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 of 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 of 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: *> \date November 2011
163: *
164: *> \ingroup double_blas_level3
165: *
166: *> \par Further Details:
167: * =====================
168: *>
169: *> \verbatim
170: *>
171: *> Level 3 Blas routine.
172: *>
173: *>
174: *> -- Written on 8-February-1989.
175: *> Jack Dongarra, Argonne National Laboratory.
176: *> Iain Duff, AERE Harwell.
177: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
178: *> Sven Hammarling, Numerical Algorithms Group Ltd.
179: *> \endverbatim
180: *>
181: * =====================================================================
182: SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
183: *
184: * -- Reference BLAS level3 routine (version 3.4.0) --
185: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
186: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
187: * November 2011
188: *
189: * .. Scalar Arguments ..
190: DOUBLE PRECISION ALPHA
191: INTEGER LDA,LDB,M,N
192: CHARACTER DIAG,SIDE,TRANSA,UPLO
193: * ..
194: * .. Array Arguments ..
195: DOUBLE PRECISION A(LDA,*),B(LDB,*)
196: * ..
197: *
198: * =====================================================================
199: *
200: * .. External Functions ..
201: LOGICAL LSAME
202: EXTERNAL LSAME
203: * ..
204: * .. External Subroutines ..
205: EXTERNAL XERBLA
206: * ..
207: * .. Intrinsic Functions ..
208: INTRINSIC MAX
209: * ..
210: * .. Local Scalars ..
211: DOUBLE PRECISION TEMP
212: INTEGER I,INFO,J,K,NROWA
213: LOGICAL LSIDE,NOUNIT,UPPER
214: * ..
215: * .. Parameters ..
216: DOUBLE PRECISION ONE,ZERO
217: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
218: * ..
219: *
220: * Test the input parameters.
221: *
222: LSIDE = LSAME(SIDE,'L')
223: IF (LSIDE) THEN
224: NROWA = M
225: ELSE
226: NROWA = N
227: END IF
228: NOUNIT = LSAME(DIAG,'N')
229: UPPER = LSAME(UPLO,'U')
230: *
231: INFO = 0
232: IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
233: INFO = 1
234: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
235: INFO = 2
236: ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
237: + (.NOT.LSAME(TRANSA,'T')) .AND.
238: + (.NOT.LSAME(TRANSA,'C'))) THEN
239: INFO = 3
240: ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
241: INFO = 4
242: ELSE IF (M.LT.0) THEN
243: INFO = 5
244: ELSE IF (N.LT.0) THEN
245: INFO = 6
246: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
247: INFO = 9
248: ELSE IF (LDB.LT.MAX(1,M)) THEN
249: INFO = 11
250: END IF
251: IF (INFO.NE.0) THEN
252: CALL XERBLA('DTRSM ',INFO)
253: RETURN
254: END IF
255: *
256: * Quick return if possible.
257: *
258: IF (M.EQ.0 .OR. N.EQ.0) RETURN
259: *
260: * And when alpha.eq.zero.
261: *
262: IF (ALPHA.EQ.ZERO) THEN
263: DO 20 J = 1,N
264: DO 10 I = 1,M
265: B(I,J) = ZERO
266: 10 CONTINUE
267: 20 CONTINUE
268: RETURN
269: END IF
270: *
271: * Start the operations.
272: *
273: IF (LSIDE) THEN
274: IF (LSAME(TRANSA,'N')) THEN
275: *
276: * Form B := alpha*inv( A )*B.
277: *
278: IF (UPPER) THEN
279: DO 60 J = 1,N
280: IF (ALPHA.NE.ONE) THEN
281: DO 30 I = 1,M
282: B(I,J) = ALPHA*B(I,J)
283: 30 CONTINUE
284: END IF
285: DO 50 K = M,1,-1
286: IF (B(K,J).NE.ZERO) THEN
287: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
288: DO 40 I = 1,K - 1
289: B(I,J) = B(I,J) - B(K,J)*A(I,K)
290: 40 CONTINUE
291: END IF
292: 50 CONTINUE
293: 60 CONTINUE
294: ELSE
295: DO 100 J = 1,N
296: IF (ALPHA.NE.ONE) THEN
297: DO 70 I = 1,M
298: B(I,J) = ALPHA*B(I,J)
299: 70 CONTINUE
300: END IF
301: DO 90 K = 1,M
302: IF (B(K,J).NE.ZERO) THEN
303: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
304: DO 80 I = K + 1,M
305: B(I,J) = B(I,J) - B(K,J)*A(I,K)
306: 80 CONTINUE
307: END IF
308: 90 CONTINUE
309: 100 CONTINUE
310: END IF
311: ELSE
312: *
313: * Form B := alpha*inv( A**T )*B.
