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prog.f
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! sblas2.f 02 June 2000
!
subroutine smxpy ( n1, y, n2, lda, x, a )
!
!***********************************************************************
!
!! SMXPY computes Y = Y + A * X, where A is a matrix.
!
!
! Parameters:
!
! Input, integer N1, the number of entries in Y.
!
! Input/output, real Y(N1), the vector to which A*X is to be added.
!
! Input, integer N2, the number of entries in X.
!
! Input, integer LDA, the leading dimension of the array A.
! LDA must be at least N1.
!
! Input, real X(N2), the vector to be multiplied by A.
!
! Input, real A(LDA,N2), the N1 by N2 matrix which is to multiply X.
!
integer lda
integer n2
!
real a(lda,n2)
integer i
integer j
integer n1
real x(n2)
real y(n1)
!
do j = 1, n2
do i = 1, n1
y(i) = y(i) + a(i,j) * x(j)
end do
end do
return
end
subroutine sxmpy ( n1, ldy, y, n2, ldx, x, lda, a )
!
!***********************************************************************
!
!! SXMPY computes y(1,j)=y(1,j) + sum(i= 1 to n2) x(1,i) * a(i,j)
!
!
! Parameters:
!
! Input, integer N1, the number of entries in the row vector Y.
! This is usually the number of columns in the two dimensional array Y.
!
! Input, integer LDY, the leading dimension of the array Y.
!
! Input/output, real Y(LDY,N1), an array containing the row
! vector Y as its first row. On output, X * A has been added to the
! first row of y.
!
! Input, integer N2, the number of entries in the row vector X,
! This is usually the number of columns in the two dimensional array X.
!
! Input, integer LDX, the leading dimension of the array X.
!
! Input, real X(LDX,N2), an array containing the row vector X as its
! first row.
!
! Input, integer LDA, the leading dimension of the array A.
!
! Input, real A(LDA,N1), an array which is to be multiplied by X.
!
integer lda
integer ldx
integer ldy
integer n1
integer n2
!
real a(lda,n1)
integer i
integer j
real x(ldx,n2)
real y(ldy,n1)
!
do j = 1, n2
do i = 1, n1
y(1,i) = y(1,i) + x(1,j) * a(j,i)
end do
end do
return
end
subroutine sgbmv ( trans, m, n, kl, ku, alpha, a, lda, x, incx,
& beta, y, incy )
!
!***********************************************************************
!
!! SGBMV computes Y := ALPHA * A * X + BETA * Y.
!
!
! Discussion:
!
! SGBMV can also compute Y := ALPHA * A' * X + BETA * Y.
!
! 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:
!
! trans - character.
! 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' * x + beta*y.
!
! trans = 'C' or 'C' y := alpha * a' * x + beta*y.
!
! unchanged on exit.
!
! m - integer.
! on entry, m specifies the number of rows of the matrix a.
! m must be at least 0.
! unchanged on exit.
!
! n - integer.
! on entry, n specifies the number of columns of the matrix a.
! n must be at least 0.
! unchanged on exit.
!
! kl - integer.
! on entry, kl specifies the number of sub-diagonals of the
! matrix a. kl must satisfy 0 <= kl.
! unchanged on exit.
!
! ku - integer.
! on entry, ku specifies the number of super-diagonals of the
! matrix a. ku must satisfy 0 <= ku.
! unchanged on exit.
!
! alpha - real .
! on entry, alpha specifies the scalar alpha.
! unchanged on exit.
!
! a - 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 j = 1, n
! k = ku + 1 - j
! do i = max ( 1, j - ku ), min ( m, j + kl )
! a( k + i,j) = matrix(i,j)
! end do
! end do
!
! unchanged on exit.
!
! lda - 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 ).
! unchanged on exit.
!
! x - 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.
! unchanged on exit.
!
! incx - integer.
! on entry, incx specifies the increment for the elements of
! x. incx must not be 0.
! unchanged on exit.
!
! beta - real .
! on entry, beta specifies the scalar beta. when beta is
! supplied as zero then y need not be set on input.
! unchanged on exit.
!
! y - 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.
!
! incy - integer.
! on entry, incy specifies the increment for the elements of
! y. incy must not be 0.
! unchanged on exit.
!
!
! level 2 blas routine.
!
! -- 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.
