LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ztrmm.f
Go to the documentation of this file.
1 *> \brief \b ZTRMM
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 ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
12 *
13 * .. Scalar Arguments ..
14 * COMPLEX*16 ALPHA
15 * INTEGER LDA,LDB,M,N
16 * CHARACTER DIAG,SIDE,TRANSA,UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX*16 A(LDA,*),B(LDB,*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> ZTRMM performs one of the matrix-matrix operations
29 *>
30 *> B := alpha*op( A )*B, or B := alpha*B*op( A )
31 *>
32 *> where alpha is a scalar, B is an m by n matrix, 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 or op( A ) = A**H.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] SIDE
42 *> \verbatim
43 *> SIDE is CHARACTER*1
44 *> On entry, SIDE specifies whether op( A ) multiplies B from
45 *> the left or right as follows:
46 *>
47 *> SIDE = 'L' or 'l' B := alpha*op( A )*B.
48 *>
49 *> SIDE = 'R' or 'r' B := alpha*B*op( A ).
50 *> \endverbatim
51 *>
52 *> \param[in] UPLO
53 *> \verbatim
54 *> UPLO is CHARACTER*1
55 *> On entry, UPLO specifies whether the matrix A is an upper or
56 *> lower triangular matrix as follows:
57 *>
58 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
59 *>
60 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
61 *> \endverbatim
62 *>
63 *> \param[in] TRANSA
64 *> \verbatim
65 *> TRANSA is CHARACTER*1
66 *> On entry, TRANSA specifies the form of op( A ) to be used in
67 *> the matrix multiplication as follows:
68 *>
69 *> TRANSA = 'N' or 'n' op( A ) = A.
70 *>
71 *> TRANSA = 'T' or 't' op( A ) = A**T.
72 *>
73 *> TRANSA = 'C' or 'c' op( A ) = A**H.
74 *> \endverbatim
75 *>
76 *> \param[in] DIAG
77 *> \verbatim
78 *> DIAG is CHARACTER*1
79 *> On entry, DIAG specifies whether or not A is unit triangular
80 *> as follows:
81 *>
82 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
83 *>
84 *> DIAG = 'N' or 'n' A is not assumed to be unit
85 *> triangular.
86 *> \endverbatim
87 *>
88 *> \param[in] M
89 *> \verbatim
90 *> M is INTEGER
91 *> On entry, M specifies the number of rows of B. M must be at
92 *> least zero.
93 *> \endverbatim
94 *>
95 *> \param[in] N
96 *> \verbatim
97 *> N is INTEGER
98 *> On entry, N specifies the number of columns of B. N must be
99 *> at least zero.
100 *> \endverbatim
101 *>
102 *> \param[in] ALPHA
103 *> \verbatim
104 *> ALPHA is COMPLEX*16
105 *> On entry, ALPHA specifies the scalar alpha. When alpha is
106 *> zero then A is not referenced and B need not be set before
107 *> entry.
108 *> \endverbatim
109 *>
110 *> \param[in] A
111 *> \verbatim
112 *> A is COMPLEX*16 array, dimension ( LDA, k ), where k is m
113 *> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
114 *> Before entry with UPLO = 'U' or 'u', the leading k by k
115 *> upper triangular part of the array A must contain the upper
116 *> triangular matrix and the strictly lower triangular part of
117 *> A is not referenced.
118 *> Before entry with UPLO = 'L' or 'l', the leading k by k
119 *> lower triangular part of the array A must contain the lower
120 *> triangular matrix and the strictly upper triangular part of
121 *> A is not referenced.
122 *> Note that when DIAG = 'U' or 'u', the diagonal elements of
123 *> A are not referenced either, but are assumed to be unity.
124 *> \endverbatim
125 *>
126 *> \param[in] LDA
127 *> \verbatim
128 *> LDA is INTEGER
129 *> On entry, LDA specifies the first dimension of A as declared
130 *> in the calling (sub) program. When SIDE = 'L' or 'l' then
131 *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
132 *> then LDA must be at least max( 1, n ).
