Annotation of rpl/lapack/blas/zsyr2k.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE COMPLEX ALPHA,BETA
! 4: INTEGER K,LDA,LDB,LDC,N
! 5: CHARACTER TRANS,UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * ZSYR2K performs one of the symmetric rank 2k operations
! 15: *
! 16: * C := alpha*A*B' + alpha*B*A' + beta*C,
! 17: *
! 18: * or
! 19: *
! 20: * C := alpha*A'*B + alpha*B'*A + beta*C,
! 21: *
! 22: * where alpha and beta are scalars, C is an n by n symmetric matrix
! 23: * and A and B are n by k matrices in the first case and k by n
! 24: * matrices in the second case.
! 25: *
! 26: * Arguments
! 27: * ==========
! 28: *
! 29: * UPLO - CHARACTER*1.
! 30: * On entry, UPLO specifies whether the upper or lower
! 31: * triangular part of the array C is to be referenced as
! 32: * follows:
! 33: *
! 34: * UPLO = 'U' or 'u' Only the upper triangular part of C
! 35: * is to be referenced.
! 36: *
! 37: * UPLO = 'L' or 'l' Only the lower triangular part of C
! 38: * is to be referenced.
! 39: *
! 40: * Unchanged on exit.
! 41: *
! 42: * TRANS - CHARACTER*1.
! 43: * On entry, TRANS specifies the operation to be performed as
! 44: * follows:
! 45: *
! 46: * TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
! 47: * beta*C.
! 48: *
! 49: * TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
! 50: * beta*C.
! 51: *
! 52: * Unchanged on exit.
! 53: *
! 54: * N - INTEGER.
! 55: * On entry, N specifies the order of the matrix C. N must be
! 56: * at least zero.
! 57: * Unchanged on exit.
! 58: *
! 59: * K - INTEGER.
! 60: * On entry with TRANS = 'N' or 'n', K specifies the number
! 61: * of columns of the matrices A and B, and on entry with
! 62: * TRANS = 'T' or 't', K specifies the number of rows of the
! 63: * matrices A and B. K must be at least zero.
! 64: * Unchanged on exit.
! 65: *
! 66: * ALPHA - COMPLEX*16 .
! 67: * On entry, ALPHA specifies the scalar alpha.
! 68: * Unchanged on exit.
! 69: *
! 70: * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
! 71: * k when TRANS = 'N' or 'n', and is n otherwise.
! 72: * Before entry with TRANS = 'N' or 'n', the leading n by k
! 73: * part of the array A must contain the matrix A, otherwise
! 74: * the leading k by n part of the array A must contain the
! 75: * matrix A.
! 76: * Unchanged on exit.
! 77: *
! 78: * LDA - INTEGER.
! 79: * On entry, LDA specifies the first dimension of A as declared
! 80: * in the calling (sub) program. When TRANS = 'N' or 'n'
! 81: * then LDA must be at least max( 1, n ), otherwise LDA must
! 82: * be at least max( 1, k ).
! 83: * Unchanged on exit.
! 84: *
! 85: * B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
! 86: * k when TRANS = 'N' or 'n', and is n otherwise.
! 87: * Before entry with TRANS = 'N' or 'n', the leading n by k
! 88: * part of the array B must contain the matrix B, otherwise
! 89: * the leading k by n part of the array B must contain the
! 90: * matrix B.
! 91: * Unchanged on exit.
! 92: *
! 93: * LDB - INTEGER.
! 94: * On entry, LDB specifies the first dimension of B as declared
! 95: * in the calling (sub) program. When TRANS = 'N' or 'n'
! 96: * then LDB must be at least max( 1, n ), otherwise LDB must
! 97: * be at least max( 1, k ).
! 98: * Unchanged on exit.
! 99: *
! 100: * BETA - COMPLEX*16 .
! 101: * On entry, BETA specifies the scalar beta.
! 102: * Unchanged on exit.
! 103: *
! 104: * C - COMPLEX*16 array of DIMENSION ( LDC, n ).
