SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * .. Scalar Arguments .. INTEGER INCX,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX AP(*),X(*) * .. * * Purpose * ======= * * CTPSV solves one of the systems of equations * * A*x = b, or A**T*x = b, or A**H*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular matrix, supplied in packed form. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * 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 equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A**T*x = b. * * TRANS = 'C' or 'c' A**H*x = b. * * 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 - COMPLEX 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 - COMPLEX array of dimension at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the n * element right-hand side vector b. On exit, X is overwritten * with the solution 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. * * -- 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 .. COMPLEX ZERO PARAMETER (ZERO= (0.0E+0,0.0E+0)) * .. * .. Local Scalars .. COMPLEX TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. * * 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('CTPSV ',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 AP are * accessed sequentially with one pass through AP. * IF (LSAME(TRANS,'N')) THEN * * Form x := inv( A )*x. * IF (LSAME(UPLO,'U')) THEN KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 20 J = N,1,-1 IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/AP(KK) TEMP = X(J) K = KK - 1 DO 10 I = J - 1,1,-1 X(I) = X(I) - TEMP*AP(K) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + (N-1)*INCX DO 40 J = N,1,-1 IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/AP(KK) TEMP = X(JX) IX = JX DO 30 K = KK - 1,KK - J + 1,-1 IX = IX - INCX X(IX) = X(IX) - TEMP*AP(K) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/AP(KK) TEMP = X(J) K = KK + 1 DO 50 I = J + 1,N X(I) = X(I) - TEMP*AP(K) K = K + 1 50 CONTINUE END IF KK = KK + (N-J+1) 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/AP(KK) TEMP = X(JX) IX = JX DO 70 K = KK + 1,KK + N - J IX = IX + INCX X(IX) = X(IX) - TEMP*AP(K) 70 CONTINUE END IF JX = JX + INCX KK = KK + (N-J+1) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A**T )*x or x := inv( A**H )*x. * IF (LSAME(UPLO,'U')) THEN KK = 1 IF (INCX.EQ.1) THEN DO 110 J = 1,N TEMP = X(J) K = KK IF (NOCONJ) THEN DO 90 I = 1,J - 1 TEMP = TEMP - AP(K)*X(I) K = K + 1 90 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) ELSE DO 100 I = 1,J - 1 TEMP = TEMP - CONJG(AP(K))*X(I) K = K + 1 100 CONTINUE IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) END IF X(J) = TEMP KK = KK + J 110 CONTINUE ELSE JX = KX DO 140 J = 1,N TEMP = X(JX) IX = KX IF (NOCONJ) THEN DO 120 K = KK,KK + J - 2 TEMP = TEMP - AP(K)*X(IX) IX = IX + INCX 120 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) ELSE DO 130 K = KK,KK + J - 2 TEMP = TEMP - CONJG(AP(K))*X(IX) IX = IX + INCX 130 CONTINUE IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) END IF X(JX) = TEMP JX = JX + INCX KK = KK + J 140 CONTINUE END IF ELSE KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 170 J = N,1,-1 TEMP = X(J) K = KK IF (NOCONJ) THEN DO 150 I = N,J + 1,-1 TEMP = TEMP - AP(K)*X(I) K = K - 1 150 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) ELSE DO 160 I = N,J + 1,-1 TEMP = TEMP - CONJG(AP(K))*X(I) K = K - 1 160 CONTINUE IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) END IF X(J) = TEMP KK = KK - (N-J+1) 170 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 200 J = N,1,-1 TEMP = X(JX) IX = KX IF (NOCONJ) THEN DO 180 K = KK,KK - (N- (J+1)),-1 TEMP = TEMP - AP(K)*X(IX) IX = IX - INCX 180 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) ELSE DO 190 K = KK,KK - (N- (J+1)),-1 TEMP = TEMP - CONJG(AP(K))*X(IX) IX = IX - INCX 190 CONTINUE IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) END IF X(JX) = TEMP JX = JX - INCX KK = KK - (N-J+1) 200 CONTINUE END IF END IF END IF * RETURN * * End of CTPSV . * END