SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * .. Scalar Arguments .. INTEGER INCX,K,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE COMPLEX A(LDA,*),X(*) * .. * * Purpose * ======= * * ZTBMV performs one of the matrix-vector operations * * x := A*x, or x := A**T*x, or x := A**H*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular band matrix, with ( k + 1 ) diagonals. * * Arguments * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' x := A*x. * * TRANS = 'T' or 't' x := A**T*x. * * TRANS = 'C' or 'c' x := A**H*x. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element vector x. On exit, X is overwritten with the * tranformed vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * Further Details * =============== * * Level 2 Blas routine. * The vector and matrix arguments are not referenced when N = 0, or M = 0 * * -- Written on 22-October-1986. * Jack Dongarra, Argonne National Lab. * Jeremy Du Croz, Nag Central Office. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * ===================================================================== * * .. Parameters .. DOUBLE COMPLEX ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. DOUBLE COMPLEX TEMP INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX,MIN * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (K.LT.0) THEN INFO = 5 ELSE IF (LDA.LT. (K+1)) THEN INFO = 7 ELSE IF (INCX.EQ.0) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTBMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := A*x. * IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) L = KPLUS1 - J DO 10 I = MAX(1,J-K),J - 1 X(I) = X(I) + TEMP*A(L+I,J) 10 CONTINUE IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX L = KPLUS1 - J DO 30 I = MAX(1,J-K),J - 1 X(IX) = X(IX) + TEMP*A(L+I,J) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) END IF JX = JX + INCX IF (J.GT.K) KX = KX + INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) L = 1 - J DO 50 I = MIN(N,J+K),J + 1,-1 X(I) = X(I) + TEMP*A(L+I,J) 50 CONTINUE IF (NOUNIT) X(J) = X(J)*A(1,J) END IF 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX L = 1 - J DO 70 I = MIN(N,J+K),J + 1,-1 X(IX) = X(IX) + TEMP*A(L+I,J) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(1,J) END IF JX = JX - INCX IF ((N-J).GE.K) KX = KX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x or x := A**H*x. * IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 110 J = N,1,-1 TEMP = X(J) L = KPLUS1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) DO 90 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + A(L+I,J)*X(I) 90 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) DO 100 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 100 CONTINUE END IF X(J) = TEMP 110 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 140 J = N,1,-1 TEMP = X(JX) KX = KX - INCX IX = KX L = KPLUS1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) DO 120 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + A(L+I,J)*X(IX) IX = IX - INCX 120 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) DO 130 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) IX = IX - INCX 130 CONTINUE END IF X(JX) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 170 J = 1,N TEMP = X(J) L = 1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(1,J) DO 150 I = J + 1,MIN(N,J+K) TEMP = TEMP + A(L+I,J)*X(I) 150 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) DO 160 I = J + 1,MIN(N,J+K) TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 160 CONTINUE END IF X(J) = TEMP 170 CONTINUE ELSE JX = KX DO 200 J = 1,N TEMP = X(JX) KX = KX + INCX IX = KX L = 1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(1,J) DO 180 I = J + 1,MIN(N,J+K) TEMP = TEMP + A(L+I,J)*X(IX) IX = IX + INCX 180 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) DO 190 I = J + 1,MIN(N,J+K) TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) IX = IX + INCX 190 CONTINUE END IF X(JX) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTBMV . * END