Annotation of rpl/lapack/blas/zherk.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE PRECISION ALPHA,BETA
! 4: INTEGER K,LDA,LDC,N
! 5: CHARACTER TRANS,UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE COMPLEX A(LDA,*),C(LDC,*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * ZHERK performs one of the hermitian rank k operations
! 15: *
! 16: * C := alpha*A*conjg( A' ) + beta*C,
! 17: *
! 18: * or
! 19: *
! 20: * C := alpha*conjg( A' )*A + beta*C,
! 21: *
! 22: * where alpha and beta are real scalars, C is an n by n hermitian
! 23: * matrix and A is an n by k matrix in the first case and a k by n
! 24: * matrix 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*conjg( A' ) + beta*C.
! 47: *
! 48: * TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
! 49: *
! 50: * Unchanged on exit.
! 51: *
! 52: * N - INTEGER.
! 53: * On entry, N specifies the order of the matrix C. N must be
! 54: * at least zero.
! 55: * Unchanged on exit.
! 56: *
! 57: * K - INTEGER.
! 58: * On entry with TRANS = 'N' or 'n', K specifies the number
! 59: * of columns of the matrix A, and on entry with
! 60: * TRANS = 'C' or 'c', K specifies the number of rows of the
! 61: * matrix A. K must be at least zero.
! 62: * Unchanged on exit.
! 63: *
! 64: * ALPHA - DOUBLE PRECISION .
! 65: * On entry, ALPHA specifies the scalar alpha.
! 66: * Unchanged on exit.
! 67: *
! 68: * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
! 69: * k when TRANS = 'N' or 'n', and is n otherwise.
! 70: * Before entry with TRANS = 'N' or 'n', the leading n by k
! 71: * part of the array A must contain the matrix A, otherwise
! 72: * the leading k by n part of the array A must contain the
! 73: * matrix A.
! 74: * Unchanged on exit.
! 75: *
! 76: * LDA - INTEGER.
! 77: * On entry, LDA specifies the first dimension of A as declared
! 78: * in the calling (sub) program. When TRANS = 'N' or 'n'
! 79: * then LDA must be at least max( 1, n ), otherwise LDA must
! 80: * be at least max( 1, k ).
! 81: * Unchanged on exit.
! 82: *
! 83: * BETA - DOUBLE PRECISION.
! 84: * On entry, BETA specifies the scalar beta.
! 85: * Unchanged on exit.
! 86: *
! 87: * C - COMPLEX*16 array of DIMENSION ( LDC, n ).
! 88: * Before entry with UPLO = 'U' or 'u', the leading n by n
! 89: * upper triangular part of the array C must contain the upper
! 90: * triangular part of the hermitian matrix and the strictly
! 91: * lower triangular part of C is not referenced. On exit, the
! 92: * upper triangular part of the array C is overwritten by the
! 93: * upper triangular part of the updated matrix.
! 94: * Before entry with UPLO = 'L' or 'l', the leading n by n
! 95: * lower triangular part of the array C must contain the lower
! 96: * triangular part of the hermitian matrix and the strictly
! 97: * upper triangular part of C is not referenced. On exit, the
! 98: * lower triangular part of the array C is overwritten by the
! 99: * lower triangular part of the updated matrix.
! 100: * Note that the imaginary parts of the diagonal elements need
! 101: * not be set, they are assumed to be zero, and on exit they
! 102: * are set to zero.
! 103: *
! 104: * LDC - INTEGER.
! 105: * On entry, LDC specifies the first dimension of C as declared
! 106: * in the calling (sub) program. LDC must be at least
! 107: * max( 1, n ).
! 108: * Unchanged on exit.
! 109: *
! 110: * Further Details
! 111: * ===============
! 112: *
! 113: * Level 3 Blas routine.
! 114: *
! 115: * -- Written on 8-February-1989.
! 116: * Jack Dongarra, Argonne National Laboratory.
