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430 lines
14 KiB
430 lines
14 KiB
2 years ago
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*> \brief \b ZTBSV
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
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*
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* .. Scalar Arguments ..
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* INTEGER INCX,K,LDA,N
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* CHARACTER DIAG,TRANS,UPLO
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A(LDA,*),X(*)
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZTBSV solves one of the systems of equations
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*>
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*> A*x = b, or A**T*x = b, or A**H*x = b,
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*>
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*> where b and x are n element vectors and A is an n by n unit, or
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*> non-unit, upper or lower triangular band matrix, with ( k + 1 )
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*> diagonals.
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*>
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*> No test for singularity or near-singularity is included in this
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*> routine. Such tests must be performed before calling this routine.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the matrix is an upper or
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*> lower triangular matrix as follows:
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*>
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*> UPLO = 'U' or 'u' A is an upper triangular matrix.
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*>
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*> UPLO = 'L' or 'l' A is a lower triangular matrix.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> On entry, TRANS specifies the equations to be solved as
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*> follows:
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*>
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*> TRANS = 'N' or 'n' A*x = b.
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*>
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*> TRANS = 'T' or 't' A**T*x = b.
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*>
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*> TRANS = 'C' or 'c' A**H*x = b.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> On entry, DIAG specifies whether or not A is unit
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*> triangular as follows:
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*>
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*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
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*>
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*> DIAG = 'N' or 'n' A is not assumed to be unit
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*> triangular.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> On entry, N specifies the order of the matrix A.
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*> N must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> On entry with UPLO = 'U' or 'u', K specifies the number of
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*> super-diagonals of the matrix A.
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*> On entry with UPLO = 'L' or 'l', K specifies the number of
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*> sub-diagonals of the matrix A.
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*> K must satisfy 0 .le. K.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension ( LDA, N )
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*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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*> by n part of the array A must contain the upper triangular
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*> band part of the matrix of coefficients, supplied column by
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*> column, with the leading diagonal of the matrix in row
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*> ( k + 1 ) of the array, the first super-diagonal starting at
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*> position 2 in row k, and so on. The top left k by k triangle
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*> of the array A is not referenced.
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*> The following program segment will transfer an upper
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*> triangular band matrix from conventional full matrix storage
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*> to band storage:
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*>
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*> DO 20, J = 1, N
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*> M = K + 1 - J
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*> DO 10, I = MAX( 1, J - K ), J
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*> A( M + I, J ) = matrix( I, J )
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*> 10 CONTINUE
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*> 20 CONTINUE
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*>
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*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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*> by n part of the array A must contain the lower triangular
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*> band part of the matrix of coefficients, supplied column by
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*> column, with the leading diagonal of the matrix in row 1 of
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*> the array, the first sub-diagonal starting at position 1 in
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*> row 2, and so on. The bottom right k by k triangle of the
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*> array A is not referenced.
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*> The following program segment will transfer a lower
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*> triangular band matrix from conventional full matrix storage
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*> to band storage:
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*>
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*> DO 20, J = 1, N
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*> M = 1 - J
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*> DO 10, I = J, MIN( N, J + K )
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*> A( M + I, J ) = matrix( I, J )
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*> 10 CONTINUE
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*> 20 CONTINUE
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*>
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*> Note that when DIAG = 'U' or 'u' the elements of the array A
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*> corresponding to the diagonal elements of the matrix are not
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*> referenced, but are assumed to be unity.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> On entry, LDA specifies the first dimension of A as declared
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*> in the calling (sub) program. LDA must be at least
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*> ( k + 1 ).
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*> \endverbatim
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*>
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*> \param[in,out] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension at least
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*> ( 1 + ( n - 1 )*abs( INCX ) ).
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*> Before entry, the incremented array X must contain the n
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*> element right-hand side vector b. On exit, X is overwritten
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*> with the solution vector x.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> On entry, INCX specifies the increment for the elements of
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*> X. INCX must not be zero.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16_blas_level2
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> Level 2 Blas routine.
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*>
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*> -- Written on 22-October-1986.
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*> Jack Dongarra, Argonne National Lab.
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*> Jeremy Du Croz, Nag Central Office.
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*> Sven Hammarling, Nag Central Office.
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*> Richard Hanson, Sandia National Labs.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
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*
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* -- Reference BLAS level2 routine --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INCX,K,LDA,N
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CHARACTER DIAG,TRANS,UPLO
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A(LDA,*),X(*)
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ZERO
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PARAMETER (ZERO= (0.0D+0,0.0D+0))
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* ..
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* .. Local Scalars ..