133 *> \endverbatim
134 *>
135 *> \param[in,out] B
136 *> \verbatim
137 *> B is COMPLEX*16 array, dimension ( LDB, N ).
138 *> Before entry, the leading m by n part of the array B must
139 *> contain the matrix B, and on exit is overwritten by the
140 *> transformed matrix.
141 *> \endverbatim
142 *>
143 *> \param[in] LDB
144 *> \verbatim
145 *> LDB is INTEGER
146 *> On entry, LDB specifies the first dimension of B as declared
147 *> in the calling (sub) program. LDB must be at least
148 *> max( 1, m ).
149 *> \endverbatim
150 *
151 * Authors:
152 * ========
153 *
154 *> \author Univ. of Tennessee
155 *> \author Univ. of California Berkeley
156 *> \author Univ. of Colorado Denver
157 *> \author NAG Ltd.
158 *
159 *> \ingroup complex16_blas_level3
160 *
161 *> \par Further Details:
162 * =====================
163 *>
164 *> \verbatim
165 *>
166 *> Level 3 Blas routine.
167 *>
168 *> -- Written on 8-February-1989.
169 *> Jack Dongarra, Argonne National Laboratory.
170 *> Iain Duff, AERE Harwell.
171 *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
172 *> Sven Hammarling, Numerical Algorithms Group Ltd.
173 *> \endverbatim
174 *>
175 * =====================================================================
176  SUBROUTINE ztrmm(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
177 *
178 * -- Reference BLAS level3 routine --
179 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
180 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181 *
182 * .. Scalar Arguments ..
183  COMPLEX*16 ALPHA
184  INTEGER LDA,LDB,M,N
185  CHARACTER DIAG,SIDE,TRANSA,UPLO
186 * ..
187 * .. Array Arguments ..
188  COMPLEX*16 A(LDA,*),B(LDB,*)
189 * ..
190 *
191 * =====================================================================
192 *
193 * .. External Functions ..
194  LOGICAL LSAME
195  EXTERNAL lsame
196 * ..
197 * .. External Subroutines ..
198  EXTERNAL xerbla
199 * ..
200 * .. Intrinsic Functions ..
201  INTRINSIC dconjg,max
202 * ..
203 * .. Local Scalars ..
204  COMPLEX*16 TEMP
205  INTEGER I,INFO,J,K,NROWA
206  LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
207 * ..
208 * .. Parameters ..
209  COMPLEX*16 ONE
210  parameter(one= (1.0d+0,0.0d+0))
211  COMPLEX*16 ZERO
212  parameter(zero= (0.0d+0,0.0d+0))
213 * ..
214 *
215 * Test the input parameters.
216 *
217  lside = lsame(side,'L')
218  IF (lside) THEN
219  nrowa = m
220  ELSE
221  nrowa = n
222  END IF
223  noconj = lsame(transa,'T')
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('ZTRMM ',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 or B := alpha*A**H*B.
304 *
305  IF (upper) THEN
306  DO 120 j = 1,n
307  DO 110 i = m,1,-1
308  temp = b(i,j)
309  IF (noconj) THEN
310  IF (nounit) temp = temp*a(i,i)
311  DO 90 k = 1,i - 1
312  temp = temp + a(k,i)*b(k,j)
313  90 CONTINUE
314  ELSE
315  IF (nounit) temp = temp*dconjg(a(i,i))
316  DO 100 k = 1,i - 1
317  temp = temp + dconjg(a(k,i))*b(k,j)
318  100 CONTINUE
319  END IF
320  b(i,j) = alpha*temp
321  110 CONTINUE
322  120 CONTINUE
323  ELSE
324  DO 160 j = 1,n
325  DO 150 i = 1,m
326  temp = b(i,j)
327  IF (noconj) THEN
328  IF (nounit) temp = temp*a(i,i)
329  DO 130 k = i + 1,m
330  temp = temp + a(k,i)*b(k,j)
331  130 CONTINUE
332  ELSE
333  IF (nounit) temp = temp*dconjg(a(i,i))
334  DO 140 k = i + 1,m
335  temp = temp + dconjg(a(k,i))*b(k,j)
336  140 CONTINUE
337  END IF
338  b(i,j) = alpha*temp
339  150 CONTINUE
340  160 CONTINUE
341  END IF
342  END IF
343  ELSE
344  IF (lsame(transa,'N')) THEN
345 *
346 * Form B := alpha*B*A.
