LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dtrsm.f
Go to the documentation of this file.
1 *> \brief \b DTRSM
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
12 *
13 * .. Scalar Arguments ..
14 * DOUBLE PRECISION ALPHA
15 * INTEGER LDA,LDB,M,N
16 * CHARACTER DIAG,SIDE,TRANSA,UPLO
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A(LDA,*),B(LDB,*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> DTRSM solves one of the matrix equations
29 *>
30 *> op( A )*X = alpha*B, or X*op( A ) = alpha*B,
31 *>
32 *> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
33 *> non-unit, upper or lower triangular matrix and op( A ) is one of
34 *>
35 *> op( A ) = A or op( A ) = A**T.
36 *>
37 *> The matrix X is overwritten on B.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[in] SIDE
44 *> \verbatim
45 *> SIDE is CHARACTER*1
46 *> On entry, SIDE specifies whether op( A ) appears on the left
47 *> or right of X as follows:
48 *>
49 *> SIDE = 'L' or 'l' op( A )*X = alpha*B.
50 *>
51 *> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
52 *> \endverbatim
53 *>
54 *> \param[in] UPLO
55 *> \verbatim
56 *> UPLO is CHARACTER*1
57 *> On entry, UPLO specifies whether the matrix A is an upper or
58 *> lower triangular matrix as follows:
59 *>
60 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
61 *>
62 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
63 *> \endverbatim
64 *>
65 *> \param[in] TRANSA
66 *> \verbatim
67 *> TRANSA is CHARACTER*1
68 *> On entry, TRANSA specifies the form of op( A ) to be used in
69 *> the matrix multiplication as follows:
70 *>
71 *> TRANSA = 'N' or 'n' op( A ) = A.
72 *>
73 *> TRANSA = 'T' or 't' op( A ) = A**T.
74 *>
75 *> TRANSA = 'C' or 'c' op( A ) = A**T.
76 *> \endverbatim
77 *>
78 *> \param[in] DIAG
79 *> \verbatim
80 *> DIAG is CHARACTER*1
81 *> On entry, DIAG specifies whether or not A is unit triangular
82 *> as follows:
83 *>
84 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
85 *>
86 *> DIAG = 'N' or 'n' A is not assumed to be unit
87 *> triangular.
88 *> \endverbatim
89 *>
90 *> \param[in] M
91 *> \verbatim
92 *> M is INTEGER
93 *> On entry, M specifies the number of rows of B. M must be at
94 *> least zero.
95 *> \endverbatim
96 *>
97 *> \param[in] N
98 *> \verbatim
99 *> N is INTEGER
100 *> On entry, N specifies the number of columns of B. N must be
101 *> at least zero.
102 *> \endverbatim
103 *>
104 *> \param[in] ALPHA
105 *> \verbatim
106 *> ALPHA is DOUBLE PRECISION.
107 *> On entry, ALPHA specifies the scalar alpha. When alpha is
108 *> zero then A is not referenced and B need not be set before
109 *> entry.
110 *> \endverbatim
111 *>
112 *> \param[in] A
113 *> \verbatim
114 *> A is DOUBLE PRECISION array, dimension ( LDA, k ),
115 *> where k is m when SIDE = 'L' or 'l'
116 *> and k is n when SIDE = 'R' or 'r'.
117 *> Before entry with UPLO = 'U' or 'u', the leading k by k
118 *> upper triangular part of the array A must contain the upper
119 *> triangular matrix and the strictly lower triangular part of
120 *> A is not referenced.
121 *> Before entry with UPLO = 'L' or 'l', the leading k by k
122 *> lower triangular part of the array A must contain the lower
123 *> triangular matrix and the strictly upper triangular part of
124 *> A is not referenced.
125 *> Note that when DIAG = 'U' or 'u', the diagonal elements of
126 *> A are not referenced either, but are assumed to be unity.
127 *> \endverbatim
128 *>
129 *> \param[in] LDA
130 *> \verbatim
131 *> LDA is INTEGER
132 *> On entry, LDA specifies the first dimension of A as declared
133 *> in the calling (sub) program. When SIDE = 'L' or 'l' then
134 *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
135 *> then LDA must be at least max( 1, n ).
136 *> \endverbatim
137 *>
138 *> \param[in,out] B
139 *> \verbatim
140 *> B is DOUBLE PRECISION array, dimension ( LDB, N )
141 *> Before entry, the leading m by n part of the array B must
142 *> contain the right-hand side matrix B, and on exit is
143 *> overwritten by the solution matrix X.
144 *> \endverbatim
145 *>
146 *> \param[in] LDB
147 *> \verbatim
148 *> LDB is INTEGER
149 *> On entry, LDB specifies the first dimension of B as declared
150 *> in the calling (sub) program. LDB must be at least
151 *> max( 1, m ).
