378 lines
13 KiB
Fortran
378 lines
13 KiB
Fortran
SUBROUTINE ZTBMVF( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
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* .. Scalar Arguments ..
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INTEGER INCX, K, LDA, N
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CHARACTER*1 DIAG, TRANS, UPLO
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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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* Purpose
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* =======
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*
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* ZTBMV performs one of the matrix-vector operations
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*
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* x := A*x, or x := A'*x, or x := conjg( A' )*x,
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*
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* where x is an n element vector and A is an n by n unit, or non-unit,
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* upper or lower triangular band matrix, with ( k + 1 ) diagonals.
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*
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* Parameters
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* ==========
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*
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* UPLO - 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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*
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* Unchanged on exit.
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the operation to be performed as
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* follows:
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*
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* TRANS = 'N' or 'n' x := A*x.
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*
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* TRANS = 'T' or 't' x := A'*x.
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*
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* TRANS = 'C' or 'c' x := conjg( A' )*x.
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*
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* Unchanged on exit.
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*
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* DIAG - 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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*
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* Unchanged on exit.
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*
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* N - 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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* Unchanged on exit.
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*
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* K - 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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* Unchanged on exit.
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*
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* A - COMPLEX*16 array of 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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* Unchanged on exit.
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*
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* LDA - 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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* Unchanged on exit.
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*
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* X - COMPLEX*16 array of 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 vector x. On exit, X is overwritten with the
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* tranformed vector x.
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*
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* INCX - 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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* Unchanged on exit.
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*
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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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*
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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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* .. 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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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX, MIN
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* ..
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* .. Executable Statements ..
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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.
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$ .NOT.LSAME( UPLO , 'L' ) )THEN
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INFO = 1
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ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
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$ .NOT.LSAME( TRANS, 'T' ).AND.
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$ .NOT.LSAME( TRANS, 'R' ).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.
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$ .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( 'ZTBMV ', 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 )
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$ RETURN
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*
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NOCONJ = LSAME( TRANS, 'N' ) .OR. 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 sequentially with one pass through A.
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*
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IF( LSAME( TRANS, 'N' ).OR.LSAME( TRANS, 'R' ) )THEN
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*
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* Form x := 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 = 1, N
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IF( X( J ).NE.ZERO )THEN
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TEMP = X( J )
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L = KPLUS1 - J
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DO 10, I = MAX( 1, J - K ), J - 1
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X( I ) = X( I ) + TEMP*A( L + I, J )
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10 CONTINUE
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IF( NOUNIT )
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$ X( J ) = X( J )*A( KPLUS1, J )
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END IF
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20 CONTINUE
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ELSE
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JX = KX
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DO 40, J = 1, N
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IF( X( JX ).NE.ZERO )THEN
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TEMP = X( JX )
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IX = KX
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L = KPLUS1 - J
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DO 30, I = MAX( 1, J - K ), J - 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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IF( NOUNIT )
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$ X( JX ) = X( JX )*A( KPLUS1, J )
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END IF
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JX = JX + INCX
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IF( J.GT.K )
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$ KX = KX + 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 = N, 1, -1
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IF( X( J ).NE.ZERO )THEN
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TEMP = X( J )
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L = 1 - J
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DO 50, I = MIN( N, J + K ), J + 1, -1
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X( I ) = X( I ) + TEMP*A( L + I, J )
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50 CONTINUE
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IF( NOUNIT )
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$ X( J ) = X( J )*A( 1, J )
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END IF
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60 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 80, J = N, 1, -1
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IF( X( JX ).NE.ZERO )THEN
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TEMP = X( JX )
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IX = KX
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L = 1 - J
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DO 70, I = MIN( N, J + K ), J + 1, -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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70 CONTINUE
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IF( NOUNIT )
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$ X( JX ) = X( JX )*A( 1, J )
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END IF
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JX = JX - INCX
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IF( ( N - J ).GE.K )
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$ KX = KX - 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 := A'*x or x := conjg( 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 110, J = N, 1, -1
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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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IF( NOUNIT )
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$ TEMP = TEMP*A( KPLUS1, J )
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DO 90, I = J - 1, MAX( 1, J - K ), -1
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TEMP = TEMP + A( L + I, J )*X( I )
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90 CONTINUE
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ELSE
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IF( NOUNIT )
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$ TEMP = TEMP*DCONJG( A( KPLUS1, J ) )
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DO 100, I = J - 1, MAX( 1, J - K ), -1
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TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I )
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100 CONTINUE
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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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KX = KX + ( N - 1 )*INCX
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JX = KX
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DO 140, J = N, 1, -1
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TEMP = X( JX )
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KX = KX - INCX
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IX = KX
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L = KPLUS1 - J
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ TEMP = TEMP*A( KPLUS1, J )
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DO 120, I = J - 1, MAX( 1, J - K ), -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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ELSE
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IF( NOUNIT )
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$ TEMP = TEMP*DCONJG( A( KPLUS1, J ) )
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DO 130, I = J - 1, MAX( 1, J - K ), -1
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TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX )
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IX = IX - INCX
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130 CONTINUE
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END IF
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X( JX ) = TEMP
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JX = JX - INCX
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140 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 170, J = 1, N
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TEMP = X( J )
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L = 1 - J
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ TEMP = TEMP*A( 1, J )
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DO 150, I = J + 1, MIN( N, J + K )
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TEMP = TEMP + A( L + I, J )*X( I )
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150 CONTINUE
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ELSE
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IF( NOUNIT )
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$ TEMP = TEMP*DCONJG( A( 1, J ) )
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DO 160, I = J + 1, MIN( N, J + K )
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TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I )
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160 CONTINUE
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END IF
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X( J ) = TEMP
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170 CONTINUE
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ELSE
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JX = KX
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DO 200, J = 1, N
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TEMP = X( JX )
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KX = KX + INCX
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IX = KX
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L = 1 - J
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IF( NOCONJ )THEN
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IF( NOUNIT )
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$ TEMP = TEMP*A( 1, J )
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DO 180, I = J + 1, MIN( N, J + K )
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TEMP = TEMP + A( L + I, J )*X( IX )
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IX = IX + INCX
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180 CONTINUE
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ELSE
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IF( NOUNIT )
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$ TEMP = TEMP*DCONJG( A( 1, J ) )
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DO 190, I = J + 1, MIN( N, J + K )
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TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX )
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IX = IX + INCX
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190 CONTINUE
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END IF
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X( JX ) = TEMP
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JX = JX + INCX
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200 CONTINUE
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END IF
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END IF
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END IF
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*
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RETURN
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*
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* End of ZTBMV .
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*
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END
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