LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
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sgbmv.f File Reference

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Functions/Subroutines

subroutine sgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
 SGBMV More...
 

Function/Subroutine Documentation

subroutine sgbmv ( character  TRANS,
integer  M,
integer  N,
integer  KL,
integer  KU,
real  ALPHA,
real, dimension(lda,*)  A,
integer  LDA,
real, dimension(*)  X,
integer  INCX,
real  BETA,
real, dimension(*)  Y,
integer  INCY 
)

SGBMV

Purpose: 
 SGBMV  performs one of the matrix-vector operations

    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,

 where alpha and beta are scalars, x and y are vectors and A is an
 m by n band matrix, with kl sub-diagonals and ku super-diagonals.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.

              TRANS = 'C' or 'c'   y := alpha*A**T*x + beta*y.
[in]M
          M is INTEGER
           On entry, M specifies the number of rows of the matrix A.
           M must be at least zero.
[in]N
          N is INTEGER
           On entry, N specifies the number of columns of the matrix A.
           N must be at least zero.
[in]KL
          KL is INTEGER
           On entry, KL specifies the number of sub-diagonals of the
           matrix A. KL must satisfy  0 .le. KL.
[in]KU
          KU is INTEGER
           On entry, KU specifies the number of super-diagonals of the
           matrix A. KU must satisfy  0 .le. KU.
[in]ALPHA
          ALPHA is REAL
           On entry, ALPHA specifies the scalar alpha.
[in]A
          A is REAL array of DIMENSION ( LDA, n ).
           Before entry, the leading ( kl + ku + 1 ) by n part of the
           array A must contain the matrix of coefficients, supplied
           column by column, with the leading diagonal of the matrix in
           row ( ku + 1 ) of the array, the first super-diagonal
           starting at position 2 in row ku, the first sub-diagonal
           starting at position 1 in row ( ku + 2 ), and so on.
           Elements in the array A that do not correspond to elements
           in the band matrix (such as the top left ku by ku triangle)
           are not referenced.
           The following program segment will transfer a band matrix
           from conventional full matrix storage to band storage:

                 DO 20, J = 1, N
                    K = KU + 1 - J
                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                       A( K + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE
[in]LDA
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( kl + ku + 1 ).
[in]X
          X is REAL array of DIMENSION at least
           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
           Before entry, the incremented array X must contain the
           vector x.
[in]INCX
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
[in]BETA
          BETA is REAL
           On entry, BETA specifies the scalar beta. When BETA is
           supplied as zero then Y need not be set on input.
[in,out]Y
          Y is REAL array of DIMENSION at least
           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
           and at least
           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.
[in]INCY
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Further Details: 
  Level 2 Blas routine.
  The vector and matrix arguments are not referenced when N = 0, or M = 0

  -- 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.

Definition at line 186 of file sgbmv.f.

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