Annotation of rpl/lapack/blas/zher2k.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE COMPLEX ALPHA
! 4: DOUBLE PRECISION BETA
! 5: INTEGER K,LDA,LDB,LDC,N
! 6: CHARACTER TRANS,UPLO
! 7: * ..
! 8: * .. Array Arguments ..
! 9: DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
! 10: * ..
! 11: *
! 12: * Purpose
! 13: * =======
! 14: *
! 15: * ZHER2K performs one of the hermitian rank 2k operations
! 16: *
! 17: * C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
! 18: *
! 19: * or
! 20: *
! 21: * C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
! 22: *
! 23: * where alpha and beta are scalars with beta real, C is an n by n
! 24: * hermitian matrix and A and B are n by k matrices in the first case
! 25: * and k by n matrices in the second case.
! 26: *
! 27: * Arguments
! 28: * ==========
! 29: *
! 30: * UPLO - CHARACTER*1.
! 31: * On entry, UPLO specifies whether the upper or lower
! 32: * triangular part of the array C is to be referenced as
! 33: * follows:
! 34: *
! 35: * UPLO = 'U' or 'u' Only the upper triangular part of C
! 36: * is to be referenced.
! 37: *
! 38: * UPLO = 'L' or 'l' Only the lower triangular part of C
! 39: * is to be referenced.
! 40: *
! 41: * Unchanged on exit.
! 42: *
! 43: * TRANS - CHARACTER*1.
! 44: * On entry, TRANS specifies the operation to be performed as
! 45: * follows:
! 46: *
! 47: * TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
! 48: * conjg( alpha )*B*conjg( A' ) +
! 49: * beta*C.
! 50: *
! 51: * TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
! 52: * conjg( alpha )*conjg( 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 = 'C' or 'c', K specifies the number of rows of the
! 66: * matrices A and B. K must be at least zero.
! 67: * Unchanged on exit.
! 68: *
! 69: * ALPHA - COMPLEX*16 .
! 70: * On entry, ALPHA specifies the scalar alpha.
! 71: * Unchanged on exit.
! 72: *
! 73: * A - COMPLEX*16 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 - COMPLEX*16 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 - COMPLEX*16 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 hermitian 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 hermitian 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: * Note that the imaginary parts of the diagonal elements need
! 121: * not be set, they are assumed to be zero, and on exit they
! 122: * are set to zero.
! 123: *
! 124: * LDC - INTEGER.
! 125: * On entry, LDC specifies the first dimension of C as declared
! 126: * in the calling (sub) program. LDC must be at least
! 127: * max( 1, n ).
! 128: * Unchanged on exit.
! 129: *
! 130: * Further Details
! 131: * ===============
! 132: *
! 133: * Level 3 Blas routine.
! 134: *
! 135: * -- Written on 8-February-1989.
! 136: * Jack Dongarra, Argonne National Laboratory.
! 137: * Iain Duff, AERE Harwell.
! 138: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 139: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 140: *
! 141: * -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
! 142: * Ed Anderson, Cray Research Inc.
! 143: *
! 144: * =====================================================================
! 145: *
! 146: * .. External Functions ..
! 147: LOGICAL LSAME
! 148: EXTERNAL LSAME
! 149: * ..
! 150: * .. External Subroutines ..
! 151: EXTERNAL XERBLA
! 152: * ..
! 153: * .. Intrinsic Functions ..
! 154: INTRINSIC DBLE,DCONJG,MAX
! 155: * ..
! 156: * .. Local Scalars ..
! 157: DOUBLE COMPLEX TEMP1,TEMP2
! 158: INTEGER I,INFO,J,L,NROWA
! 159: LOGICAL UPPER
! 160: * ..
! 161: * .. Parameters ..
! 162: DOUBLE PRECISION ONE
! 163: PARAMETER (ONE=1.0D+0)
! 164: DOUBLE COMPLEX ZERO
! 165: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 166: * ..
! 167: *
! 168: * Test the input parameters.
! 169: *
! 170: IF (LSAME(TRANS,'N')) THEN
! 171: NROWA = N
! 172: ELSE
! 173: NROWA = K
! 174: END IF
! 175: UPPER = LSAME(UPLO,'U')
! 176: *
! 177: INFO = 0
! 178: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 179: INFO = 1
! 180: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
! 181: + (.NOT.LSAME(TRANS,'C'))) THEN
! 182: INFO = 2
! 183: ELSE IF (N.LT.0) THEN
! 184: INFO = 3
! 185: ELSE IF (K.LT.0) THEN
! 186: INFO = 4
! 187: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 188: INFO = 7
! 189: ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
! 190: INFO = 9
! 191: ELSE IF (LDC.LT.MAX(1,N)) THEN
! 192: INFO = 12
! 193: END IF
! 194: IF (INFO.NE.0) THEN
! 195: CALL XERBLA('ZHER2K',INFO)
! 196: RETURN
! 197: END IF
! 198: *
! 199: * Quick return if possible.
! 200: *
! 201: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
! 202: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
! 203: *
! 204: * And when alpha.eq.zero.