! 117: * Iain Duff, AERE Harwell.
! 118: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 119: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 120: *
! 121: * -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
! 122: * Ed Anderson, Cray Research Inc.
! 123: *
! 124: * =====================================================================
! 125: *
! 126: * .. External Functions ..
! 127: LOGICAL LSAME
! 128: EXTERNAL LSAME
! 129: * ..
! 130: * .. External Subroutines ..
! 131: EXTERNAL XERBLA
! 132: * ..
! 133: * .. Intrinsic Functions ..
! 134: INTRINSIC DBLE,DCMPLX,DCONJG,MAX
! 135: * ..
! 136: * .. Local Scalars ..
! 137: DOUBLE COMPLEX TEMP
! 138: DOUBLE PRECISION RTEMP
! 139: INTEGER I,INFO,J,L,NROWA
! 140: LOGICAL UPPER
! 141: * ..
! 142: * .. Parameters ..
! 143: DOUBLE PRECISION ONE,ZERO
! 144: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
! 145: * ..
! 146: *
! 147: * Test the input parameters.
! 148: *
! 149: IF (LSAME(TRANS,'N')) THEN
! 150: NROWA = N
! 151: ELSE
! 152: NROWA = K
! 153: END IF
! 154: UPPER = LSAME(UPLO,'U')
! 155: *
! 156: INFO = 0
! 157: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 158: INFO = 1
! 159: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
! 160: + (.NOT.LSAME(TRANS,'C'))) THEN
! 161: INFO = 2
! 162: ELSE IF (N.LT.0) THEN
! 163: INFO = 3
! 164: ELSE IF (K.LT.0) THEN
! 165: INFO = 4
! 166: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 167: INFO = 7
! 168: ELSE IF (LDC.LT.MAX(1,N)) THEN
! 169: INFO = 10
! 170: END IF
! 171: IF (INFO.NE.0) THEN
! 172: CALL XERBLA('ZHERK ',INFO)
! 173: RETURN
! 174: END IF
! 175: *
! 176: * Quick return if possible.
! 177: *
! 178: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
! 179: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
! 180: *
! 181: * And when alpha.eq.zero.
! 182: *
! 183: IF (ALPHA.EQ.ZERO) THEN
! 184: IF (UPPER) THEN
! 185: IF (BETA.EQ.ZERO) THEN
! 186: DO 20 J = 1,N
! 187: DO 10 I = 1,J
! 188: C(I,J) = ZERO
! 189: 10 CONTINUE
! 190: 20 CONTINUE
! 191: ELSE
! 192: DO 40 J = 1,N
! 193: DO 30 I = 1,J - 1
! 194: C(I,J) = BETA*C(I,J)
! 195: 30 CONTINUE
! 196: C(J,J) = BETA*DBLE(C(J,J))
! 197: 40 CONTINUE
! 198: END IF
! 199: ELSE
! 200: IF (BETA.EQ.ZERO) THEN
! 201: DO 60 J = 1,N
! 202: DO 50 I = J,N
! 203: C(I,J) = ZERO
! 204: 50 CONTINUE
! 205: 60 CONTINUE
! 206: ELSE
! 207: DO 80 J = 1,N
! 208: C(J,J) = BETA*DBLE(C(J,J))
! 209: DO 70 I = J + 1,N
! 210: C(I,J) = BETA*C(I,J)
! 211: 70 CONTINUE
! 212: 80 CONTINUE
! 213: END IF
! 214: END IF
! 215: RETURN
! 216: END IF
! 217: *
! 218: * Start the operations.
! 219: *
! 220: IF (LSAME(TRANS,'N')) THEN
! 221: *
! 222: * Form C := alpha*A*conjg( A' ) + beta*C.
