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