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SUBROUTINE <a name="SSBMV.1"></a><a href="ssbmv.f.html#SSBMV.1">SSBMV</a>(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
<span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> REAL ALPHA,BETA
INTEGER INCX,INCY,K,LDA,N
CHARACTER UPLO
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL 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="SSBMV.14"></a><a href="ssbmv.f.html#SSBMV.1">SSBMV</a> performs the matrix-vector operation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> y := alpha*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 n element vectors and
</span><span class="comment">*</span><span class="comment"> A is an n by n symmetric band matrix, with k 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"> UPLO - CHARACTER*1.
</span><span class="comment">*</span><span class="comment"> On entry, UPLO specifies whether the upper or lower
</span><span class="comment">*</span><span class="comment"> triangular part of the band matrix A is being supplied 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"> UPLO = 'U' or 'u' The upper triangular part of A is
</span><span class="comment">*</span><span class="comment"> being supplied.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO = 'L' or 'l' The lower triangular part of A is
</span><span class="comment">*</span><span class="comment"> being supplied.
</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"> N - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, N specifies the order 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"> K - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, K specifies the number of super-diagonals of the
</span><span class="comment">*</span><span class="comment"> matrix A. K must satisfy 0 .le. K.
</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 - REAL .
</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 - REAL array of DIMENSION ( LDA, n ).
</span><span class="comment">*</span><span class="comment"> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
</span><span class="comment">*</span><span class="comment"> by n part of the array A must contain the upper triangular
</span><span class="comment">*</span><span class="comment"> band part of the symmetric matrix, supplied column by
</span><span class="comment">*</span><span class="comment"> column, with the leading diagonal of the matrix in row
</span><span class="comment">*</span><span class="comment"> ( k + 1 ) of the array, the first super-diagonal starting at
</span><span class="comment">*</span><span class="comment"> position 2 in row k, and so on. The top left k by k triangle
</span><span class="comment">*</span><span class="comment"> of the array A is not referenced.
</span><span class="comment">*</span><span class="comment"> The following program segment will transfer the upper
</span><span class="comment">*</span><span class="comment"> triangular part of a symmetric band matrix from conventional
</span><span class="comment">*</span><span class="comment"> 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"> M = K + 1 - J
</span><span class="comment">*</span><span class="comment"> DO 10, I = MAX( 1, J - K ), J
</span><span class="comment">*</span><span class="comment"> A( M + 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"> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
</span><span class="comment">*</span><span class="comment"> by n part of the array A must contain the lower triangular
</span><span class="comment">*</span><span class="comment"> band part of the symmetric matrix, supplied column by
</span><span class="comment">*</span><span class="comment"> column, with the leading diagonal of the matrix in row 1 of
</span><span class="comment">*</span><span class="comment"> the array, the first sub-diagonal starting at position 1 in
</span><span class="comment">*</span><span class="comment"> row 2, and so on. The bottom right k by k triangle of the
</span><span class="comment">*</span><span class="comment"> array A is not referenced.
</span><span class="comment">*</span><span class="comment"> The following program segment will transfer the lower
</span><span class="comment">*</span><span class="comment"> triangular part of a symmetric band matrix from conventional
</span><span class="comment">*</span><span class="comment"> 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"> M = 1 - J
</span><span class="comment">*</span><span class="comment"> DO 10, I = J, MIN( N, J + K )
</span><span class="comment">*</span><span class="comment"> A( M + 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"> ( k + 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 - REAL array of DIMENSION at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( n - 1 )*abs( INCX ) ).
</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 - REAL .
</span><span class="comment">*</span><span class="comment"> On entry, BETA specifies the scalar beta.
</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 - REAL array of DIMENSION at least
</span><span class="comment">*</span><span class="comment"> ( 1 + ( n - 1 )*abs( INCY ) ).
</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"> 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> REAL ONE,ZERO
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> REAL TEMP1,TEMP2
INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.140"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.141"></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.144"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
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