Annotation of rpl/lapack/blas/dsyr2k.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE PRECISION ALPHA,BETA
! 4: INTEGER K,LDA,LDB,LDC,N
! 5: CHARACTER TRANS,UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * DSYR2K 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: * TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
! 53: * beta*C.
! 54: *
! 55: * Unchanged on exit.
! 56: *
! 57: * N - INTEGER.
! 58: * On entry, N specifies the order of the matrix C. N must be
! 59: * at least zero.
! 60: * Unchanged on exit.
! 61: *
! 62: * K - INTEGER.
! 63: * On entry with TRANS = 'N' or 'n', K specifies the number
! 64: * of columns of the matrices A and B, and on entry with
! 65: * TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
! 66: * of rows of the matrices A and B. K must be at least zero.
! 67: * Unchanged on exit.
! 68: *
! 69: * ALPHA - DOUBLE PRECISION.
! 70: * On entry, ALPHA specifies the scalar alpha.
! 71: * Unchanged on exit.
! 72: *
! 73: * A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
! 74: * k when TRANS = 'N' or 'n', and is n otherwise.
! 75: * Before entry with TRANS = 'N' or 'n', the leading n by k
! 76: * part of the array A must contain the matrix A, otherwise
! 77: * the leading k by n part of the array A must contain the
! 78: * matrix A.
! 79: * Unchanged on exit.
! 80: *
! 81: * LDA - INTEGER.
! 82: * On entry, LDA specifies the first dimension of A as declared
! 83: * in the calling (sub) program. When TRANS = 'N' or 'n'
! 84: * then LDA must be at least max( 1, n ), otherwise LDA must
! 85: * be at least max( 1, k ).
! 86: * Unchanged on exit.
! 87: *
! 88: * B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
! 89: * k when TRANS = 'N' or 'n', and is n otherwise.
! 90: * Before entry with TRANS = 'N' or 'n', the leading n by k
! 91: * part of the array B must contain the matrix B, otherwise
! 92: * the leading k by n part of the array B must contain the
! 93: * matrix B.
! 94: * Unchanged on exit.
! 95: *
! 96: * LDB - INTEGER.
! 97: * On entry, LDB specifies the first dimension of B as declared
! 98: * in the calling (sub) program. When TRANS = 'N' or 'n'
! 99: * then LDB must be at least max( 1, n ), otherwise LDB must
! 100: * be at least max( 1, k ).
! 101: * Unchanged on exit.
! 102: *
! 103: * BETA - DOUBLE PRECISION.
! 104: * On entry, BETA specifies the scalar beta.
! 105: * Unchanged on exit.
! 106: *
! 107: * C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
! 108: * Before entry with UPLO = 'U' or 'u', the leading n by n
! 109: * upper triangular part of the array C must contain the upper
! 110: * triangular part of the symmetric matrix and the strictly
! 111: * lower triangular part of C is not referenced. On exit, the
! 112: * upper triangular part of the array C is overwritten by the
! 113: * upper triangular part of the updated matrix.
! 114: * Before entry with UPLO = 'L' or 'l', the leading n by n
! 115: * lower triangular part of the array C must contain the lower
! 116: * triangular part of the symmetric matrix and the strictly
! 117: * upper triangular part of C is not referenced. On exit, the
! 118: * lower triangular part of the array C is overwritten by the
! 119: * lower triangular part of the updated matrix.
! 120: *
! 121: * LDC - INTEGER.
! 122: * On entry, LDC specifies the first dimension of C as declared
! 123: * in the calling (sub) program. LDC must be at least
! 124: * max( 1, n ).
! 125: * Unchanged on exit.
! 126: *
! 127: * Further Details
! 128: * ===============
! 129: *
! 130: * Level 3 Blas routine.
! 131: *
! 132: *
! 133: * -- Written on 8-February-1989.
! 134: * Jack Dongarra, Argonne National Laboratory.
! 135: * Iain Duff, AERE Harwell.
! 136: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 137: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 138: *
! 139: * =====================================================================
! 140: *
! 141: * .. External Functions ..
! 142: LOGICAL LSAME
! 143: EXTERNAL LSAME
! 144: * ..
! 145: * .. External Subroutines ..
! 146: EXTERNAL XERBLA
! 147: * ..
! 148: * .. Intrinsic Functions ..
! 149: INTRINSIC MAX
! 150: * ..
! 151: * .. Local Scalars ..
! 152: DOUBLE PRECISION TEMP1,TEMP2
! 153: INTEGER I,INFO,J,L,NROWA
! 154: LOGICAL UPPER
! 155: * ..
! 156: * .. Parameters ..
! 157: DOUBLE PRECISION ONE,ZERO
! 158: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
! 159: * ..
! 160: *
! 161: * Test the input parameters.
! 162: *
! 163: IF (LSAME(TRANS,'N')) THEN
! 164: NROWA = N
! 165: ELSE
! 166: NROWA = K
! 167: END IF
! 168: UPPER = LSAME(UPLO,'U')
! 169: *
! 170: INFO = 0
! 171: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 172: INFO = 1
! 173: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
! 174: + (.NOT.LSAME(TRANS,'T')) .AND.
