*> \brief \b CTBSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,K,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTBSV 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 band matrix, with ( k + 1 )
*> diagonals.
*>
*> No test for singularity or near-singularity is included in this
*> routine. Such tests must be performed before calling this routine.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> ( k + 1 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,K,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
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 CONJG,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('CTBSV ',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 by sequentially with one pass through A.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
IF (LSAME(UPLO,'U')) THEN
KPLUS1 = K + 1
IF (INCX.EQ.1) THEN
DO 20 J = N,1,-1
IF (X(J).NE.ZERO) THEN
L = KPLUS1 - J
IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
TEMP = X(J)
DO 10 I = J - 1,MAX(1,J-K),-1
X(I) = X(I) - TEMP*A(L+I,J)
10 CONTINUE
END IF
20 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 40 J = N,1,-1
KX = KX - INCX
IF (X(JX).NE.ZERO) THEN
IX = KX
L = KPLUS1 - J
IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
TEMP = X(JX)
DO 30 I = J - 1,MAX(1,J-K),-1
X(IX) = X(IX) - TEMP*A(L+I,J)
IX = IX - INCX
30 CONTINUE
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
L = 1 - J
IF (NOUNIT) X(J) = X(J)/A(1,J)
TEMP = X(J)
DO 50 I = J + 1,MIN(N,J+K)
X(I) = X(I) - TEMP*A(L+I,J)
50 CONTINUE
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
KX = KX + INCX
IF (X(JX).NE.ZERO) THEN
IX = KX
L = 1 - J
IF (NOUNIT) X(JX) = X(JX)/A(1,J)
TEMP = X(JX)
DO 70 I = J + 1,MIN(N,J+K)
X(IX) = X(IX) - TEMP*A(L+I,J)
IX = IX + INCX
70 CONTINUE
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A**T )*x or x := inv( A**H )*x.
*
IF (LSAME(UPLO,'U')) THEN
KPLUS1 = K + 1
IF (INCX.EQ.1) THEN
DO 110 J = 1,N
TEMP = X(J)
L = KPLUS1 - J
IF (NOCONJ) THEN
DO 90 I = MAX(1,J-K),J - 1
TEMP = TEMP - A(L+I,J)*X(I)
90 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
ELSE
DO 100 I = MAX(1,J-K),J - 1
TEMP = TEMP - CONJG(A(L+I,J))*X(I)
100 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
END IF
X(J) = TEMP
110 CONTINUE
ELSE
JX = KX
DO 140 J = 1,N
TEMP = X(JX)
IX = KX
L = KPLUS1 - J
IF (NOCONJ) THEN
DO 120 I = MAX(1,J-K),J - 1
TEMP = TEMP - A(L+I,J)*X(IX)
IX = IX + INCX
120 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
ELSE
DO 130 I = MAX(1,J-K),J - 1
TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
IX = IX + INCX
130 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
END IF
X(JX) = TEMP
JX = JX + INCX
IF (J.GT.K) KX = KX + INCX
140 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 170 J = N,1,-1
TEMP = X(J)
L = 1 - J
IF (NOCONJ) THEN
DO 150 I = MIN(N,J+K),J + 1,-1
TEMP = TEMP - A(L+I,J)*X(I)
150 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(1,J)
ELSE
DO 160 I = MIN(N,J+K),J + 1,-1
TEMP = TEMP - CONJG(A(L+I,J))*X(I)
160 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
END IF
X(J) = TEMP
170 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 200 J = N,1,-1
TEMP = X(JX)
IX = KX
L = 1 - J
IF (NOCONJ) THEN
DO 180 I = MIN(N,J+K),J + 1,-1
TEMP = TEMP - A(L+I,J)*X(IX)
IX = IX - INCX
180 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(1,J)
ELSE
DO 190 I = MIN(N,J+K),J + 1,-1
TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
IX = IX - INCX
190 CONTINUE
IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
END IF
X(JX) = TEMP
JX = JX - INCX
IF ((N-J).GE.K) KX = KX - INCX
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of CTBSV
*
END