! 105: * Before entry with UPLO = 'U' or 'u', the leading n by n
! 106: * upper triangular part of the array C must contain the upper
! 107: * triangular part of the symmetric matrix and the strictly
! 108: * lower triangular part of C is not referenced. On exit, the
! 109: * upper triangular part of the array C is overwritten by the
! 110: * upper triangular part of the updated matrix.
! 111: * Before entry with UPLO = 'L' or 'l', the leading n by n
! 112: * lower triangular part of the array C must contain the lower
! 113: * triangular part of the symmetric matrix and the strictly
! 114: * upper triangular part of C is not referenced. On exit, the
! 115: * lower triangular part of the array C is overwritten by the
! 116: * lower triangular part of the updated matrix.
! 117: *
! 118: * LDC - INTEGER.
! 119: * On entry, LDC specifies the first dimension of C as declared
! 120: * in the calling (sub) program. LDC must be at least
! 121: * max( 1, n ).
! 122: * Unchanged on exit.
! 123: *
! 124: * Further Details
! 125: * ===============
! 126: *
! 127: * Level 3 Blas routine.
! 128: *
! 129: * -- Written on 8-February-1989.
! 130: * Jack Dongarra, Argonne National Laboratory.
! 131: * Iain Duff, AERE Harwell.
! 132: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 133: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 134: *
! 135: * =====================================================================
! 136: *
! 137: * .. External Functions ..
! 138: LOGICAL LSAME
! 139: EXTERNAL LSAME
! 140: * ..
! 141: * .. External Subroutines ..
! 142: EXTERNAL XERBLA
! 143: * ..
! 144: * .. Intrinsic Functions ..
! 145: INTRINSIC MAX
! 146: * ..
! 147: * .. Local Scalars ..
! 148: DOUBLE COMPLEX TEMP1,TEMP2
! 149: INTEGER I,INFO,J,L,NROWA
! 150: LOGICAL UPPER
! 151: * ..
! 152: * .. Parameters ..
! 153: DOUBLE COMPLEX ONE
! 154: PARAMETER (ONE= (1.0D+0,0.0D+0))
! 155: DOUBLE COMPLEX ZERO
! 156: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 157: * ..
! 158: *
! 159: * Test the input parameters.
! 160: *
! 161: IF (LSAME(TRANS,'N')) THEN
! 162: NROWA = N
! 163: ELSE
! 164: NROWA = K
! 165: END IF
! 166: UPPER = LSAME(UPLO,'U')
! 167: *
! 168: INFO = 0
! 169: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 170: INFO = 1
! 171: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
! 172: + (.NOT.LSAME(TRANS,'T'))) THEN
! 173: INFO = 2
! 174: ELSE IF (N.LT.0) THEN
! 175: INFO = 3
! 176: ELSE IF (K.LT.0) THEN
! 177: INFO = 4
! 178: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 179: INFO = 7
! 180: ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
! 181: INFO = 9
! 182: ELSE IF (LDC.LT.MAX(1,N)) THEN
! 183: INFO = 12
! 184: END IF
! 185: IF (INFO.NE.0) THEN
! 186: CALL XERBLA('ZSYR2K',INFO)
! 187: RETURN
! 188: END IF
! 189: *
! 190: * Quick return if possible.
! 191: *
! 192: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
! 193: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
! 194: *
! 195: * And when alpha.eq.zero.
! 196: *
! 197: IF (ALPHA.EQ.ZERO) THEN
! 198: IF (UPPER) THEN
! 199: IF (BETA.EQ.ZERO) THEN
! 200: DO 20 J = 1,N
! 201: DO 10 I = 1,J
! 202: C(I,J) = ZERO
! 203: 10 CONTINUE
! 204: 20 CONTINUE
! 205: ELSE
! 206: DO 40 J = 1,N
! 207: DO 30 I = 1,J
! 208: C(I,J) = BETA*C(I,J)
! 209: 30 CONTINUE
! 210: 40 CONTINUE
! 211: END IF
! 212: ELSE
! 213: IF (BETA.EQ.ZERO) THEN
! 214: DO 60 J = 1,N
! 215: DO 50 I = J,N
! 216: C(I,J) = ZERO
! 217: 50 CONTINUE
! 218: 60 CONTINUE
! 219: ELSE
! 220: DO 80 J = 1,N
! 221: DO 70 I = J,N
! 222: C(I,J) = BETA*C(I,J)
! 223: 70 CONTINUE
! 224: 80 CONTINUE
! 225: END IF
! 226: END IF
! 227: RETURN
! 228: END IF
! 229: *
! 230: * Start the operations.
