,n
276  DO 40 k = 1,m
277  IF (b(k,j).NE.zero) THEN
278  temp = alpha*b(k,j)
279  DO 30 i = 1,k - 1
280  b(i,j) = b(i,j) + temp*a(i,k)
281  30 CONTINUE
282  IF (nounit) temp = temp*a(k,k)
283  b(k,j) = temp
284  END IF
285  40 CONTINUE
286  50 CONTINUE
287  ELSE
288  DO 80 j = 1,n
289  DO 70 k = m,1,-1
290  IF (b(k,j).NE.zero) THEN
291  temp = alpha*b(k,j)
292  b(k,j) = temp
293  IF (nounit) b(k,j) = b(k,j)*a(k,k)
294  DO 60 i = k + 1,m
295  b(i,j) = b(i,j) + temp*a(i,k)
296  60 CONTINUE
297  END IF
298  70 CONTINUE
299  80 CONTINUE
300  END IF
301  ELSE
302 *
303 * Form B := alpha*A**T*B.
304 *
305  IF (upper) THEN
306  DO 110 j = 1,n
307  DO 100 i = m,1,-1
308  temp = b(i,j)
309  IF (nounit) temp = temp*a(i,i)
310  DO 90 k = 1,i - 1
311  temp = temp + a(k,i)*b(k,j)
312  90 CONTINUE
313  b(i,j) = alpha*temp
314  100 CONTINUE
315  110 CONTINUE
316  ELSE
317  DO 140 j = 1,n
318  DO 130 i = 1,m
319  temp = b(i,j)
320  IF (nounit) temp = temp*a(i,i)
321  DO 120 k = i + 1,m
322  temp = temp + a(k,i)*b(k,j)
323  120 CONTINUE
324  b(i,j) = alpha*temp
325  130 CONTINUE
326  140 CONTINUE
327  END IF
328  END IF
329  ELSE
330  IF (lsame(transa,'N')) THEN
331 *
332 * Form B := alpha*B*A.
333 *
334  IF (upper) THEN
335  DO 180 j = n,1,-1
336  temp = alpha
337  IF (nounit) temp = temp*a(j,j)
338  DO 150 i = 1,m
339  b(i,j) = temp*b(i,j)
340  150 CONTINUE
341  DO 170 k = 1,j - 1
342  IF (a(k,j).NE.zero) THEN
343  temp = alpha*a(k,j)
344  DO 160 i = 1,m
345  b(i,j) = b(i,j) + temp*b(i,k)
346  160 CONTINUE
347  END IF
348  170 CONTINUE
349  180 CONTINUE
350  ELSE
351  DO 220 j = 1,n
352  temp = alpha
353  IF (nounit) temp = temp*a(j,j)
354  DO 190 i = 1,m
355  b(i,j) = temp*b(i,j)
356  190 CONTINUE
357  DO 210 k = j + 1,n
358  IF (a(k,j).NE.zero) THEN
359  temp = alpha*a(k,j)
360  DO 200 i = 1,m
361  b(i,j) = b(i,j) + temp*b(i,k)
362  200 CONTINUE
363  END IF
364  210 CONTINUE
365  220 CONTINUE
366  END IF
367  ELSE
368 *
369 * Form B := alpha*B*A**T.
370 *
371  IF (upper) THEN
372  DO 260 k = 1,n
373  DO 240 j = 1,k - 1
374  IF (a(j,k).NE.zero) THEN
375  temp = alpha*a(j,k)
376  DO 230 i = 1,m
377  b(i,j) = b(i,j) + temp*b(i,k)
378  230 CONTINUE
379  END IF
380  240 CONTINUE
381  temp = alpha
382  IF (nounit) temp = temp*a(k,k)
383  IF (temp.NE.one) THEN
384  DO 250 i = 1,m
385  b(i,k) = temp*b(i,k)
386  250 CONTINUE
387  END IF
388  260 CONTINUE
389  ELSE
390  DO 300 k = n,1,-1
391  DO 280 j = k + 1,n
392  IF (a(j,k).NE.zero) THEN
393  temp = alpha*a(j,k)
394  DO 270 i = 1,m
395  b(i,j) = b(i,j) + temp*b(i,k)
396  270 CONTINUE
397  END IF
398  280 CONTINUE
399  temp = alpha
400  IF (nounit) temp = temp*a(k,k)
401  IF (temp.NE.one) THEN
402  DO 290 i = 1,m
403  b(i,k) = temp*b(i,k)
404  290 CONTINUE
405  END IF
406  300 CONTINUE
407  END IF
408  END IF
409  END IF
410 *
411  RETURN
412 *
413 * End of DTRMM .
414 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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