Annotation of rpl/lapack/blas/ztrsm.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZTRSM
1.1 bertrand 2: *
1.8 ! bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.8 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.8 ! bertrand 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
1.1 bertrand 39: *
1.8 ! bertrand 40: * Arguments:
1.1 bertrand 41: * ==========
42: *
1.8 ! bertrand 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 November 2011
! 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)
1.1 bertrand 182: *
1.8 ! bertrand 183: * -- Reference BLAS level3 routine (version 3.4.0) --
! 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: * November 2011
1.1 bertrand 187: *
1.8 ! bertrand 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: * ..
1.1 bertrand 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 ..
1.8 ! bertrand 210: COMPLEX*16 TEMP
1.1 bertrand 211: INTEGER I,INFO,J,K,NROWA
212: LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
213: * ..
214: * .. Parameters ..
1.8 ! bertrand 215: COMPLEX*16 ONE
1.1 bertrand 216: PARAMETER (ONE= (1.0D+0,0.0D+0))
1.8 ! bertrand 217: COMPLEX*16 ZERO
1.1 bertrand 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: *
1.7 bertrand 315: * Form B := alpha*inv( A**T )*B
316: * or B := alpha*inv( A**H )*B.
1.1 bertrand 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: *
1.7 bertrand 406: * Form B := alpha*B*inv( A**T )
407: * or B := alpha*B*inv( A**H ).
1.1 bertrand 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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