314: *
315: IF (UPPER) THEN
316: DO 130 J = 1,N
317: DO 120 I = 1,M
318: TEMP = ALPHA*B(I,J)
319: DO 110 K = 1,I - 1
320: TEMP = TEMP - A(K,I)*B(K,J)
321: 110 CONTINUE
322: IF (NOUNIT) TEMP = TEMP/A(I,I)
323: B(I,J) = TEMP
324: 120 CONTINUE
325: 130 CONTINUE
326: ELSE
327: DO 160 J = 1,N
328: DO 150 I = M,1,-1
329: TEMP = ALPHA*B(I,J)
330: DO 140 K = I + 1,M
331: TEMP = TEMP - A(K,I)*B(K,J)
332: 140 CONTINUE
333: IF (NOUNIT) TEMP = TEMP/A(I,I)
334: B(I,J) = TEMP
335: 150 CONTINUE
336: 160 CONTINUE
337: END IF
338: END IF
339: ELSE
340: IF (LSAME(TRANSA,'N')) THEN
341: *
342: * Form B := alpha*B*inv( A ).
343: *
344: IF (UPPER) THEN
345: DO 210 J = 1,N
346: IF (ALPHA.NE.ONE) THEN
347: DO 170 I = 1,M
348: B(I,J) = ALPHA*B(I,J)
349: 170 CONTINUE
350: END IF
351: DO 190 K = 1,J - 1
352: IF (A(K,J).NE.ZERO) THEN
353: DO 180 I = 1,M
354: B(I,J) = B(I,J) - A(K,J)*B(I,K)
355: 180 CONTINUE
356: END IF
357: 190 CONTINUE
358: IF (NOUNIT) THEN
359: TEMP = ONE/A(J,J)
360: DO 200 I = 1,M
361: B(I,J) = TEMP*B(I,J)
362: 200 CONTINUE
363: END IF
364: 210 CONTINUE
365: ELSE
366: DO 260 J = N,1,-1
367: IF (ALPHA.NE.ONE) THEN
368: DO 220 I = 1,M
369: B(I,J) = ALPHA*B(I,J)
370: 220 CONTINUE
371: END IF
372: DO 240 K = J + 1,N
373: IF (A(K,J).NE.ZERO) THEN
374: DO 230 I = 1,M
375: B(I,J) = B(I,J) - A(K,J)*B(I,K)
376: 230 CONTINUE
377: END IF
378: 240 CONTINUE
379: IF (NOUNIT) THEN
380: TEMP = ONE/A(J,J)
381: DO 250 I = 1,M
382: B(I,J) = TEMP*B(I,J)
383: 250 CONTINUE
384: END IF
385: 260 CONTINUE
386: END IF
387: ELSE
388: *
389: * Form B := alpha*B*inv( A**T ).
390: *
391: IF (UPPER) THEN
392: DO 310 K = N,1,-1
393: IF (NOUNIT) THEN
394: TEMP = ONE/A(K,K)
395: DO 270 I = 1,M
396: B(I,K) = TEMP*B(I,K)
397: 270 CONTINUE
398: END IF
399: DO 290 J = 1,K - 1
400: IF (A(J,K).NE.ZERO) THEN
401: TEMP = A(J,K)
402: DO 280 I = 1,M
403: B(I,J) = B(I,J) - TEMP*B(I,K)
404: 280 CONTINUE
405: END IF
406: 290 CONTINUE
407: IF (ALPHA.NE.ONE) THEN
408: DO 300 I = 1,M
409: B(I,K) = ALPHA*B(I,K)
410: 300 CONTINUE
411: END IF
412: 310 CONTINUE
413: ELSE
414: DO 360 K = 1,N
415: IF (NOUNIT) THEN
416: TEMP = ONE/A(K,K)
417: DO 320 I = 1,M
418: B(I,K) = TEMP*B(I,K)
419: 320 CONTINUE
420: END IF
421: DO 340 J = K + 1,N
422: IF (A(J,K).NE.ZERO) THEN
423: TEMP = A(J,K)
424: DO 330 I = 1,M
425: B(I,J) = B(I,J) - TEMP*B(I,K)
426: 330 CONTINUE
427: END IF
428: 340 CONTINUE
429: IF (ALPHA.NE.ONE) THEN
430: DO 350 I = 1,M
431: B(I,K) = ALPHA*B(I,K)
432: 350 CONTINUE
433: END IF
434: 360 CONTINUE
435: END IF
436: END IF
437: END IF
438: *
439: RETURN
440: *
441: * End of DTRSM .
442: *
443: END
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