! 175: + (.NOT.LSAME(TRANS,'C'))) THEN
! 176: INFO = 2
! 177: ELSE IF (N.LT.0) THEN
! 178: INFO = 3
! 179: ELSE IF (K.LT.0) THEN
! 180: INFO = 4
! 181: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 182: INFO = 7
! 183: ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
! 184: INFO = 9
! 185: ELSE IF (LDC.LT.MAX(1,N)) THEN
! 186: INFO = 12
! 187: END IF
! 188: IF (INFO.NE.0) THEN
! 189: CALL XERBLA('DSYR2K',INFO)
! 190: RETURN
! 191: END IF
! 192: *
! 193: * Quick return if possible.
! 194: *
! 195: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
! 196: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
! 197: *
! 198: * And when alpha.eq.zero.
! 199: *
! 200: IF (ALPHA.EQ.ZERO) THEN
! 201: IF (UPPER) THEN
! 202: IF (BETA.EQ.ZERO) THEN
! 203: DO 20 J = 1,N
! 204: DO 10 I = 1,J
! 205: C(I,J) = ZERO
! 206: 10 CONTINUE
! 207: 20 CONTINUE
! 208: ELSE
! 209: DO 40 J = 1,N
! 210: DO 30 I = 1,J
! 211: C(I,J) = BETA*C(I,J)
! 212: 30 CONTINUE
! 213: 40 CONTINUE
! 214: END IF
! 215: ELSE
! 216: IF (BETA.EQ.ZERO) THEN
! 217: DO 60 J = 1,N
! 218: DO 50 I = J,N
! 219: C(I,J) = ZERO
! 220: 50 CONTINUE
! 221: 60 CONTINUE
! 222: ELSE
! 223: DO 80 J = 1,N
! 224: DO 70 I = J,N
! 225: C(I,J) = BETA*C(I,J)
! 226: 70 CONTINUE
! 227: 80 CONTINUE
! 228: END IF
! 229: END IF
! 230: RETURN
! 231: END IF
! 232: *
! 233: * Start the operations.
! 234: *
! 235: IF (LSAME(TRANS,'N')) THEN
! 236: *
! 237: * Form C := alpha*A*B' + alpha*B*A' + C.
! 238: *
! 239: IF (UPPER) THEN
! 240: DO 130 J = 1,N
! 241: IF (BETA.EQ.ZERO) THEN
! 242: DO 90 I = 1,J
! 243: C(I,J) = ZERO
! 244: 90 CONTINUE
! 245: ELSE IF (BETA.NE.ONE) THEN
! 246: DO 100 I = 1,J
! 247: C(I,J) = BETA*C(I,J)
! 248: 100 CONTINUE
! 249: END IF
! 250: DO 120 L = 1,K
! 251: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 252: TEMP1 = ALPHA*B(J,L)
! 253: TEMP2 = ALPHA*A(J,L)
! 254: DO 110 I = 1,J
! 255: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 256: + B(I,L)*TEMP2
! 257: 110 CONTINUE
! 258: END IF
! 259: 120 CONTINUE
! 260: 130 CONTINUE
! 261: ELSE
! 262: DO 180 J = 1,N
! 263: IF (BETA.EQ.ZERO) THEN
! 264: DO 140 I = J,N
! 265: C(I,J) = ZERO
! 266: 140 CONTINUE
! 267: ELSE IF (BETA.NE.ONE) THEN
! 268: DO 150 I = J,N
! 269: C(I,J) = BETA*C(I,J)
! 270: 150 CONTINUE
! 271: END IF
! 272: DO 170 L = 1,K
! 273: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 274: TEMP1 = ALPHA*B(J,L)
! 275: TEMP2 = ALPHA*A(J,L)
! 276: DO 160 I = J,N
! 277: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 278: + B(I,L)*TEMP2
! 279: 160 CONTINUE
! 280: END IF
! 281: 170 CONTINUE
! 282: 180 CONTINUE
! 283: END IF
! 284: ELSE
! 285: *
! 286: * Form C := alpha*A'*B + alpha*B'*A + C.
! 287: *
! 288: IF (UPPER) THEN
! 289: DO 210 J = 1,N
! 290: DO 200 I = 1,J
! 291: TEMP1 = ZERO
! 292: TEMP2 = ZERO
! 293: DO 190 L = 1,K
! 294: TEMP1 = TEMP1 + A(L,I)*B(L,J)
! 295: TEMP2 = TEMP2 + B(L,I)*A(L,J)
! 296: 190 CONTINUE
! 297: IF (BETA.EQ.ZERO) THEN
! 298: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
! 299: ELSE
! 300: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 301: + ALPHA*TEMP2
! 302: END IF
! 303: 200 CONTINUE
! 304: 210 CONTINUE
! 305: ELSE
! 306: DO 240 J = 1,N
! 307: DO 230 I = J,N
! 308: TEMP1 = ZERO
! 309: TEMP2 = ZERO
! 310: DO 220 L = 1,K
! 311: TEMP1 = TEMP1 + A(L,I)*B(L,J)
! 312: TEMP2 = TEMP2 + B(L,I)*A(L,J)
! 313: 220 CONTINUE
! 314: IF (BETA.EQ.ZERO) THEN
! 315: C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
! 316: ELSE
! 317: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 318: + ALPHA*TEMP2
! 319: END IF
! 320: 230 CONTINUE
! 321: 240 CONTINUE
! 322: END IF
! 323: END IF
! 324: *
! 325: RETURN
! 326: *
! 327: * End of DSYR2K.
! 328: *
! 329: END
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