!
integer lda
!
real alpha
real beta
integer incx
integer incy
integer kl
integer ku
integer m
integer n
character trans
real a( lda, * ), x( * ), y( * )
real temp
integer i, info, ix, iy, j, jx, jy, k, kup1, kx, ky
integer lenx, leny
logical lsame
external lsame
external xerbla
!
! test the input parameters.
!
info = 0
if ( .not.lsame ( trans, 'N' ).and.
& .not.lsame ( trans, 'T' ).and.
& .not.lsame ( trans, 'C' ) ) then
info = 1
else if ( m < 0 ) then
info = 2
else if ( n < 0 ) then
info = 3
else if ( kl < 0 ) then
info = 4
else if ( ku < 0 ) then
info = 5
else if ( lda < ( kl + ku + 1 ) ) then
info = 8
else if ( incx == 0 ) then
info = 10
else if ( incy == 0 ) then
info = 13
end if
if ( info /= 0 ) then
call xerbla ( 'sgbmv ', info )
return
end if
!
! Quick return if possible.
!
if ( m == 0 ) then
return
else if ( n == 0 ) then
return
else if ( alpha == 0.0 .and. beta == 1.0 ) then
return
end if
!
! set lenx and leny, the lengths of the vectors x and y, and set
! up the start points in x and y.
!
if ( lsame ( trans, 'N' ) ) then
lenx = n
leny = m
else
lenx = m
leny = n
end if
if ( incx > 0 ) then
kx = 1
else
kx = 1 - ( lenx - 1 ) * incx
end if
if ( incy > 0 ) then
ky = 1
else
ky = 1 - ( leny - 1 ) * incy
end if
!
! Start the operations. in this version the elements of A are
! accessed sequentially with one pass through the band part of A.
!
! First form y := beta*y.
!
if ( beta /= 1.0 ) then
if ( incy == 1 ) then
if ( beta == 0.0 ) then
do i = 1, leny
y(i) = 0.0
end do
else
do i = 1, leny
y(i) = beta * y(i)
end do
end if
else
iy = ky
if ( beta == 0.0 ) then
do i = 1, leny
y(iy) = 0.0
iy = iy + incy
end do
else
do i = 1, leny
y(iy) = beta * y(iy)
iy = iy + incy
end do
end if
end if
end if
if ( alpha == 0.0 ) then
return
end if
kup1 = ku + 1
if ( lsame ( trans, 'N' ) ) then
!
! Form y := alpha * a * x + y.
!
jx = kx
if ( incy == 1 ) then
do j = 1, n
if ( x(jx) /= 0.0 ) then
temp = alpha * x(jx)
k = kup1 - j
do i = max ( 1, j - ku ), min ( m, j + kl )
y(i) = y(i) + temp * a( k + i,j)
end do
end if
jx = jx + incx
end do
else
do j = 1, n
if ( x(jx) /= 0.0 ) then
temp = alpha * x(jx)
iy = ky
k = kup1 - j
do i = max ( 1, j - ku ), min ( m, j + kl )
y(iy) = y(iy) + temp * a( k + i,j)
iy = iy + incy
end do
end if
jx = jx + incx
if ( j>ku ) then
ky = ky + incy
end if
end do
end if
else
!
! Form y := alpha * a' * x + y.
!
jy = ky
if ( incx == 1 ) then
do j = 1, n
temp = 0.0
k = kup1 - j
do i = max ( 1, j - ku ), min ( m, j + kl )
temp = temp + a( k + i,j) * x(i)
end do
y(jy) = y(jy) + alpha * temp
jy = jy + incy
end do
else
do j = 1, n
temp = 0.0
ix = kx
k = kup1 - j
do i = max ( 1, j - ku ), min ( m, j + kl )
temp = temp + a( k + i,j) * x(ix)
ix = ix + incx
end do
y(jy) = y(jy) + alpha * temp
jy = jy + incy
if ( j>ku ) then
kx = kx + incx
end if
end do
end if
end if
return
end
subroutine sgemv ( trans, m, n, alpha, a, lda, x, incx,
& beta, y, incy )
!
!***********************************************************************
!
!! SGEMV performs one of the matrix-vector operations
!
! y := alpha * a * x + beta*y, or y := alpha * a'*x + beta*y,
!
! where alpha and beta are scalars, x and y are vectors and a is an
! m by n matrix.
!
! Parameters:
!
! trans - character.
! 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' * x + beta*y.
!
! trans = 'C' or 'C' y := alpha * a' * x + beta*y.
!
! unchanged on exit.
!
! m - integer.
! on entry, m specifies the number of rows of the matrix a.
