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