Annotation of rpl/lapack/blas/zhbmv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE COMPLEX ALPHA,BETA
! 4: INTEGER INCX,INCY,K,LDA,N
! 5: CHARACTER UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * ZHBMV performs the matrix-vector operation
! 15: *
! 16: * y := alpha*A*x + beta*y,
! 17: *
! 18: * where alpha and beta are scalars, x and y are n element vectors and
! 19: * A is an n by n hermitian band matrix, with k super-diagonals.
! 20: *
! 21: * Arguments
! 22: * ==========
! 23: *
! 24: * UPLO - CHARACTER*1.
! 25: * On entry, UPLO specifies whether the upper or lower
! 26: * triangular part of the band matrix A is being supplied as
! 27: * follows:
! 28: *
! 29: * UPLO = 'U' or 'u' The upper triangular part of A is
! 30: * being supplied.
! 31: *
! 32: * UPLO = 'L' or 'l' The lower triangular part of A is
! 33: * being supplied.
! 34: *
! 35: * Unchanged on exit.
! 36: *
! 37: * N - INTEGER.
! 38: * On entry, N specifies the order of the matrix A.
! 39: * N must be at least zero.
! 40: * Unchanged on exit.
! 41: *
! 42: * K - INTEGER.
! 43: * On entry, K specifies the number of super-diagonals of the
! 44: * matrix A. K must satisfy 0 .le. K.
! 45: * Unchanged on exit.
! 46: *
! 47: * ALPHA - COMPLEX*16 .
! 48: * On entry, ALPHA specifies the scalar alpha.
! 49: * Unchanged on exit.
! 50: *
! 51: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
! 52: * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
! 53: * by n part of the array A must contain the upper triangular
! 54: * band part of the hermitian matrix, supplied column by
! 55: * column, with the leading diagonal of the matrix in row
! 56: * ( k + 1 ) of the array, the first super-diagonal starting at
! 57: * position 2 in row k, and so on. The top left k by k triangle
! 58: * of the array A is not referenced.
! 59: * The following program segment will transfer the upper
! 60: * triangular part of a hermitian band matrix from conventional
! 61: * full matrix storage to band storage:
! 62: *
! 63: * DO 20, J = 1, N
! 64: * M = K + 1 - J
! 65: * DO 10, I = MAX( 1, J - K ), J
! 66: * A( M + I, J ) = matrix( I, J )
! 67: * 10 CONTINUE
! 68: * 20 CONTINUE
! 69: *
! 70: * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
! 71: * by n part of the array A must contain the lower triangular
! 72: * band part of the hermitian matrix, supplied column by
! 73: * column, with the leading diagonal of the matrix in row 1 of
! 74: * the array, the first sub-diagonal starting at position 1 in
! 75: * row 2, and so on. The bottom right k by k triangle of the
! 76: * array A is not referenced.
! 77: * The following program segment will transfer the lower
! 78: * triangular part of a hermitian band matrix from conventional
! 79: * full matrix storage to band storage:
! 80: *
! 81: * DO 20, J = 1, N
! 82: * M = 1 - J
! 83: * DO 10, I = J, MIN( N, J + K )
! 84: * A( M + I, J ) = matrix( I, J )
! 85: * 10 CONTINUE
! 86: * 20 CONTINUE
! 87: *
! 88: * Note that the imaginary parts of the diagonal elements need
! 89: * not be set and are assumed to be zero.
! 90: * Unchanged on exit.
! 91: *
! 92: * LDA - INTEGER.
! 93: * On entry, LDA specifies the first dimension of A as declared
! 94: * in the calling (sub) program. LDA must be at least
! 95: * ( k + 1 ).
! 96: * Unchanged on exit.
! 97: *
! 98: * X - COMPLEX*16 array of DIMENSION at least
! 99: * ( 1 + ( n - 1 )*abs( INCX ) ).
! 100: * Before entry, the incremented array X must contain the
! 101: * vector x.
! 102: * Unchanged on exit.
! 103: *
! 104: * INCX - INTEGER.
! 105: * On entry, INCX specifies the increment for the elements of
! 106: * X. INCX must not be zero.
! 107: * Unchanged on exit.
! 108: *
! 109: * BETA - COMPLEX*16 .
! 110: * On entry, BETA specifies the scalar beta.
! 111: * Unchanged on exit.
! 112: *
! 113: * Y - COMPLEX*16 array of DIMENSION at least
! 114: * ( 1 + ( n - 1 )*abs( INCY ) ).
! 115: * Before entry, the incremented array Y must contain the
! 116: * vector y. On exit, Y is overwritten by the updated vector y.
! 117: *
! 118: * INCY - INTEGER.
! 119: * On entry, INCY specifies the increment for the elements of
! 120: * Y. INCY must not be zero.
! 121: * Unchanged on exit.
! 122: *
! 123: * Further Details
! 124: * ===============
! 125: *
! 126: * Level 2 Blas routine.
! 127: *
! 128: * -- Written on 22-October-1986.
! 129: * Jack Dongarra, Argonne National Lab.
! 130: * Jeremy Du Croz, Nag Central Office.
! 131: * Sven Hammarling, Nag Central Office.
! 132: * Richard Hanson, Sandia National Labs.
! 133: *
! 134: * =====================================================================
! 135: *
! 136: * .. Parameters ..
! 137: DOUBLE COMPLEX ONE
! 138: PARAMETER (ONE= (1.0D+0,0.0D+0))
! 139: DOUBLE COMPLEX ZERO
! 140: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 141: * ..
! 142: * .. Local Scalars ..
