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SUBROUTINE <a name="ZGBMV.1"></a><a href="zgbmv.f.html#ZGBMV.1">ZGBMV</a>(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
<span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER TRANS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZGBMV.14"></a><a href="zgbmv.f.html#ZGBMV.1">ZGBMV</a> performs one of the matrix-vector operations
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> y := alpha*conjg( A' )*x + beta*y,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where alpha and beta are scalars, x and y are vectors and A is an
</span><span class="comment">*</span><span class="comment"> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> ==========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS - CHARACTER*1.
</span><span class="comment">*</span><span class="comment"> On entry, TRANS specifies the operation to be performed as
</span><span class="comment">*</span><span class="comment"> follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, M specifies the number of rows of the matrix A.
</span><span class="comment">*</span><span class="comment"> M must be at least zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, N specifies the number of columns of the matrix A.
</span><span class="comment">*</span><span class="comment"> N must be at least zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KL - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, KL specifies the number of sub-diagonals of the
</span><span class="comment">*</span><span class="comment"> matrix A. KL must satisfy 0 .le. KL.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KU - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, KU specifies the number of super-diagonals of the
</span><span class="comment">*</span><span class="comment"> matrix A. KU must satisfy 0 .le. KU.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ALPHA - COMPLEX*16 .
</span><span class="comment">*</span><span class="comment"> On entry, ALPHA specifies the scalar alpha.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A - COMPLEX*16 array of DIMENSION ( LDA, n ).
</span><span class="comment">*</span><span class="comment"> Before entry, the leading ( kl + ku + 1 ) by n part of the
</span><span class="comment">*</span><span class="comment"> array A must contain the matrix of coefficients, supplied
</span><span class="comment">*</span><span class="comment"> column by column, with the leading diagonal of the matrix in
</span><span class="comment">*</span><span class="comment"> row ( ku + 1 ) of the array, the first super-diagonal
</span><span class="comment">*</span><span class="comment"> starting at position 2 in row ku, the first sub-diagonal
</span><span class="comment">*</span><span class="comment"> starting at position 1 in row ( ku + 2 ), and so on.
</span><span class="comment">*</span><span class="comment"> Elements in the array A that do not correspond to elements
</span><span class="comment">*</span><span class="comment"> in the band matrix (such as the top left ku by ku triangle)
</span><span class="comment">*</span><span class="comment"> are not referenced.
</span><span class="comment">*</span><span class="comment"> The following program segment will transfer a band matrix
</span><span class="comment">*</span><span class="comment"> from conventional full matrix storage to band storage:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DO 20, J = 1, N
</span><span class="comment">*</span><span class="comment"> K = KU + 1 - J
</span><span class="comment">*</span><span class="comment"> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
</span><span class="comment">*</span><span class="comment"> A( K + I, J ) = matrix( I, J )
</span><span class="comment">*</span><span class="comment"> 10 CONTINUE
</span><span class="comment">*</span><span class="comment"> 20 CONTINUE
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, LDA specifies the first dimension of A as declared
</span><span class="comment">*</span><span class="comment"> in the calling (sub) program. LDA must be at least
</span><span class="comment">*</span><span class="comment"> ( kl + ku + 1 ).
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> X - COMPLEX*16 array of DIMENSION at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
</span><span class="comment">*</span><span class="comment"> and at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
</span><span class="comment">*</span><span class="comment"> Before entry, the incremented array X must contain the
</span><span class="comment">*</span><span class="comment"> vector x.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INCX - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, INCX specifies the increment for the elements of
</span><span class="comment">*</span><span class="comment"> X. INCX must not be zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BETA - COMPLEX*16 .
</span><span class="comment">*</span><span class="comment"> On entry, BETA specifies the scalar beta. When BETA is
</span><span class="comment">*</span><span class="comment"> supplied as zero then Y need not be set on input.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Y - COMPLEX*16 array of DIMENSION at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
</span><span class="comment">*</span><span class="comment"> and at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
</span><span class="comment">*</span><span class="comment"> Before entry, the incremented array Y must contain the
</span><span class="comment">*</span><span class="comment"> vector y. On exit, Y is overwritten by the updated vector y.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INCY - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, INCY specifies the increment for the elements of
</span><span class="comment">*</span><span class="comment"> Y. INCY must not be zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Level 2 Blas routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- Written on 22-October-1986.
</span><span class="comment">*</span><span class="comment"> Jack Dongarra, Argonne National Lab.
</span><span class="comment">*</span><span class="comment"> Jeremy Du Croz, Nag Central Office.
</span><span class="comment">*</span><span class="comment"> Sven Hammarling, Nag Central Office.
</span><span class="comment">*</span><span class="comment"> Richard Hanson, Sandia National Labs.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
LOGICAL NOCONJ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.143"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.144"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="XERBLA.147"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC DCONJG,MAX,MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
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