! 205: *
! 206: IF (ALPHA.EQ.ZERO) THEN
! 207: IF (UPPER) THEN
! 208: IF (BETA.EQ.DBLE(ZERO)) THEN
! 209: DO 20 J = 1,N
! 210: DO 10 I = 1,J
! 211: C(I,J) = ZERO
! 212: 10 CONTINUE
! 213: 20 CONTINUE
! 214: ELSE
! 215: DO 40 J = 1,N
! 216: DO 30 I = 1,J - 1
! 217: C(I,J) = BETA*C(I,J)
! 218: 30 CONTINUE
! 219: C(J,J) = BETA*DBLE(C(J,J))
! 220: 40 CONTINUE
! 221: END IF
! 222: ELSE
! 223: IF (BETA.EQ.DBLE(ZERO)) THEN
! 224: DO 60 J = 1,N
! 225: DO 50 I = J,N
! 226: C(I,J) = ZERO
! 227: 50 CONTINUE
! 228: 60 CONTINUE
! 229: ELSE
! 230: DO 80 J = 1,N
! 231: C(J,J) = BETA*DBLE(C(J,J))
! 232: DO 70 I = J + 1,N
! 233: C(I,J) = BETA*C(I,J)
! 234: 70 CONTINUE
! 235: 80 CONTINUE
! 236: END IF
! 237: END IF
! 238: RETURN
! 239: END IF
! 240: *
! 241: * Start the operations.
! 242: *
! 243: IF (LSAME(TRANS,'N')) THEN
! 244: *
! 245: * Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
! 246: * C.
! 247: *
! 248: IF (UPPER) THEN
! 249: DO 130 J = 1,N
! 250: IF (BETA.EQ.DBLE(ZERO)) THEN
! 251: DO 90 I = 1,J
! 252: C(I,J) = ZERO
! 253: 90 CONTINUE
! 254: ELSE IF (BETA.NE.ONE) THEN
! 255: DO 100 I = 1,J - 1
! 256: C(I,J) = BETA*C(I,J)
! 257: 100 CONTINUE
! 258: C(J,J) = BETA*DBLE(C(J,J))
! 259: ELSE
! 260: C(J,J) = DBLE(C(J,J))
! 261: END IF
! 262: DO 120 L = 1,K
! 263: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 264: TEMP1 = ALPHA*DCONJG(B(J,L))
! 265: TEMP2 = DCONJG(ALPHA*A(J,L))
! 266: DO 110 I = 1,J - 1
! 267: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 268: + B(I,L)*TEMP2
! 269: 110 CONTINUE
! 270: C(J,J) = DBLE(C(J,J)) +
! 271: + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
! 272: END IF
! 273: 120 CONTINUE
! 274: 130 CONTINUE
! 275: ELSE
! 276: DO 180 J = 1,N
! 277: IF (BETA.EQ.DBLE(ZERO)) THEN
! 278: DO 140 I = J,N
! 279: C(I,J) = ZERO
! 280: 140 CONTINUE
! 281: ELSE IF (BETA.NE.ONE) THEN
! 282: DO 150 I = J + 1,N
! 283: C(I,J) = BETA*C(I,J)
! 284: 150 CONTINUE
! 285: C(J,J) = BETA*DBLE(C(J,J))
! 286: ELSE
! 287: C(J,J) = DBLE(C(J,J))
! 288: END IF
! 289: DO 170 L = 1,K
! 290: IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
! 291: TEMP1 = ALPHA*DCONJG(B(J,L))
! 292: TEMP2 = DCONJG(ALPHA*A(J,L))
! 293: DO 160 I = J + 1,N
! 294: C(I,J) = C(I,J) + A(I,L)*TEMP1 +
! 295: + B(I,L)*TEMP2
! 296: 160 CONTINUE
! 297: C(J,J) = DBLE(C(J,J)) +
! 298: + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
! 299: END IF
! 300: 170 CONTINUE
! 301: 180 CONTINUE
! 302: END IF
! 303: ELSE
! 304: *
! 305: * Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
! 306: * C.
! 307: *
! 308: IF (UPPER) THEN
! 309: DO 210 J = 1,N
! 310: DO 200 I = 1,J
! 311: TEMP1 = ZERO
! 312: TEMP2 = ZERO
! 313: DO 190 L = 1,K
! 314: TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
! 315: TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
! 316: 190 CONTINUE
! 317: IF (I.EQ.J) THEN
! 318: IF (BETA.EQ.DBLE(ZERO)) THEN
! 319: C(J,J) = DBLE(ALPHA*TEMP1+
! 320: + DCONJG(ALPHA)*TEMP2)
! 321: ELSE
! 322: C(J,J) = BETA*DBLE(C(J,J)) +
! 323: + DBLE(ALPHA*TEMP1+
! 324: + DCONJG(ALPHA)*TEMP2)
! 325: END IF
! 326: ELSE
! 327: IF (BETA.EQ.DBLE(ZERO)) THEN
! 328: C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
! 329: ELSE
! 330: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 331: + DCONJG(ALPHA)*TEMP2
! 332: END IF
! 333: END IF
! 334: 200 CONTINUE
! 335: 210 CONTINUE
! 336: ELSE
! 337: DO 240 J = 1,N
! 338: DO 230 I = J,N
! 339: TEMP1 = ZERO
! 340: TEMP2 = ZERO
! 341: DO 220 L = 1,K
! 342: TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
! 343: TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
! 344: 220 CONTINUE
! 345: IF (I.EQ.J) THEN
! 346: IF (BETA.EQ.DBLE(ZERO)) THEN
! 347: C(J,J) = DBLE(ALPHA*TEMP1+
! 348: + DCONJG(ALPHA)*TEMP2)
! 349: ELSE
! 350: C(J,J) = BETA*DBLE(C(J,J)) +
! 351: + DBLE(ALPHA*TEMP1+
! 352: + DCONJG(ALPHA)*TEMP2)
! 353: END IF
! 354: ELSE
! 355: IF (BETA.EQ.DBLE(ZERO)) THEN
! 356: C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
! 357: ELSE
! 358: C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
! 359: + DCONJG(ALPHA)*TEMP2
! 360: END IF
! 361: END IF
! 362: 230 CONTINUE
! 363: 240 CONTINUE
! 364: END IF
! 365: END IF
! 366: *
! 367: RETURN
! 368: *
! 369: * End of ZHER2K.
! 370: *
! 371: END
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