! 231: *
! 232: IF (LSAME(TRANS,'N')) THEN
! 233: *
! 234: * Form C := alpha*A*B' + alpha*B*A' + C.
! 235: *
! 236: IF (UPPER) THEN
! 237: DO 130 J = 1,N
! 238: IF (BETA.EQ.ZERO) THEN
! 239: DO 90 I = 1,J
! 240: C(I,J) = ZERO
! 241: 90 CONTINUE
! 242: ELSE IF (BETA.NE.ONE) THEN
! 243: DO 100 I = 1,J
! 244: C(I,J) = BETA*C(I,J)
! 245: 100 CONTINUE
! 246: END IF
! 247: DO 120 L = 1,K
! 248: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 249: TEMP1 = ALPHA*B(J,L)
! 250: TEMP2 = ALPHA*A(J,L)
! 251: DO 110 I = 1,J
! 252: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 253: + B(I,L)*TEMP2
! 254: 110 CONTINUE
! 255: END IF
! 256: 120 CONTINUE
! 257: 130 CONTINUE
! 258: ELSE
! 259: DO 180 J = 1,N
! 260: IF (BETA.EQ.ZERO) THEN
! 261: DO 140 I = J,N
! 262: C(I,J) = ZERO
! 263: 140 CONTINUE
! 264: ELSE IF (BETA.NE.ONE) THEN
! 265: DO 150 I = J,N
! 266: C(I,J) = BETA*C(I,J)
! 267: 150 CONTINUE
! 268: END IF
! 269: DO 170 L = 1,K
! 270: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 271: TEMP1 = ALPHA*B(J,L)
! 272: TEMP2 = ALPHA*A(J,L)
! 273: DO 160 I = J,N
! 274: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 275: + B(I,L)*TEMP2
! 276: 160 CONTINUE
! 277: END IF
! 278: 170 CONTINUE
! 279: 180 CONTINUE
! 280: END IF
! 281: ELSE
! 282: *
! 283: * Form C := alpha*A'*B + alpha*B'*A + C.
! 284: *
! 285: IF (UPPER) THEN
! 286: DO 210 J = 1,N
! 287: DO 200 I = 1,J
! 288: TEMP1 = ZERO
! 289: TEMP2 = ZERO
! 290: DO 190 L = 1,K
! 291: TEMP1 = TEMP1 + A(L,I)*B(L,J)
! 292: TEMP2 = TEMP2 + B(L,I)*A(L,J)
! 293: 190 CONTINUE
! 294: IF (BETA.EQ.ZERO) THEN
! 295: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
! 296: ELSE
! 297: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 298: + ALPHA*TEMP2
! 299: END IF
! 300: 200 CONTINUE
! 301: 210 CONTINUE
! 302: ELSE
! 303: DO 240 J = 1,N
! 304: DO 230 I = J,N
! 305: TEMP1 = ZERO
! 306: TEMP2 = ZERO
! 307: DO 220 L = 1,K
! 308: TEMP1 = TEMP1 + A(L,I)*B(L,J)
! 309: TEMP2 = TEMP2 + B(L,I)*A(L,J)
! 310: 220 CONTINUE
! 311: IF (BETA.EQ.ZERO) THEN
! 312: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
! 313: ELSE
! 314: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 315: + ALPHA*TEMP2
! 316: END IF
! 317: 230 CONTINUE
! 318: 240 CONTINUE
! 319: END IF
! 320: END IF
! 321: *
! 322: RETURN
! 323: *
! 324: * End of ZSYR2K.
! 325: *
! 326: END
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