Annotation of rpl/lapack/blas/zsyr2k.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZSYR2K
! 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 ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * COMPLEX*16 ALPHA,BETA
! 15: * INTEGER K,LDA,LDB,LDC,N
! 16: * CHARACTER TRANS,UPLO
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> ZSYR2K performs one of the symmetric rank 2k operations
! 29: *>
! 30: *> C := alpha*A*B**T + alpha*B*A**T + beta*C,
! 31: *>
! 32: *> or
! 33: *>
! 34: *> C := alpha*A**T*B + alpha*B**T*A + beta*C,
! 35: *>
! 36: *> where alpha and beta are scalars, C is an n by n symmetric matrix
! 37: *> and A and B are n by k matrices in the first case and k by n
! 38: *> matrices in the second case.
! 39: *> \endverbatim
! 40: *
! 41: * Arguments:
! 42: * ==========
! 43: *
! 44: *> \param[in] UPLO
! 45: *> \verbatim
! 46: *> UPLO is CHARACTER*1
! 47: *> On entry, UPLO specifies whether the upper or lower
! 48: *> triangular part of the array C is to be referenced as
! 49: *> follows:
! 50: *>
! 51: *> UPLO = 'U' or 'u' Only the upper triangular part of C
! 52: *> is to be referenced.
! 53: *>
! 54: *> UPLO = 'L' or 'l' Only the lower triangular part of C
! 55: *> is to be referenced.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] TRANS
! 59: *> \verbatim
! 60: *> TRANS is CHARACTER*1
! 61: *> On entry, TRANS specifies the operation to be performed as
! 62: *> follows:
! 63: *>
! 64: *> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T +
! 65: *> beta*C.
! 66: *>
! 67: *> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
! 68: *> beta*C.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] N
! 72: *> \verbatim
! 73: *> N is INTEGER
! 74: *> On entry, N specifies the order of the matrix C. N must be
! 75: *> at least zero.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] K
! 79: *> \verbatim
! 80: *> K is INTEGER
! 81: *> On entry with TRANS = 'N' or 'n', K specifies the number
! 82: *> of columns of the matrices A and B, and on entry with
! 83: *> TRANS = 'T' or 't', K specifies the number of rows of the
! 84: *> matrices A and B. K must be at least zero.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] ALPHA
! 88: *> \verbatim
! 89: *> ALPHA is COMPLEX*16
! 90: *> On entry, ALPHA specifies the scalar alpha.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] A
! 94: *> \verbatim
! 95: *> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
! 96: *> k when TRANS = 'N' or 'n', and is n otherwise.
! 97: *> Before entry with TRANS = 'N' or 'n', the leading n by k
! 98: *> part of the array A must contain the matrix A, otherwise
! 99: *> the leading k by n part of the array A must contain the
! 100: *> matrix A.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] LDA
! 104: *> \verbatim
! 105: *> LDA is INTEGER
! 106: *> On entry, LDA specifies the first dimension of A as declared
! 107: *> in the calling (sub) program. When TRANS = 'N' or 'n'
! 108: *> then LDA must be at least max( 1, n ), otherwise LDA must
! 109: *> be at least max( 1, k ).
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[in] B
! 113: *> \verbatim
! 114: *> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
! 115: *> k when TRANS = 'N' or 'n', and is n otherwise.
! 116: *> Before entry with TRANS = 'N' or 'n', the leading n by k
! 117: *> part of the array B must contain the matrix B, otherwise
! 118: *> the leading k by n part of the array B must contain the
! 119: *> matrix B.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[in] LDB
! 123: *> \verbatim
! 124: *> LDB is INTEGER
! 125: *> On entry, LDB specifies the first dimension of B as declared
! 126: *> in the calling (sub) program. When TRANS = 'N' or 'n'
! 127: *> then LDB must be at least max( 1, n ), otherwise LDB must
! 128: *> be at least max( 1, k ).
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[in] BETA
! 132: *> \verbatim
! 133: *> BETA is COMPLEX*16
! 134: *> On entry, BETA specifies the scalar beta.
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[in,out] C
! 138: *> \verbatim
! 139: *> C is COMPLEX*16 array of DIMENSION ( LDC, n ).
! 140: *> Before entry with UPLO = 'U' or 'u', the leading n by n
! 141: *> upper triangular part of the array C must contain the upper
! 142: *> triangular part of the symmetric matrix and the strictly
! 143: *> lower triangular part of C is not referenced. On exit, the
! 144: *> upper triangular part of the array C is overwritten by the
! 145: *> upper triangular part of the updated matrix.
! 146: *> Before entry with UPLO = 'L' or 'l', the leading n by n
! 147: *> lower triangular part of the array C must contain the lower
! 148: *> triangular part of the symmetric matrix and the strictly
! 149: *> upper triangular part of C is not referenced. On exit, the
! 150: *> lower triangular part of the array C is overwritten by the
! 151: *> lower triangular part of the updated matrix.
! 152: *> \endverbatim
! 153: *>
! 154: *> \param[in] LDC
! 155: *> \verbatim
! 156: *> LDC is INTEGER
! 157: *> On entry, LDC specifies the first dimension of C as declared
! 158: *> in the calling (sub) program. LDC must be at least
! 159: *> max( 1, n ).
! 160: *> \endverbatim
! 161: *
! 162: * Authors:
! 163: * ========
! 164: *
! 165: *> \author Univ. of Tennessee
! 166: *> \author Univ. of California Berkeley
! 167: *> \author Univ. of Colorado Denver
! 168: *> \author NAG Ltd.
! 169: *
! 170: *> \date November 2011
! 171: *
! 172: *> \ingroup complex16_blas_level3
! 173: *
! 174: *> \par Further Details:
! 175: * =====================
! 176: *>
! 177: *> \verbatim
! 178: *>
! 179: *> Level 3 Blas routine.
! 180: *>
! 181: *> -- Written on 8-February-1989.
! 182: *> Jack Dongarra, Argonne National Laboratory.
! 183: *> Iain Duff, AERE Harwell.
! 184: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 185: *> Sven Hammarling, Numerical Algorithms Group Ltd.
! 186: *> \endverbatim
! 187: *>
! 188: * =====================================================================
1.1 bertrand 189: SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
1.8 ! bertrand 190: *
! 191: * -- Reference BLAS level3 routine (version 3.4.0) --
! 192: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 193: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 194: * November 2011
! 195: *
1.1 bertrand 196: * .. Scalar Arguments ..
1.8 ! bertrand 197: COMPLEX*16 ALPHA,BETA
1.1 bertrand 198: INTEGER K,LDA,LDB,LDC,N
199: CHARACTER TRANS,UPLO
200: * ..
201: * .. Array Arguments ..
1.8 ! bertrand 202: COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
1.1 bertrand 203: * ..
204: *
205: * =====================================================================
206: *
207: * .. External Functions ..
208: LOGICAL LSAME
209: EXTERNAL LSAME
210: * ..
211: * .. External Subroutines ..
212: EXTERNAL XERBLA
213: * ..
214: * .. Intrinsic Functions ..
215: INTRINSIC MAX
216: * ..
217: * .. Local Scalars ..
1.8 ! bertrand 218: COMPLEX*16 TEMP1,TEMP2
1.1 bertrand 219: INTEGER I,INFO,J,L,NROWA
220: LOGICAL UPPER
221: * ..
222: * .. Parameters ..
1.8 ! bertrand 223: COMPLEX*16 ONE
1.1 bertrand 224: PARAMETER (ONE= (1.0D+0,0.0D+0))
1.8 ! bertrand 225: COMPLEX*16 ZERO
1.1 bertrand 226: PARAMETER (ZERO= (0.0D+0,0.0D+0))
227: * ..
228: *
229: * Test the input parameters.
230: *
231: IF (LSAME(TRANS,'N')) THEN
232: NROWA = N
233: ELSE
234: NROWA = K
235: END IF
236: UPPER = LSAME(UPLO,'U')
237: *
238: INFO = 0
239: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
240: INFO = 1
241: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
242: + (.NOT.LSAME(TRANS,'T'))) THEN
243: INFO = 2
244: ELSE IF (N.LT.0) THEN
245: INFO = 3
246: ELSE IF (K.LT.0) THEN
247: INFO = 4
248: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
249: INFO = 7
250: ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
251: INFO = 9
252: ELSE IF (LDC.LT.MAX(1,N)) THEN
253: INFO = 12
254: END IF
255: IF (INFO.NE.0) THEN
256: CALL XERBLA('ZSYR2K',INFO)
257: RETURN
258: END IF
259: *
260: * Quick return if possible.