152 *> \endverbatim
153 *
154 * Authors:
155 * ========
156 *
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
160 *> \author NAG Ltd.
161 *
162 *> \ingroup double_blas_level3
163 *
164 *> \par Further Details:
165 * =====================
166 *>
167 *> \verbatim
168 *>
169 *> Level 3 Blas routine.
170 *>
171 *>
172 *> -- Written on 8-February-1989.
173 *> Jack Dongarra, Argonne National Laboratory.
174 *> Iain Duff, AERE Harwell.
175 *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
176 *> Sven Hammarling, Numerical Algorithms Group Ltd.
177 *> \endverbatim
178 *>
179 * =====================================================================
180  SUBROUTINE dtrsm(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
181 *
182 * -- Reference BLAS level3 routine --
183 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
184 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
185 *
186 * .. Scalar Arguments ..
187  DOUBLE PRECISION ALPHA
188  INTEGER LDA,LDB,M,N
189  CHARACTER DIAG,SIDE,TRANSA,UPLO
190 * ..
191 * .. Array Arguments ..
192  DOUBLE PRECISION A(LDA,*),B(LDB,*)
193 * ..
194 *
195 * =====================================================================
196 *
197 * .. External Functions ..
198  LOGICAL LSAME
199  EXTERNAL lsame
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL xerbla
203 * ..
204 * .. Intrinsic Functions ..
205  INTRINSIC max
206 * ..
207 * .. Local Scalars ..
208  DOUBLE PRECISION TEMP
209  INTEGER I,INFO,J,K,NROWA
210  LOGICAL LSIDE,NOUNIT,UPPER
211 * ..
212 * .. Parameters ..
213  DOUBLE PRECISION ONE,ZERO
214  parameter(one=1.0d+0,zero=0.0d+0)
215 * ..
216 *
217 * Test the input parameters.
218 *
219  lside = lsame(side,'L')
220  IF (lside) THEN
221  nrowa = m
222  ELSE
223  nrowa = n
224  END IF
225  nounit = lsame(diag,'N')
226  upper = lsame(uplo,'U')
227 *
228  info = 0
229  IF ((.NOT.lside) .AND. (.NOT.lsame(side,'R'))) THEN
230  info = 1
231  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
232  info = 2
233  ELSE IF ((.NOT.lsame(transa,'N')) .AND.
234  + (.NOT.lsame(transa,'T')) .AND.
235  + (.NOT.lsame(transa,'C'))) THEN
236  info = 3
237  ELSE IF ((.NOT.lsame(diag,'U')) .AND. (.NOT.lsame(diag,'N'))) THEN
238  info = 4
239  ELSE IF (m.LT.0) THEN
240  info = 5
241  ELSE IF (n.LT.0) THEN
242  info = 6
243  ELSE IF (lda.LT.max(1,nrowa)) THEN
244  info = 9
245  ELSE IF (ldb.LT.max(1,m)) THEN
246  info = 11
247  END IF
248  IF (info.NE.0) THEN
249  CALL xerbla('DTRSM ',info)
250  RETURN
251  END IF
252 *
253 * Quick return if possible.
254 *
255  IF (m.EQ.0 .OR. n.EQ.0) RETURN
256 *
257 * And when alpha.eq.zero.
258 *
259  IF (alpha.EQ.zero) THEN
260  DO 20 j = 1,n
261  DO 10 i = 1,m
262  b(i,j) = zero
263  10 CONTINUE
264  20 CONTINUE
265  RETURN
266  END IF
267 *
268 * Start the operations.
269 *
270  IF (lside) THEN
271  IF (lsame(transa,'N')) THEN
272 *
273 * Form B := alpha*inv( A )*B.
274 *
275  IF (upper) THEN
276  DO 60 j = 1,n
277  IF (alpha.NE.one) THEN
278  DO 30 i = 1,m
279  b(i,j) = alpha*b(i,j)
280  30 CONTINUE
281  END IF
282  DO 50 k = m,1,-1
283  IF (b(k,j).NE.zero) THEN
284  IF (nounit) b(k,j) = b(k,j)/a(k,k)
285  DO 40 i = 1,k - 1
286  b(i,j) = b(i,j) - b(k,j)*a(i,k)
287  40 CONTINUE
288  END IF
289  50 CONTINUE
290  60 CONTINUE
291  ELSE
292  DO 100 j = 1,n
293  IF (alpha.NE.one) THEN
294  DO 70 i = 1,m
295  b(i,j) = alpha*b(i,j)
296  70 CONTINUE
297  END IF
298  DO 90 k = 1,m
299  IF (b(k,j).NE.zero) THEN
300  IF (nounit) b(k,j) = b(k,j)/a(k,k)
301  DO 80 i = k + 1,m
302  b(i,j) = b(i,j) - b(k,j)*a(i,k)
303  80 CONTINUE
304  END IF
305  90 CONTINUE
306  100 CONTINUE
307  END IF
308  ELSE
309 *
310 * Form B := alpha*inv( A**T )*B.