! m must be at least 0.
! unchanged on exit.
!
! n - integer.
! on entry, n specifies the number of columns of the matrix a.
! n must be at least 0.
! unchanged on exit.
!
! alpha - real .
! on entry, alpha specifies the scalar alpha.
! unchanged on exit.
!
! a - real array of dimension ( lda, n ).
! before entry, the leading m by n part of the array a must
! contain the matrix of coefficients.
! unchanged on exit.
!
! lda - integer.
! on entry, lda specifies the first dimension of a as declared
! in the calling (sub) program. lda must be at least
! max ( 1, m ).
! unchanged on exit.
!
! x - 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.
! unchanged on exit.
!
! incx - integer.
! on entry, incx specifies the increment for the elements of
! x. incx must not be 0.
! unchanged on exit.
!
! beta - real .
! on entry, beta specifies the scalar beta. when beta is
! supplied as zero then y need not be set on input.
! unchanged on exit.
!
! y - 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 with beta non-zero, the incremented array y
! must contain the vector y. on exit, y is overwritten by the
! updated vector y.
!
! incy - integer.
! on entry, incy specifies the increment for the elements of
! y. incy must not be 0.
! unchanged on exit.
!
!
! level 2 blas routine.
!
! -- 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.
!
!
real alpha, beta
integer incx, incy, lda, m, n
character trans
! .. array arguments ..
real a( lda, * ), x( * ), y( * )
real temp
integer i, info, ix, iy, j, jx, jy, kx, ky, lenx, leny
! .. external functions ..
logical lsame
external lsame
! .. external subroutines ..
external xerbla
! .. intrinsic functions ..
intrinsic max
! ..
! .. executable statements ..
!
! test the input parameters.
!
info = 0
if ( .not.lsame ( trans, 'N' ).and.
& .not.lsame ( trans, 'T' ).and.
& .not.lsame ( trans, 'C' ) ) then
info = 1
else if ( m < 0 ) then
info = 2
else if ( n < 0 ) then
info = 3
else if ( lda < max ( 1, m ) ) then
info = 6
else if ( incx == 0 ) then
info = 8
else if ( incy == 0 ) then
info = 11
end if
if ( info /= 0 ) then
call xerbla ( 'sgemv ', info )
return
end if
!
! Quick return if possible.
!
if ( ( m == 0 ).or.( n== 0 ).or.
& ( ( alpha == 0.0 ).and.( beta== 1.0 ) ) )
& return
!
! set lenx and leny, the lengths of the vectors x and y, and set
! up the start points in x and y.
!
if ( lsame ( trans, 'N' ) ) then
lenx = n
leny = m
else
lenx = m
leny = n
end if
if ( incx > 0 ) then
kx = 1
else
kx = 1 - ( lenx - 1 ) * incx
end if
if ( incy > 0 ) then
ky = 1
else
ky = 1 - ( leny - 1 ) * incy
end if
!
! Start the operations. in this version the elements of a are
! accessed sequentially with one pass through a.
!
! First form y := beta*y.
!
if ( beta /= 1.0 ) then
if ( incy == 1 ) then
if ( beta == 0.0 ) then
do i = 1, leny
y(i) = 0.0
end do
else
do i = 1, leny
y(i) = beta * y(i)
end do
end if
else
iy = ky
if ( beta == 0.0 ) then
do i = 1, leny
y(iy) = 0.0
iy = iy + incy
end do
else
do i = 1, leny
y(iy) = beta * y(iy)
iy = iy + incy
end do
end if
end if
end if
if ( alpha == 0.0 ) then
return
end if
if ( lsame ( trans, 'N' ) ) then
!
! Form y := alpha * a * x + y.
!
jx = kx
if ( incy == 1 ) then
do j = 1, n
if ( x(jx) /= 0.0 ) then
temp = alpha * x(jx)
do i = 1, m
y(i) = y(i) + temp * a(i,j)
end do
end if
jx = jx + incx
end do
else
do j = 1, n
if ( x(jx) /= 0.0 ) then
temp = alpha * x(jx)
iy = ky
do i = 1, m
y(iy) = y(iy) + temp * a(i,j)
iy = iy + incy
end do
end if
jx = jx + incx
end do
end if
else
!
! Form y := alpha * a' * x + y.