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COMPLEX*16 TEMP
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INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
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LOGICAL NOCONJ,NOUNIT
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG,MAX,MIN
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* ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
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+ .NOT.LSAME(TRANS,'C')) THEN
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INFO = 2
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ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
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INFO = 3
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ELSE IF (N.LT.0) THEN
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INFO = 4
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ELSE IF (K.LT.0) THEN
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INFO = 5
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ELSE IF (LDA.LT. (K+1)) THEN
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INFO = 7
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ELSE IF (INCX.EQ.0) THEN
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INFO = 9
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('ZTBSV ',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF (N.EQ.0) RETURN
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*
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NOCONJ = LSAME(TRANS,'T')
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NOUNIT = LSAME(DIAG,'N')
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*
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* Set up the start point in X if the increment is not unity. This
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* will be ( N - 1 )*INCX too small for descending loops.
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*
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IF (INCX.LE.0) THEN
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KX = 1 - (N-1)*INCX
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ELSE IF (INCX.NE.1) THEN
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KX = 1
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END IF
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*
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* Start the operations. In this version the elements of A are
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* accessed by sequentially with one pass through A.
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*
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form x := inv( A )*x.
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*
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IF (LSAME(UPLO,'U')) THEN
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KPLUS1 = K + 1
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IF (INCX.EQ.1) THEN
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DO 20 J = N,1,-1
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IF (X(J).NE.ZERO) THEN
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L = KPLUS1 - J
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IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
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TEMP = X(J)
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DO 10 I = J - 1,MAX(1,J-K),-1
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X(I) = X(I) - TEMP*A(L+I,J)
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10 CONTINUE
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END IF
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20 CONTINUE
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ELSE
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KX = KX + (N-1)*INCX
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JX = KX
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DO 40 J = N,1,-1
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KX = KX - INCX
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IF (X(JX).NE.ZERO) THEN
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IX = KX
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L = KPLUS1 - J
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IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
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TEMP = X(JX)
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DO 30 I = J - 1,MAX(1,J-K),-1
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X(IX) = X(IX) - TEMP*A(L+I,J)
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IX = IX - INCX
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30 CONTINUE
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END IF
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JX = JX - INCX
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40 CONTINUE
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END IF
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ELSE
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IF (INCX.EQ.1) THEN
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DO 60 J = 1,N
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IF (X(J).NE.ZERO) THEN
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L = 1 - J
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IF (NOUNIT) X(J) = X(J)/A(1,J)
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TEMP = X(J)
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DO 50 I = J + 1,MIN(N,J+K)
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X(I) = X(I) - TEMP*A(L+I,J)
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE
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JX = KX
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DO 80 J = 1,N
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KX = KX + INCX
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IF (X(JX).NE.ZERO) THEN
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IX = KX
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L = 1 - J
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IF (NOUNIT) X(JX) = X(JX)/A(1,J)
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TEMP = X(JX)
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DO 70 I = J + 1,MIN(N,J+K)
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X(IX) = X(IX) - TEMP*A(L+I,J)
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IX = IX + INCX
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70 CONTINUE
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END IF
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JX = JX + INCX
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80 CONTINUE
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END IF
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END IF
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ELSE
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*
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* Form x := inv( A**T )*x or x := inv( A**H )*x.
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*
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IF (LSAME(UPLO,'U')) THEN
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KPLUS1 = K + 1
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IF (INCX.EQ.1) THEN
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DO 110 J = 1,N
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TEMP = X(J)
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L = KPLUS1 - J
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IF (NOCONJ) THEN
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DO 90 I = MAX(1,J-K),J - 1
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TEMP = TEMP - A(L+I,J)*X(I)
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90 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
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ELSE
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DO 100 I = MAX(1,J-K),J - 1
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TEMP = TEMP - DCONJG(A(L+I,J))*X(I)
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100 CONTINUE
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IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J))
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END IF
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X(J) = TEMP
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110 CONTINUE
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ELSE
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JX = KX
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DO 140 J = 1,N
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TEMP = X(JX)
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IX = KX
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L = KPLUS1 - J
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IF (NOCONJ) THEN
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DO 120 I = MAX(1,J-K),J - 1
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TEMP = TEMP - A(L+I,J)*X(IX)
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IX = IX + INCX
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120 CONTINUE
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
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ELSE
|
||
|
|
DO 130 I = MAX(1,J-K),J - 1
|
||
|
|
TEMP = TEMP - DCONJG(A(L+I,J))*X(IX)
|
||
|
|
IX = IX + INCX
|
||
|
|
130 CONTINUE
|
||
|
|
IF (NOUNIT) TEMP = TEMP/DCONJG(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 - DCONJG(A(L+I,J))*X(I)
|
||
|
|
160 CONTINUE
|
||
|
|
IF (NOUNIT) TEMP = TEMP/DCONJG(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 - DCONJG(A(L+I,J))*X(IX)
|
||
|
|
IX = IX - INCX
|
||
|
|
190 CONTINUE
|
||
|
|
IF (NOUNIT) TEMP = TEMP/DCONJG(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 ZTBSV
|
||
|
|
*
|
||
|
|
END
|