SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * .. Scalar Arguments .. INTEGER INCX,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION AP(*),X(*) * .. * * Purpose * ======= * * DTPMV performs one of the matrix-vector operations * * x := A*x, or x := A**T*x, * * where x is an n element vector and A is an n by n unit, or non-unit, * upper or lower triangular matrix, supplied in packed form. * * 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**T*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. * * AP - DOUBLE PRECISION array of DIMENSION at least * ( ( n*( n + 1 ) )/2 ). * Before entry with UPLO = 'U' or 'u', the array AP must * contain the upper triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) * respectively, and so on. * Before entry with UPLO = 'L' or 'l', the array AP must * contain the lower triangular matrix packed sequentially, * column by column, so that AP( 1 ) contains a( 1, 1 ), * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) * respectively, and so on. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced, but are assumed to be unity. * Unchanged on exit. * * X - DOUBLE PRECISION 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 PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * * 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 (INCX.EQ.0) THEN INFO = 7 END IF IF (INFO.NE.0) THEN CALL XERBLA('DTPMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * 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 AP are * accessed sequentially with one pass through AP. * IF (LSAME(TRANS,'N')) THEN * * Form x:= A*x. * IF (LSAME(UPLO,'U')) THEN KK = 1 IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) K = KK DO 10 I = 1,J - 1 X(I) = X(I) + TEMP*AP(K) K = K + 1 10 CONTINUE IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 30 K = KK,KK + J - 2 X(IX) = X(IX) + TEMP*AP(K) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) K = KK DO 50 I = N,J + 1,-1 X(I) = X(I) + TEMP*AP(K) K = K - 1 50 CONTINUE IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) END IF KK = KK - (N-J+1) 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 DO 70 K = KK,KK - (N- (J+1)),-1 X(IX) = X(IX) + TEMP*AP(K) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) END IF JX = JX - INCX KK = KK - (N-J+1) 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x. * IF (LSAME(UPLO,'U')) THEN KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 100 J = N,1,-1 TEMP = X(J) IF (NOUNIT) TEMP = TEMP*AP(KK) K = KK - 1 DO 90 I = J - 1,1,-1 TEMP = TEMP + AP(K)*X(I) K = K - 1 90 CONTINUE X(J) = TEMP KK = KK - J 100 CONTINUE ELSE JX = KX + (N-1)*INCX DO 120 J = N,1,-1 TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*AP(KK) DO 110 K = KK - 1,KK - J + 1,-1 IX = IX - INCX TEMP = TEMP + AP(K)*X(IX) 110 CONTINUE X(JX) = TEMP JX = JX - INCX KK = KK - J 120 CONTINUE END IF ELSE KK = 1 IF (INCX.EQ.1) THEN DO 140 J = 1,N TEMP = X(J) IF (NOUNIT) TEMP = TEMP*AP(KK) K = KK + 1 DO 130 I = J + 1,N TEMP = TEMP + AP(K)*X(I) K = K + 1 130 CONTINUE X(J) = TEMP KK = KK + (N-J+1) 140 CONTINUE ELSE JX = KX DO 160 J = 1,N TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*AP(KK) DO 150 K = KK + 1,KK + N - J IX = IX + INCX TEMP = TEMP + AP(K)*X(IX) 150 CONTINUE X(JX) = TEMP JX = JX + INCX KK = KK + (N-J+1) 160 CONTINUE END IF END IF END IF * RETURN * * End of DTPMV . * END