!
jy = ky
if ( incx == 1 ) then
do j = 1, n
temp = 0.0
do i = 1, m
temp = temp + a(i,j) * x(i)
end do
y(jy) = y(jy) + alpha * temp
jy = jy + incy
end do
else
do j = 1, n
temp = 0.0
ix = kx
do i = 1, m
temp = temp + a(i,j) * x(ix)
ix = ix + incx
end do
y(jy) = y(jy) + alpha * temp
jy = jy + incy
end do
end if
end if
return
end
subroutine sger ( m, n, alpha, x, incx, y, incy, a, lda )
!
!***********************************************************************
!
!! SGER performs the rank 1 operation
!
! a := alpha * x*y' + a,
!
! where alpha is a scalar, x is an m element vector, y is an n element
! vector and a is an m by n matrix.
!
! Parameters:
!
! m - integer.
! on entry, m specifies the number of rows of the matrix a.
! m must be at least 0.
! unchanged on exit.
!
! n - integer.
! on entry, n specifies the number of columns of the matrix a.
! n must be at least 0.
! unchanged on exit.
!
! alpha - real .
! on entry, alpha specifies the scalar alpha.
! unchanged on exit.
!
! x - real array of dimension at least
! ( 1 + ( m - 1 ) * abs( incx ) ).
! before entry, the incremented array x must contain the m
! element vector x.
! unchanged on exit.
!
! incx - integer.
! on entry, incx specifies the increment for the elements of
! x. incx must not be 0.
! unchanged on exit.
!
! y - real array of dimension at least
! ( 1 + ( n - 1 ) * abs( incy ) ).
! before entry, the incremented array y must contain the n
! element vector y.
! unchanged on exit.
!
! incy - integer.
! on entry, incy specifies the increment for the elements of
! y. incy must not be 0.
! unchanged on exit.
!
! a - real array of dimension ( lda, n ).
! before entry, the leading m by n part of the array a must
! contain the matrix of coefficients. on exit, a is
! overwritten by the updated matrix.
!
! lda - integer.
! on entry, lda specifies the first dimension of a as declared
! in the calling (sub) program. lda must be at least
! max ( 1, m ).
! unchanged on exit.
!
!
! level 2 blas routine.
!
! -- 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.
!
real alpha
integer incx, incy, lda, m, n
! .. array arguments ..
real a( lda, * ), x( * ), y( * )
! ..
!
! .. local scalars ..
real temp
integer i, info, ix, j, jy, kx
! .. external subroutines ..
external xerbla
! .. intrinsic functions ..
intrinsic max
! ..
! .. executable statements ..
!
! test the input parameters.
!
info = 0
if ( m < 0 ) then
info = 1
else if ( n < 0 ) then
info = 2
else if ( incx == 0 ) then
info = 5
else if ( incy == 0 ) then
info = 7
else if ( lda < max ( 1, m ) ) then
info = 9
end if
if ( info /= 0 ) then
call xerbla ( 'sger ', info )
return
end if
!
! Quick return if possible.
!
if ( ( m == 0 ).or.( n== 0 ).or.( alpha==0.0 ) ) then
return
end if
!
! Start the operations. in this version the elements of a are
! accessed sequentially with one pass through a.
!
if ( incy > 0 ) then
jy = 1
else
jy = 1 - ( n - 1 ) * incy
end if
if ( incx == 1 ) then
do j = 1, n
if ( y(jy) /= 0.0 ) then
temp = alpha * y(jy)
do i = 1, m
a(i,j) = a(i,j) + x(i) * temp
end do
end if
jy = jy + incy
end do
else
if ( incx > 0 ) then
kx = 1
else
kx = 1 - ( m - 1 ) * incx
end if
do j = 1, n
if ( y(jy) /= 0.0 ) then
temp = alpha * y(jy)
ix = kx
do i = 1, m
a(i,j) = a(i,j) + x(ix) * temp
ix = ix + incx
end do
end if
jy = jy + incy
end do
end if
return
end
subroutine ssbmv ( uplo, n, k, alpha, a, lda, x, incx,
& beta, y, incy )
!
!***********************************************************************
!
!! SSBMV performs the matrix-vector operation
!
! y := alpha * a * x + beta*y,
!
! where alpha and beta are scalars, x and y are n element vectors and
! a is an n by n symmetric band matrix, with k super-diagonals.
!
! Parameters:
!
! uplo - character.
! on entry, uplo specifies whether the upper or lower
! triangular part of the band matrix a is being supplied as
! follows:
!
! uplo = 'U' or 'U' the upper triangular part of a is
! being supplied.
!