261: *
262: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
263: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
264: *
265: * And when alpha.eq.zero.
266: *
267: IF (ALPHA.EQ.ZERO) THEN
268: IF (UPPER) THEN
269: IF (BETA.EQ.ZERO) THEN
270: DO 20 J = 1,N
271: DO 10 I = 1,J
272: C(I,J) = ZERO
273: 10 CONTINUE
274: 20 CONTINUE
275: ELSE
276: DO 40 J = 1,N
277: DO 30 I = 1,J
278: C(I,J) = BETA*C(I,J)
279: 30 CONTINUE
280: 40 CONTINUE
281: END IF
282: ELSE
283: IF (BETA.EQ.ZERO) THEN
284: DO 60 J = 1,N
285: DO 50 I = J,N
286: C(I,J) = ZERO
287: 50 CONTINUE
288: 60 CONTINUE
289: ELSE
290: DO 80 J = 1,N
291: DO 70 I = J,N
292: C(I,J) = BETA*C(I,J)
293: 70 CONTINUE
294: 80 CONTINUE
295: END IF
296: END IF
297: RETURN
298: END IF
299: *
300: * Start the operations.
301: *
302: IF (LSAME(TRANS,'N')) THEN
303: *
1.7 bertrand 304: * Form C := alpha*A*B**T + alpha*B*A**T + C.
1.1 bertrand 305: *
306: IF (UPPER) THEN
307: DO 130 J = 1,N
308: IF (BETA.EQ.ZERO) THEN
309: DO 90 I = 1,J
310: C(I,J) = ZERO
311: 90 CONTINUE
312: ELSE IF (BETA.NE.ONE) THEN
313: DO 100 I = 1,J
314: C(I,J) = BETA*C(I,J)
315: 100 CONTINUE
316: END IF
317: DO 120 L = 1,K
318: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
319: TEMP1 = ALPHA*B(J,L)
320: TEMP2 = ALPHA*A(J,L)
321: DO 110 I = 1,J
322: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
323: + B(I,L)*TEMP2
324: 110 CONTINUE
325: END IF
326: 120 CONTINUE
327: 130 CONTINUE
328: ELSE
329: DO 180 J = 1,N
330: IF (BETA.EQ.ZERO) THEN
331: DO 140 I = J,N
332: C(I,J) = ZERO
333: 140 CONTINUE
334: ELSE IF (BETA.NE.ONE) THEN
335: DO 150 I = J,N
336: C(I,J) = BETA*C(I,J)
337: 150 CONTINUE
338: END IF
339: DO 170 L = 1,K
340: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
341: TEMP1 = ALPHA*B(J,L)
342: TEMP2 = ALPHA*A(J,L)
343: DO 160 I = J,N
344: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
345: + B(I,L)*TEMP2
346: 160 CONTINUE
347: END IF
348: 170 CONTINUE
349: 180 CONTINUE
350: END IF
351: ELSE
352: *
1.7 bertrand 353: * Form C := alpha*A**T*B + alpha*B**T*A + C.
1.1 bertrand 354: *
355: IF (UPPER) THEN
356: DO 210 J = 1,N
357: DO 200 I = 1,J
358: TEMP1 = ZERO
359: TEMP2 = ZERO
360: DO 190 L = 1,K
361: TEMP1 = TEMP1 + A(L,I)*B(L,J)
362: TEMP2 = TEMP2 + B(L,I)*A(L,J)
363: 190 CONTINUE
364: IF (BETA.EQ.ZERO) THEN
365: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
366: ELSE
367: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
368: + ALPHA*TEMP2
369: END IF
370: 200 CONTINUE
371: 210 CONTINUE
372: ELSE
373: DO 240 J = 1,N
374: DO 230 I = J,N
375: TEMP1 = ZERO
376: TEMP2 = ZERO
377: DO 220 L = 1,K
378: TEMP1 = TEMP1 + A(L,I)*B(L,J)
379: TEMP2 = TEMP2 + B(L,I)*A(L,J)
380: 220 CONTINUE
381: IF (BETA.EQ.ZERO) THEN
382: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
383: ELSE
384: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
385: + ALPHA*TEMP2
386: END IF
387: 230 CONTINUE
388: 240 CONTINUE
389: END IF
390: END IF
391: *
392: RETURN
393: *
394: * End of ZSYR2K.
395: *
396: END
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