1: *> \brief \b ZTRSM
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 ZTRSM(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: *> ZTRSM 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 or op( A ) = A**H.
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**H.
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 COMPLEX*16
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 COMPLEX*16 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 COMPLEX*16 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 December 2016
163: *
164: *> \ingroup complex16_blas_level3
165: *
166: *> \par Further Details:
167: * =====================
168: *>
169: *> \verbatim
170: *>
171: *> Level 3 Blas routine.
172: *>
173: *> -- Written on 8-February-1989.
174: *> Jack Dongarra, Argonne National Laboratory.
175: *> Iain Duff, AERE Harwell.
176: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
177: *> Sven Hammarling, Numerical Algorithms Group Ltd.
178: *> \endverbatim
179: *>
180: * =====================================================================
181: SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
182: *
183: * -- Reference BLAS level3 routine (version 3.7.0) --
184: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
185: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
186: * December 2016
187: *
188: * .. Scalar Arguments ..
189: COMPLEX*16 ALPHA
190: INTEGER LDA,LDB,M,N
191: CHARACTER DIAG,SIDE,TRANSA,UPLO
192: * ..
193: * .. Array Arguments ..
194: COMPLEX*16 A(LDA,*),B(LDB,*)
195: * ..
196: *
197: * =====================================================================
198: *
199: * .. External Functions ..
200: LOGICAL LSAME
201: EXTERNAL LSAME
202: * ..
203: * .. External Subroutines ..
204: EXTERNAL XERBLA
205: * ..
206: * .. Intrinsic Functions ..
207: INTRINSIC DCONJG,MAX
208: * ..
209: * .. Local Scalars ..
210: COMPLEX*16 TEMP
211: INTEGER I,INFO,J,K,NROWA
212: LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
213: * ..
214: * .. Parameters ..
215: COMPLEX*16 ONE
216: PARAMETER (ONE= (1.0D+0,0.0D+0))
217: COMPLEX*16 ZERO
218: PARAMETER (ZERO= (0.0D+0,0.0D+0))
219: * ..
220: *
221: * Test the input parameters.
222: *
223: LSIDE = LSAME(SIDE,'L')
224: IF (LSIDE) THEN
225: NROWA = M
226: ELSE
227: NROWA = N
228: END IF
229: NOCONJ = LSAME(TRANSA,'T')
230: NOUNIT = LSAME(DIAG,'N')
231: UPPER = LSAME(UPLO,'U')
232: *
233: INFO = 0
234: IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
235: INFO = 1
236: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
237: INFO = 2
238: ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
239: + (.NOT.LSAME(TRANSA,'T')) .AND.
240: + (.NOT.LSAME(TRANSA,'C'))) THEN
241: INFO = 3
242: ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
243: INFO = 4
244: ELSE IF (M.LT.0) THEN
245: INFO = 5
246: ELSE IF (N.LT.0) THEN
247: INFO = 6
248: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
249: INFO = 9
250: ELSE IF (LDB.LT.MAX(1,M)) THEN
251: INFO = 11
252: END IF
253: IF (INFO.NE.0) THEN
254: CALL XERBLA('ZTRSM ',INFO)
255: RETURN
256: END IF
257: *
258: * Quick return if possible.
259: *
260: IF (M.EQ.0 .OR. N.EQ.0) RETURN
261: *
262: * And when alpha.eq.zero.
263: *
264: IF (ALPHA.EQ.ZERO) THEN
265: DO 20 J = 1,N
266: DO 10 I = 1,M
267: B(I,J) = ZERO
268: 10 CONTINUE
269: 20 CONTINUE
270: RETURN
271: END IF
272: *
273: * Start the operations.
274: *
275: IF (LSIDE) THEN
276: IF (LSAME(TRANSA,'N')) THEN
277: *
278: * Form B := alpha*inv( A )*B.
279: *
280: IF (UPPER) THEN
281: DO 60 J = 1,N
282: IF (ALPHA.NE.ONE) THEN
283: DO 30 I = 1,M
284: B(I,J) = ALPHA*B(I,J)
285: 30 CONTINUE
286: END IF
287: DO 50 K = M,1,-1
288: IF (B(K,J).NE.ZERO) THEN
289: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
290: DO 40 I = 1,K - 1
291: B(I,J) = B(I,J) - B(K,J)*A(I,K)
292: 40 CONTINUE
293: END IF
294: 50 CONTINUE
295: 60 CONTINUE
296: ELSE
297: DO 100 J = 1,N
298: IF (ALPHA.NE.ONE) THEN
299: DO 70 I = 1,M
300: B(I,J) = ALPHA*B(I,J)
301: 70 CONTINUE
302: END IF
303: DO 90 K = 1,M
304: IF (B(K,J).NE.ZERO) THEN
305: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
306: DO 80 I = K + 1,M
307: B(I,J) = B(I,J) - B(K,J)*A(I,K)
308: 80 CONTINUE
309: END IF
310: 90 CONTINUE
311: 100 CONTINUE
312: END IF
313: ELSE
314: *
315: * Form B := alpha*inv( A**T )*B
316: * or B := alpha*inv( A**H )*B.