! uplo = 'L' or 'L' the lower triangular part of a is
! being supplied.
!
! unchanged on exit.
!
! n - integer.
! on entry, n specifies the order of the matrix a.
! n must be at least 0.
! unchanged on exit.
!
! k - integer.
! on entry, k specifies the number of super-diagonals of the
! matrix a. k must satisfy 0 <= k.
! unchanged on exit.
!
! alpha - real .
! on entry, alpha specifies the scalar alpha.
! unchanged on exit.
!
! a - real array of dimension ( lda, n ).
! before entry with uplo = 'U' or 'U', the leading ( k + 1 )
! by n part of the array a must contain the upper triangular
! band part of the symmetric matrix, supplied column by
! column, with the leading diagonal of the matrix in row
! ( k + 1 ) of the array, the first super-diagonal starting at
! position 2 in row k, and so on. the top left k by k triangle
! of the array a is not referenced.
! the following program segment will transfer the upper
! triangular part of a symmetric band matrix from conventional
! full matrix storage to band storage:
!
! do j = 1, n
! m = k + 1 - j
! do i = max ( 1, j - k ), j
! a( m + i,j) = matrix(i,j)
! end do
! end do
!
! before entry with uplo = 'L' or 'L', the leading ( k + 1 )
! by n part of the array a must contain the lower triangular
! band part of the symmetric matrix, supplied column by
! column, with the leading diagonal of the matrix in row 1 of
! the array, the first sub-diagonal starting at position 1 in
! row 2, and so on. the bottom right k by k triangle of the
! array a is not referenced.
! the following program segment will transfer the lower
! triangular part of a symmetric band matrix from conventional
! full matrix storage to band storage:
!
! do j = 1, n
! m = 1 - j
! do i = j, min ( n, j + k )
! a( m + i,j) = matrix(i,j)
! end do
! end do
!
! unchanged on exit.
!
! lda - integer.
! on entry, lda specifies the first dimension of a as declared
! in the calling (sub) program. lda must be at least
! ( k + 1 ).
! unchanged on exit.
!
! x - real array of dimension at least
! ( 1 + ( n - 1 ) * abs( incx ) ).
! before entry, the incremented array x must contain the
! vector x.
! unchanged on exit.
!
! incx - integer.
! on entry, incx specifies the increment for the elements of
! x. incx must not be 0.
! unchanged on exit.
!
! beta - real .
! on entry, beta specifies the scalar beta.
! unchanged on exit.
!
! y - real array of dimension at least
! ( 1 + ( n - 1 ) * abs( incy ) ).
! before entry, the incremented array y must contain the
! vector y. on exit, y is overwritten by the updated vector y.
!
! incy - integer.
! on entry, incy specifies the increment for the elements of
! y. incy must not be 0.
! unchanged on exit.
!
!
! level 2 blas routine.
!
! -- 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.
!
real alpha, beta
integer incx, incy, k, lda, n
character uplo
! .. array arguments ..
real a( lda, * ), x( * ), y( * )
! ..
!
! .. local scalars ..
real temp1, temp2
integer i, info, ix, iy, j, jx, jy, kplus1, kx, ky, l
! .. external functions ..
logical lsame
external lsame
! .. external subroutines ..
external xerbla
! .. intrinsic functions ..
intrinsic max, min
! ..
! .. executable statements ..
!
! test the input parameters.
!
info = 0
if ( .not.lsame ( uplo, 'U' ).and.
& .not.lsame ( uplo, 'L' ) ) then
info = 1
else if ( n < 0 ) then
info = 2
else if ( k < 0 ) then
info = 3
else if ( lda < ( k + 1 ) ) then
info = 6
else if ( incx == 0 ) then
info = 8
else if ( incy == 0 ) then
info = 11
end if
if ( info /= 0 ) then
call xerbla ( 'ssbmv ', info )
return
end if
!
! Quick return if possible.
!
if ( ( n == 0 ).or.( ( alpha== 0.0 ).and.( beta== 1.0 ) ) ) then
return
end if
!
! set up the start points in x and y.
!
if ( incx>0 ) then
kx = 1
else
kx = 1 - ( n - 1 ) * incx
end if
if ( incy>0 ) then
ky = 1
else
ky = 1 - ( n - 1 ) * incy
end if
!
! start the operations. in this version the elements of the array a
! are accessed sequentially with one pass through a.
!
! first form y := beta*y.
!
if ( beta /= 1.0 ) then
if ( incy == 1 ) then