Annotation of rpl/lapack/blas/zher2k.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZHER2K
! 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 ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * COMPLEX*16 ALPHA
! 15: * DOUBLE PRECISION BETA
! 16: * INTEGER K,LDA,LDB,LDC,N
! 17: * CHARACTER TRANS,UPLO
! 18: * ..
! 19: * .. Array Arguments ..
! 20: * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
! 21: * ..
! 22: *
! 23: *
! 24: *> \par Purpose:
! 25: * =============
! 26: *>
! 27: *> \verbatim
! 28: *>
! 29: *> ZHER2K performs one of the hermitian rank 2k operations
! 30: *>
! 31: *> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
! 32: *>
! 33: *> or
! 34: *>
! 35: *> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
! 36: *>
! 37: *> where alpha and beta are scalars with beta real, C is an n by n
! 38: *> hermitian matrix and A and B are n by k matrices in the first case
! 39: *> and k by n matrices in the second case.
! 40: *> \endverbatim
! 41: *
! 42: * Arguments:
! 43: * ==========
! 44: *
! 45: *> \param[in] UPLO
! 46: *> \verbatim
! 47: *> UPLO is CHARACTER*1
! 48: *> On entry, UPLO specifies whether the upper or lower
! 49: *> triangular part of the array C is to be referenced as
! 50: *> follows:
! 51: *>
! 52: *> UPLO = 'U' or 'u' Only the upper triangular part of C
! 53: *> is to be referenced.
! 54: *>
! 55: *> UPLO = 'L' or 'l' Only the lower triangular part of C
! 56: *> is to be referenced.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] TRANS
! 60: *> \verbatim
! 61: *> TRANS is CHARACTER*1
! 62: *> On entry, TRANS specifies the operation to be performed as
! 63: *> follows:
! 64: *>
! 65: *> TRANS = 'N' or 'n' C := alpha*A*B**H +
! 66: *> conjg( alpha )*B*A**H +
! 67: *> beta*C.
! 68: *>
! 69: *> TRANS = 'C' or 'c' C := alpha*A**H*B +
! 70: *> conjg( alpha )*B**H*A +
! 71: *> beta*C.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] N
! 75: *> \verbatim
! 76: *> N is INTEGER
! 77: *> On entry, N specifies the order of the matrix C. N must be
! 78: *> at least zero.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] K
! 82: *> \verbatim
! 83: *> K is INTEGER
! 84: *> On entry with TRANS = 'N' or 'n', K specifies the number
! 85: *> of columns of the matrices A and B, and on entry with
! 86: *> TRANS = 'C' or 'c', K specifies the number of rows of the
! 87: *> matrices A and B. K must be at least zero.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] ALPHA
! 91: *> \verbatim
! 92: *> ALPHA is COMPLEX*16 .
! 93: *> On entry, ALPHA specifies the scalar alpha.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] A
! 97: *> \verbatim
! 98: *> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
! 99: *> k when TRANS = 'N' or 'n', and is n otherwise.
! 100: *> Before entry with TRANS = 'N' or 'n', the leading n by k
! 101: *> part of the array A must contain the matrix A, otherwise
! 102: *> the leading k by n part of the array A must contain the
! 103: *> matrix A.
! 104: *> \endverbatim
! 105: *>
! 106: *> \param[in] LDA
! 107: *> \verbatim
! 108: *> LDA is INTEGER
! 109: *> On entry, LDA specifies the first dimension of A as declared
! 110: *> in the calling (sub) program. When TRANS = 'N' or 'n'
! 111: *> then LDA must be at least max( 1, n ), otherwise LDA must
! 112: *> be at least max( 1, k ).
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[in] B
! 116: *> \verbatim
! 117: *> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
! 118: *> k when TRANS = 'N' or 'n', and is n otherwise.
! 119: *> Before entry with TRANS = 'N' or 'n', the leading n by k
! 120: *> part of the array B must contain the matrix B, otherwise
! 121: *> the leading k by n part of the array B must contain the
! 122: *> matrix B.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in] LDB
! 126: *> \verbatim
! 127: *> LDB is INTEGER
! 128: *> On entry, LDB specifies the first dimension of B as declared
! 129: *> in the calling (sub) program. When TRANS = 'N' or 'n'
! 130: *> then LDB must be at least max( 1, n ), otherwise LDB must
! 131: *> be at least max( 1, k ).
! 132: *> Unchanged on exit.
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[in] BETA
! 136: *> \verbatim
! 137: *> BETA is DOUBLE PRECISION .
! 138: *> On entry, BETA specifies the scalar beta.
! 139: *> \endverbatim
! 140: *>
! 141: *> \param[in,out] C
! 142: *> \verbatim
! 143: *> C is COMPLEX*16 array of DIMENSION ( LDC, n ).
! 144: *> Before entry with UPLO = 'U' or 'u', the leading n by n
! 145: *> upper triangular part of the array C must contain the upper
! 146: *> triangular part of the hermitian matrix and the strictly
! 147: *> lower triangular part of C is not referenced. On exit, the
! 148: *> upper triangular part of the array C is overwritten by the
! 149: *> upper triangular part of the updated matrix.