317: *
318: IF (UPPER) THEN
319: DO 140 J = 1,N
320: DO 130 I = 1,M
321: TEMP = ALPHA*B(I,J)
322: IF (NOCONJ) THEN
323: DO 110 K = 1,I - 1
324: TEMP = TEMP - A(K,I)*B(K,J)
325: 110 CONTINUE
326: IF (NOUNIT) TEMP = TEMP/A(I,I)
327: ELSE
328: DO 120 K = 1,I - 1
329: TEMP = TEMP - DCONJG(A(K,I))*B(K,J)
330: 120 CONTINUE
331: IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I))
332: END IF
333: B(I,J) = TEMP
334: 130 CONTINUE
335: 140 CONTINUE
336: ELSE
337: DO 180 J = 1,N
338: DO 170 I = M,1,-1
339: TEMP = ALPHA*B(I,J)
340: IF (NOCONJ) THEN
341: DO 150 K = I + 1,M
342: TEMP = TEMP - A(K,I)*B(K,J)
343: 150 CONTINUE
344: IF (NOUNIT) TEMP = TEMP/A(I,I)
345: ELSE
346: DO 160 K = I + 1,M
347: TEMP = TEMP - DCONJG(A(K,I))*B(K,J)
348: 160 CONTINUE
349: IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I))
350: END IF
351: B(I,J) = TEMP
352: 170 CONTINUE
353: 180 CONTINUE
354: END IF
355: END IF
356: ELSE
357: IF (LSAME(TRANSA,'N')) THEN
358: *
359: * Form B := alpha*B*inv( A ).
360: *
361: IF (UPPER) THEN
362: DO 230 J = 1,N
363: IF (ALPHA.NE.ONE) THEN
364: DO 190 I = 1,M
365: B(I,J) = ALPHA*B(I,J)
366: 190 CONTINUE
367: END IF
368: DO 210 K = 1,J - 1
369: IF (A(K,J).NE.ZERO) THEN
370: DO 200 I = 1,M
371: B(I,J) = B(I,J) - A(K,J)*B(I,K)
372: 200 CONTINUE
373: END IF
374: 210 CONTINUE
375: IF (NOUNIT) THEN
376: TEMP = ONE/A(J,J)
377: DO 220 I = 1,M
378: B(I,J) = TEMP*B(I,J)
379: 220 CONTINUE
380: END IF
381: 230 CONTINUE
382: ELSE
383: DO 280 J = N,1,-1
384: IF (ALPHA.NE.ONE) THEN
385: DO 240 I = 1,M
386: B(I,J) = ALPHA*B(I,J)
387: 240 CONTINUE
388: END IF
389: DO 260 K = J + 1,N
390: IF (A(K,J).NE.ZERO) THEN
391: DO 250 I = 1,M
392: B(I,J) = B(I,J) - A(K,J)*B(I,K)
393: 250 CONTINUE
394: END IF
395: 260 CONTINUE
396: IF (NOUNIT) THEN
397: TEMP = ONE/A(J,J)
398: DO 270 I = 1,M
399: B(I,J) = TEMP*B(I,J)
400: 270 CONTINUE
401: END IF
402: 280 CONTINUE
403: END IF
404: ELSE
405: *
406: * Form B := alpha*B*inv( A**T )
407: * or B := alpha*B*inv( A**H ).
408: *
409: IF (UPPER) THEN
410: DO 330 K = N,1,-1
411: IF (NOUNIT) THEN
412: IF (NOCONJ) THEN
413: TEMP = ONE/A(K,K)
414: ELSE
415: TEMP = ONE/DCONJG(A(K,K))
416: END IF
417: DO 290 I = 1,M
418: B(I,K) = TEMP*B(I,K)
419: 290 CONTINUE
420: END IF
421: DO 310 J = 1,K - 1
422: IF (A(J,K).NE.ZERO) THEN
423: IF (NOCONJ) THEN
424: TEMP = A(J,K)
425: ELSE
426: TEMP = DCONJG(A(J,K))
427: END IF
428: DO 300 I = 1,M
429: B(I,J) = B(I,J) - TEMP*B(I,K)
430: 300 CONTINUE
431: END IF
432: 310 CONTINUE
433: IF (ALPHA.NE.ONE) THEN
434: DO 320 I = 1,M
435: B(I,K) = ALPHA*B(I,K)
436: 320 CONTINUE
437: END IF
438: 330 CONTINUE
439: ELSE
440: DO 380 K = 1,N
441: IF (NOUNIT) THEN
442: IF (NOCONJ) THEN
443: TEMP = ONE/A(K,K)
444: ELSE
445: TEMP = ONE/DCONJG(A(K,K))
446: END IF
447: DO 340 I = 1,M
448: B(I,K) = TEMP*B(I,K)
449: 340 CONTINUE
450: END IF
451: DO 360 J = K + 1,N
452: IF (A(J,K).NE.ZERO) THEN
453: IF (NOCONJ) THEN
454: TEMP = A(J,K)
455: ELSE
456: TEMP = DCONJG(A(J,K))
457: END IF
458: DO 350 I = 1,M
459: B(I,J) = B(I,J) - TEMP*B(I,K)
460: 350 CONTINUE
461: END IF
462: 360 CONTINUE
463: IF (ALPHA.NE.ONE) THEN
464: DO 370 I = 1,M
465: B(I,K) = ALPHA*B(I,K)
466: 370 CONTINUE
467: END IF
468: 380 CONTINUE
469: END IF
470: END IF
471: END IF
472: *
473: RETURN
474: *
475: * End of ZTRSM .
476: *
477: END
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