347 *
348  IF (upper) THEN
349  DO 200 j = n,1,-1
350  temp = alpha
351  IF (nounit) temp = temp*a(j,j)
352  DO 170 i = 1,m
353  b(i,j) = temp*b(i,j)
354  170 CONTINUE
355  DO 190 k = 1,j - 1
356  IF (a(k,j).NE.zero) THEN
357  temp = alpha*a(k,j)
358  DO 180 i = 1,m
359  b(i,j) = b(i,j) + temp*b(i,k)
360  180 CONTINUE
361  END IF
362  190 CONTINUE
363  200 CONTINUE
364  ELSE
365  DO 240 j = 1,n
366  temp = alpha
367  IF (nounit) temp = temp*a(j,j)
368  DO 210 i = 1,m
369  b(i,j) = temp*b(i,j)
370  210 CONTINUE
371  DO 230 k = j + 1,n
372  IF (a(k,j).NE.zero) THEN
373  temp = alpha*a(k,j)
374  DO 220 i = 1,m
375  b(i,j) = b(i,j) + temp*b(i,k)
376  220 CONTINUE
377  END IF
378  230 CONTINUE
379  240 CONTINUE
380  END IF
381  ELSE
382 *
383 * Form B := alpha*B*A**T or B := alpha*B*A**H.
384 *
385  IF (upper) THEN
386  DO 280 k = 1,n
387  DO 260 j = 1,k - 1
388  IF (a(j,k).NE.zero) THEN
389  IF (noconj) THEN
390  temp = alpha*a(j,k)
391  ELSE
392  temp = alpha*dconjg(a(j,k))
393  END IF
394  DO 250 i = 1,m
395  b(i,j) = b(i,j) + temp*b(i,k)
396  250 CONTINUE
397  END IF
398  260 CONTINUE
399  temp = alpha
400  IF (nounit) THEN
401  IF (noconj) THEN
402  temp = temp*a(k,k)
403  ELSE
404  temp = temp*dconjg(a(k,k))
405  END IF
406  END IF
407  IF (temp.NE.one) THEN
408  DO 270 i = 1,m
409  b(i,k) = temp*b(i,k)
410  270 CONTINUE
411  END IF
412  280 CONTINUE
413  ELSE
414  DO 320 k = n,1,-1
415  DO 300 j = k + 1,n
416  IF (a(j,k).NE.zero) THEN
417  IF (noconj) THEN
418  temp = alpha*a(j,k)
419  ELSE
420  temp = alpha*dconjg(a(j,k))
421  END IF
422  DO 290 i = 1,m
423  b(i,j) = b(i,j) + temp*b(i,k)
424  290 CONTINUE
425  END IF
426  300 CONTINUE
427  temp = alpha
428  IF (nounit) THEN
429  IF (noconj) THEN
430  temp = temp*a(k,k)
431  ELSE
432  temp = temp*dconjg(a(k,k))
433  END IF
434  END IF
435  IF (temp.NE.one) THEN
436  DO 310 i = 1,m
437  b(i,k) = temp*b(i,k)
438  310 CONTINUE
439  END IF
440  320 CONTINUE
441  END IF
442  END IF
443  END IF
444 *
445  RETURN
446 *
447 * End of ZTRMM
448 *
449  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:177