! 150: *> Before entry with UPLO = 'L' or 'l', the leading n by n
! 151: *> lower triangular part of the array C must contain the lower
! 152: *> triangular part of the hermitian matrix and the strictly
! 153: *> upper triangular part of C is not referenced. On exit, the
! 154: *> lower triangular part of the array C is overwritten by the
! 155: *> lower triangular part of the updated matrix.
! 156: *> Note that the imaginary parts of the diagonal elements need
! 157: *> not be set, they are assumed to be zero, and on exit they
! 158: *> are set to zero.
! 159: *> \endverbatim
! 160: *>
! 161: *> \param[in] LDC
! 162: *> \verbatim
! 163: *> LDC is INTEGER
! 164: *> On entry, LDC specifies the first dimension of C as declared
! 165: *> in the calling (sub) program. LDC must be at least
! 166: *> max( 1, n ).
! 167: *> \endverbatim
! 168: *
! 169: * Authors:
! 170: * ========
! 171: *
! 172: *> \author Univ. of Tennessee
! 173: *> \author Univ. of California Berkeley
! 174: *> \author Univ. of Colorado Denver
! 175: *> \author NAG Ltd.
! 176: *
! 177: *> \date November 2011
! 178: *
! 179: *> \ingroup complex16_blas_level3
! 180: *
! 181: *> \par Further Details:
! 182: * =====================
! 183: *>
! 184: *> \verbatim
! 185: *>
! 186: *> Level 3 Blas routine.
! 187: *>
! 188: *> -- Written on 8-February-1989.
! 189: *> Jack Dongarra, Argonne National Laboratory.
! 190: *> Iain Duff, AERE Harwell.
! 191: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 192: *> Sven Hammarling, Numerical Algorithms Group Ltd.
! 193: *>
! 194: *> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
! 195: *> Ed Anderson, Cray Research Inc.
! 196: *> \endverbatim
! 197: *>
! 198: * =====================================================================
1.1 bertrand 199: SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
1.8 ! bertrand 200: *
! 201: * -- Reference BLAS level3 routine (version 3.4.0) --
! 202: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 203: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 204: * November 2011
! 205: *
1.1 bertrand 206: * .. Scalar Arguments ..
1.8 ! bertrand 207: COMPLEX*16 ALPHA
1.1 bertrand 208: DOUBLE PRECISION BETA
209: INTEGER K,LDA,LDB,LDC,N
210: CHARACTER TRANS,UPLO
211: * ..
212: * .. Array Arguments ..
1.8 ! bertrand 213: COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
1.1 bertrand 214: * ..
215: *
216: * =====================================================================
217: *
218: * .. External Functions ..
219: LOGICAL LSAME
220: EXTERNAL LSAME
221: * ..
222: * .. External Subroutines ..
223: EXTERNAL XERBLA
224: * ..
225: * .. Intrinsic Functions ..
226: INTRINSIC DBLE,DCONJG,MAX
227: * ..
228: * .. Local Scalars ..
1.8 ! bertrand 229: COMPLEX*16 TEMP1,TEMP2
1.1 bertrand 230: INTEGER I,INFO,J,L,NROWA
231: LOGICAL UPPER
232: * ..
233: * .. Parameters ..
234: DOUBLE PRECISION ONE
235: PARAMETER (ONE=1.0D+0)
1.8 ! bertrand 236: COMPLEX*16 ZERO
1.1 bertrand 237: PARAMETER (ZERO= (0.0D+0,0.0D+0))
238: * ..
239: *
240: * Test the input parameters.
241: *
242: IF (LSAME(TRANS,'N')) THEN
243: NROWA = N
244: ELSE
245: NROWA = K
246: END IF
247: UPPER = LSAME(UPLO,'U')
248: *
249: INFO = 0
250: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
251: INFO = 1
252: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
253: + (.NOT.LSAME(TRANS,'C'))) THEN
254: INFO = 2
255: ELSE IF (N.LT.0) THEN
256: INFO = 3
257: ELSE IF (K.LT.0) THEN
258: INFO = 4
259: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
260: INFO = 7
261: ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
262: INFO = 9
263: ELSE IF (LDC.LT.MAX(1,N)) THEN
264: INFO = 12
265: END IF
266: IF (INFO.NE.0) THEN
267: CALL XERBLA('ZHER2K',INFO)
268: RETURN
269: END IF
270: *
271: * Quick return if possible.
272: *
273: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
274: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
275: *
276: * And when alpha.eq.zero.
277: *
278: IF (ALPHA.EQ.ZERO) THEN
279: IF (UPPER) THEN
280: IF (BETA.EQ.DBLE(ZERO)) THEN
281: DO 20 J = 1,N
282: DO 10 I = 1,J
283: C(I,J) = ZERO
284: 10 CONTINUE
285: 20 CONTINUE
286: ELSE
287: DO 40 J = 1,N
288: DO 30 I = 1,J - 1
289: C(I,J) = BETA*C(I,J)
290: 30 CONTINUE
291: C(J,J) = BETA*DBLE(C(J,J))
292: 40 CONTINUE
293: END IF
294: ELSE
295: IF (BETA.EQ.DBLE(ZERO)) THEN
296: DO 60 J = 1,N
297: DO 50 I = J,N
298: C(I,J) = ZERO
299: 50 CONTINUE
300: 60 CONTINUE
301: ELSE
302: DO 80 J = 1,N
303: C(J,J) = BETA*DBLE(C(J,J))
304: DO 70 I = J + 1,N
305: C(I,J) = BETA*C(I,J)
306: 70 CONTINUE
307: 80 CONTINUE
308: END IF
309: END IF
310: RETURN
311: END IF
312: *
313: * Start the operations.