! 223: *
! 224: IF (UPPER) THEN
! 225: DO 130 J = 1,N
! 226: IF (BETA.EQ.ZERO) THEN
! 227: DO 90 I = 1,J
! 228: C(I,J) = ZERO
! 229: 90 CONTINUE
! 230: ELSE IF (BETA.NE.ONE) THEN
! 231: DO 100 I = 1,J - 1
! 232: C(I,J) = BETA*C(I,J)
! 233: 100 CONTINUE
! 234: C(J,J) = BETA*DBLE(C(J,J))
! 235: ELSE
! 236: C(J,J) = DBLE(C(J,J))
! 237: END IF
! 238: DO 120 L = 1,K
! 239: IF (A(J,L).NE.DCMPLX(ZERO)) THEN
! 240: TEMP = ALPHA*DCONJG(A(J,L))
! 241: DO 110 I = 1,J - 1
! 242: C(I,J) = C(I,J) + TEMP*A(I,L)
! 243: 110 CONTINUE
! 244: C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(I,L))
! 245: END IF
! 246: 120 CONTINUE
! 247: 130 CONTINUE
! 248: ELSE
! 249: DO 180 J = 1,N
! 250: IF (BETA.EQ.ZERO) THEN
! 251: DO 140 I = J,N
! 252: C(I,J) = ZERO
! 253: 140 CONTINUE
! 254: ELSE IF (BETA.NE.ONE) THEN
! 255: C(J,J) = BETA*DBLE(C(J,J))
! 256: DO 150 I = J + 1,N
! 257: C(I,J) = BETA*C(I,J)
! 258: 150 CONTINUE
! 259: ELSE
! 260: C(J,J) = DBLE(C(J,J))
! 261: END IF
! 262: DO 170 L = 1,K
! 263: IF (A(J,L).NE.DCMPLX(ZERO)) THEN
! 264: TEMP = ALPHA*DCONJG(A(J,L))
! 265: C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(J,L))
! 266: DO 160 I = J + 1,N
! 267: C(I,J) = C(I,J) + TEMP*A(I,L)
! 268: 160 CONTINUE
! 269: END IF
! 270: 170 CONTINUE
! 271: 180 CONTINUE
! 272: END IF
! 273: ELSE
! 274: *
! 275: * Form C := alpha*conjg( A' )*A + beta*C.
! 276: *
! 277: IF (UPPER) THEN
! 278: DO 220 J = 1,N
! 279: DO 200 I = 1,J - 1
! 280: TEMP = ZERO
! 281: DO 190 L = 1,K
! 282: TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
! 283: 190 CONTINUE
! 284: IF (BETA.EQ.ZERO) THEN
! 285: C(I,J) = ALPHA*TEMP
! 286: ELSE
! 287: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
! 288: END IF
! 289: 200 CONTINUE
! 290: RTEMP = ZERO
! 291: DO 210 L = 1,K
! 292: RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
! 293: 210 CONTINUE
! 294: IF (BETA.EQ.ZERO) THEN
! 295: C(J,J) = ALPHA*RTEMP
! 296: ELSE
! 297: C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
! 298: END IF
! 299: 220 CONTINUE
! 300: ELSE
! 301: DO 260 J = 1,N
! 302: RTEMP = ZERO
! 303: DO 230 L = 1,K
! 304: RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
! 305: 230 CONTINUE
! 306: IF (BETA.EQ.ZERO) THEN
! 307: C(J,J) = ALPHA*RTEMP
! 308: ELSE
! 309: C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
! 310: END IF
! 311: DO 250 I = J + 1,N
! 312: TEMP = ZERO
! 313: DO 240 L = 1,K
! 314: TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
! 315: 240 CONTINUE
! 316: IF (BETA.EQ.ZERO) THEN
! 317: C(I,J) = ALPHA*TEMP
! 318: ELSE
! 319: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
! 320: END IF
! 321: 250 CONTINUE
! 322: 260 CONTINUE
! 323: END IF
! 324: END IF
! 325: *
! 326: RETURN
! 327: *
! 328: * End of ZHERK .
! 329: *
! 330: END
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