311 *
312  IF (upper) THEN
313  DO 130 j = 1,n
314  DO 120 i = 1,m
315  temp = alpha*b(i,j)
316  DO 110 k = 1,i - 1
317  temp = temp - a(k,i)*b(k,j)
318  110 CONTINUE
319  IF (nounit) temp = temp/a(i,i)
320  b(i,j) = temp
321  120 CONTINUE
322  130 CONTINUE
323  ELSE
324  DO 160 j = 1,n
325  DO 150 i = m,1,-1
326  temp = alpha*b(i,j)
327  DO 140 k = i + 1,m
328  temp = temp - a(k,i)*b(k,j)
329  140 CONTINUE
330  IF (nounit) temp = temp/a(i,i)
331  b(i,j) = temp
332  150 CONTINUE
333  160 CONTINUE
334  END IF
335  END IF
336  ELSE
337  IF (lsame(transa,'N')) THEN
338 *
339 * Form B := alpha*B*inv( A ).
340 *
341  IF (upper) THEN
342  DO 210 j = 1,n
343  IF (alpha.NE.one) THEN
344  DO 170 i = 1,m
345  b(i,j) = alpha*b(i,j)
346  170 CONTINUE
347  END IF
348  DO 190 k = 1,j - 1
349  IF (a(k,j).NE.zero) THEN
350  DO 180 i = 1,m
351  b(i,j) = b(i,j) - a(k,j)*b(i,k)
352  180 CONTINUE
353  END IF
354  190 CONTINUE
355  IF (nounit) THEN
356  temp = one/a(j,j)
357  DO 200 i = 1,m
358  b(i,j) = temp*b(i,j)
359  200 CONTINUE
360  END IF
361  210 CONTINUE
362  ELSE
363  DO 260 j = n,1,-1
364  IF (alpha.NE.one) THEN
365  DO 220 i = 1,m
366  b(i,j) = alpha*b(i,j)
367  220 CONTINUE
368  END IF
369  DO 240 k = j + 1,n
370  IF (a(k,j).NE.zero) THEN
371  DO 230 i = 1,m
372  b(i,j) = b(i,j) - a(k,j)*b(i,k)
373  230 CONTINUE
374  END IF
375  240 CONTINUE
376  IF (nounit) THEN
377  temp = one/a(j,j)
378  DO 250 i = 1,m
379  b(i,j) = temp*b(i,j)
380  250 CONTINUE
381  END IF
382  260 CONTINUE
383  END IF
384  ELSE
385 *
386 * Form B := alpha*B*inv( A**T ).
387 *
388  IF (upper) THEN
389  DO 310 k = n,1,-1
390  IF (nounit) THEN
391  temp = one/a(k,k)
392  DO 270 i = 1,m
393  b(i,k) = temp*b(i,k)
394  270 CONTINUE
395  END IF
396  DO 290 j = 1,k - 1
397  IF (a(j,k).NE.zero) THEN
398  temp = a(j,k)
399  DO 280 i = 1,m
400  b(i,j) = b(i,j) - temp*b(i,k)
401  280 CONTINUE
402  END IF
403  290 CONTINUE
404  IF (alpha.NE.one) THEN
405  DO 300 i = 1,m
406  b(i,k) = alpha*b(i,k)
407  300 CONTINUE
408  END IF
409  310 CONTINUE
410  ELSE
411  DO 360 k = 1,n
412  IF (nounit) THEN
413  temp = one/a(k,k)
414  DO 320 i = 1,m
415  b(i,k) = temp*b(i,k)
416  320 CONTINUE
417  END IF
418  DO 340 j = k + 1,n
419  IF (a(j,k).NE.zero) THEN
420  temp = a(j,k)
421  DO 330 i = 1,m
422  b(i,j) = b(i,j) - temp*b(i,k)
423  330 CONTINUE
424  END IF
425  340 CONTINUE
426  IF (alpha.NE.one) THEN
427  DO 350 i = 1,m
428  b(i,k) = alpha*b(i,k)
429  350 CONTINUE
430  END IF
431  360 CONTINUE
432  END IF
433  END IF
434  END IF
435 *
436  RETURN
437 *
438 * End of DTRSM
439 *
440  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181