314: *
315: IF (LSAME(TRANS,'N')) THEN
316: *
1.7 bertrand 317: * Form C := alpha*A*B**H + conjg( alpha )*B*A**H +
1.1 bertrand 318: * C.
319: *
320: IF (UPPER) THEN
321: DO 130 J = 1,N
322: IF (BETA.EQ.DBLE(ZERO)) THEN
323: DO 90 I = 1,J
324: C(I,J) = ZERO
325: 90 CONTINUE
326: ELSE IF (BETA.NE.ONE) THEN
327: DO 100 I = 1,J - 1
328: C(I,J) = BETA*C(I,J)
329: 100 CONTINUE
330: C(J,J) = BETA*DBLE(C(J,J))
331: ELSE
332: C(J,J) = DBLE(C(J,J))
333: END IF
334: DO 120 L = 1,K
335: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
336: TEMP1 = ALPHA*DCONJG(B(J,L))
337: TEMP2 = DCONJG(ALPHA*A(J,L))
338: DO 110 I = 1,J - 1
339: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
340: + B(I,L)*TEMP2
341: 110 CONTINUE
342: C(J,J) = DBLE(C(J,J)) +
343: + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
344: END IF
345: 120 CONTINUE
346: 130 CONTINUE
347: ELSE
348: DO 180 J = 1,N
349: IF (BETA.EQ.DBLE(ZERO)) THEN
350: DO 140 I = J,N
351: C(I,J) = ZERO
352: 140 CONTINUE
353: ELSE IF (BETA.NE.ONE) THEN
354: DO 150 I = J + 1,N
355: C(I,J) = BETA*C(I,J)
356: 150 CONTINUE
357: C(J,J) = BETA*DBLE(C(J,J))
358: ELSE
359: C(J,J) = DBLE(C(J,J))
360: END IF
361: DO 170 L = 1,K
362: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
363: TEMP1 = ALPHA*DCONJG(B(J,L))
364: TEMP2 = DCONJG(ALPHA*A(J,L))
365: DO 160 I = J + 1,N
366: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
367: + B(I,L)*TEMP2
368: 160 CONTINUE
369: C(J,J) = DBLE(C(J,J)) +
370: + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
371: END IF
372: 170 CONTINUE
373: 180 CONTINUE
374: END IF
375: ELSE
376: *
1.7 bertrand 377: * Form C := alpha*A**H*B + conjg( alpha )*B**H*A +
1.1 bertrand 378: * C.
379: *
380: IF (UPPER) THEN
381: DO 210 J = 1,N
382: DO 200 I = 1,J
383: TEMP1 = ZERO
384: TEMP2 = ZERO
385: DO 190 L = 1,K
386: TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
387: TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
388: 190 CONTINUE
389: IF (I.EQ.J) THEN
390: IF (BETA.EQ.DBLE(ZERO)) THEN
391: C(J,J) = DBLE(ALPHA*TEMP1+
392: + DCONJG(ALPHA)*TEMP2)
393: ELSE
394: C(J,J) = BETA*DBLE(C(J,J)) +
395: + DBLE(ALPHA*TEMP1+
396: + DCONJG(ALPHA)*TEMP2)
397: END IF
398: ELSE
399: IF (BETA.EQ.DBLE(ZERO)) THEN
400: C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
401: ELSE
402: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
403: + DCONJG(ALPHA)*TEMP2
404: END IF
405: END IF
406: 200 CONTINUE
407: 210 CONTINUE
408: ELSE
409: DO 240 J = 1,N
410: DO 230 I = J,N
411: TEMP1 = ZERO
412: TEMP2 = ZERO
413: DO 220 L = 1,K
414: TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
415: TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
416: 220 CONTINUE
417: IF (I.EQ.J) THEN
418: IF (BETA.EQ.DBLE(ZERO)) THEN
419: C(J,J) = DBLE(ALPHA*TEMP1+
420: + DCONJG(ALPHA)*TEMP2)
421: ELSE
422: C(J,J) = BETA*DBLE(C(J,J)) +
423: + DBLE(ALPHA*TEMP1+
424: + DCONJG(ALPHA)*TEMP2)
425: END IF
426: ELSE
427: IF (BETA.EQ.DBLE(ZERO)) THEN
428: C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
429: ELSE
430: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
431: + DCONJG(ALPHA)*TEMP2
432: END IF
433: END IF
434: 230 CONTINUE
435: 240 CONTINUE
436: END IF
437: END IF
438: *
439: RETURN
440: *
441: * End of ZHER2K.
442: *
443: END
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