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
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