! 143: DOUBLE COMPLEX TEMP1,TEMP2
! 144: INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
! 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,MIN
! 155: * ..
! 156: *
! 157: * Test the input parameters.
! 158: *
! 159: INFO = 0
! 160: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
! 161: INFO = 1
! 162: ELSE IF (N.LT.0) THEN
! 163: INFO = 2
! 164: ELSE IF (K.LT.0) THEN
! 165: INFO = 3
! 166: ELSE IF (LDA.LT. (K+1)) THEN
! 167: INFO = 6
! 168: ELSE IF (INCX.EQ.0) THEN
! 169: INFO = 8
! 170: ELSE IF (INCY.EQ.0) THEN
! 171: INFO = 11
! 172: END IF
! 173: IF (INFO.NE.0) THEN
! 174: CALL XERBLA('ZHBMV ',INFO)
! 175: RETURN
! 176: END IF
! 177: *
! 178: * Quick return if possible.
! 179: *
! 180: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
! 181: *
! 182: * Set up the start points in X and Y.
! 183: *
! 184: IF (INCX.GT.0) THEN
! 185: KX = 1
! 186: ELSE
! 187: KX = 1 - (N-1)*INCX
! 188: END IF
! 189: IF (INCY.GT.0) THEN
! 190: KY = 1
! 191: ELSE
! 192: KY = 1 - (N-1)*INCY
! 193: END IF
! 194: *
! 195: * Start the operations. In this version the elements of the array A
! 196: * are accessed sequentially with one pass through A.
! 197: *
! 198: * First form y := beta*y.
! 199: *
! 200: IF (BETA.NE.ONE) THEN
! 201: IF (INCY.EQ.1) THEN
! 202: IF (BETA.EQ.ZERO) THEN
! 203: DO 10 I = 1,N
! 204: Y(I) = ZERO
! 205: 10 CONTINUE
! 206: ELSE
! 207: DO 20 I = 1,N
! 208: Y(I) = BETA*Y(I)
! 209: 20 CONTINUE
! 210: END IF
! 211: ELSE
! 212: IY = KY
! 213: IF (BETA.EQ.ZERO) THEN
! 214: DO 30 I = 1,N
! 215: Y(IY) = ZERO
! 216: IY = IY + INCY
! 217: 30 CONTINUE
! 218: ELSE
! 219: DO 40 I = 1,N
! 220: Y(IY) = BETA*Y(IY)
! 221: IY = IY + INCY
! 222: 40 CONTINUE
! 223: END IF
! 224: END IF
! 225: END IF
! 226: IF (ALPHA.EQ.ZERO) RETURN
! 227: IF (LSAME(UPLO,'U')) THEN
! 228: *
! 229: * Form y when upper triangle of A is stored.
! 230: *
! 231: KPLUS1 = K + 1
! 232: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
! 233: DO 60 J = 1,N
! 234: TEMP1 = ALPHA*X(J)
! 235: TEMP2 = ZERO
! 236: L = KPLUS1 - J
! 237: DO 50 I = MAX(1,J-K),J - 1
! 238: Y(I) = Y(I) + TEMP1*A(L+I,J)
! 239: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
! 240: 50 CONTINUE
! 241: Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
! 242: 60 CONTINUE
! 243: ELSE
! 244: JX = KX
! 245: JY = KY
! 246: DO 80 J = 1,N
! 247: TEMP1 = ALPHA*X(JX)
! 248: TEMP2 = ZERO
! 249: IX = KX
! 250: IY = KY
! 251: L = KPLUS1 - J
! 252: DO 70 I = MAX(1,J-K),J - 1
! 253: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
! 254: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
! 255: IX = IX + INCX
! 256: IY = IY + INCY
! 257: 70 CONTINUE
! 258: Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
! 259: JX = JX + INCX
! 260: JY = JY + INCY
! 261: IF (J.GT.K) THEN
! 262: KX = KX + INCX
! 263: KY = KY + INCY
! 264: END IF
! 265: 80 CONTINUE
! 266: END IF
! 267: ELSE
! 268: *
! 269: * Form y when lower triangle of A is stored.
! 270: *
! 271: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
! 272: DO 100 J = 1,N
! 273: TEMP1 = ALPHA*X(J)
! 274: TEMP2 = ZERO
! 275: Y(J) = Y(J) + TEMP1*DBLE(A(1,J))
! 276: L = 1 - J
! 277: DO 90 I = J + 1,MIN(N,J+K)
! 278: Y(I) = Y(I) + TEMP1*A(L+I,J)
! 279: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
! 280: 90 CONTINUE
! 281: Y(J) = Y(J) + ALPHA*TEMP2
! 282: 100 CONTINUE
! 283: ELSE
! 284: JX = KX
! 285: JY = KY
! 286: DO 120 J = 1,N
! 287: TEMP1 = ALPHA*X(JX)
! 288: TEMP2 = ZERO
! 289: Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J))
! 290: L = 1 - J
! 291: IX = JX
! 292: IY = JY
! 293: DO 110 I = J + 1,MIN(N,J+K)
! 294: IX = IX + INCX
! 295: IY = IY + INCY
! 296: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
! 297: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
! 298: 110 CONTINUE
! 299: Y(JY) = Y(JY) + ALPHA*TEMP2
! 300: JX = JX + INCX
! 301: JY = JY + INCY
! 302: 120 CONTINUE
! 303: END IF
! 304: END IF
! 305: *
! 306: RETURN
! 307: *
! 308: * End of ZHBMV .
! 309: *
! 310: END
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