func main() {
flag.Parse()
if flag.NArg() == 0 {
log.Fatal("missing file name")
}
name := flag.Args()[0]
f, err := os.Open(name)
if err != nil {
log.Fatal(err)
}
defer f.Close()
var r io.Reader
if path.Ext(name) == ".gz" {
gz, err := gzip.NewReader(f)
if err != nil {
log.Fatal(err)
}
name = strings.TrimSuffix(name, ".gz")
r = gz
} else {
r = f
}
var aDok *sparse.DOK
switch path.Ext(name) {
case ".mtx":
aDok, err = readMatrixMarket(r)
case ".rsa":
log.Fatal("reading of Harwell-Boeing format not yet implemented")
default:
log.Fatal("unknown file extension")
}
if err != nil {
log.Fatal(err)
}
a := sparse.NewCSR(aDok)
n, _ := a.Dims()
x := make([]float64, n)
for i := range x {
x[i] = 1
}
b := make([]float64, n)
sparse.MulMatVec(1, false, a, x, 1, 0, b, 1)
for i := range x {
x[i] = 0
}
result, err := iterative.Solve(a, b, x, nil, &iterative.CG{})
if err != nil {
log.Fatal(err)
}
if len(result.X) > 10 {
fmt.Println("Solution[:10]:", result.X[:10])
} else {
fmt.Println("Solution:", result.X)
}
}
func iterate(method Method, a sparse.Matrix, b *mat64.Vector, settings *Settings, ctx *Context, stats *Stats) error {
bNorm := mat64.Norm(b, 2)
if bNorm == 0 {
bNorm = 1
}
op := method.Init(ctx)
for {
switch op {
case NoOperation:
case ComputeAp:
ctx.Ap.ScaleVec(0, ctx.Ap)
sparse.MulMatVec(ctx.Ap, 1, false, a, ctx.P)
stats.MatVecMultiplies++
case ComputeAq:
ctx.Aq.ScaleVec(0, ctx.Aq)
sparse.MulMatVec(ctx.Aq, 1, false, a, ctx.Q)
stats.MatVecMultiplies++
case SolvePreconditioner:
// TODO(vladimir-ch): Add preconditioners.
// Z = Residual
ctx.Z.CopyVec(ctx.Residual)
stats.PrecondionerSolves++
case CheckConvergence:
stats.Iterations++
stats.Residual = mat64.Norm(ctx.Residual, 2) / bNorm
fmt.Println(stats.Residual)
if stats.Residual < settings.Tolerance {
return nil
}
if stats.Iterations == settings.Iterations {
return errors.New("iterative: reached iteration limit")
}
}
op = method.Iterate(ctx)
}
}
func Solve(a sparse.Matrix, b, xInit *mat64.Vector, settings *Settings, method Method) (result Result, err error) {
stats := Stats{
StartTime: time.Now(),
}
dim, c := a.Dims()
if dim != c {
panic("iterative: matrix is not square")
}
if xInit != nil && dim != xInit.Len() {
panic("iterative: mismatched size of the initial guess")
}
if b.Len() != dim {
panic("iterative: mismatched size of the right-hand side vector")
}
if xInit == nil {
xInit = mat64.NewVector(dim, nil)
}
if settings == nil {
settings = DefaultSettings(dim)
}
ctx := Context{
X: mat64.NewVector(dim, nil),
Residual: mat64.NewVector(dim, nil),
}
// X = xInit
ctx.X.CopyVec(xInit)
if mat64.Norm(ctx.X, math.Inf(1)) > 0 {
// Residual = Ax
sparse.MulMatVec(ctx.Residual, 1, false, a, ctx.X)
stats.MatVecMultiplies++
}
// Residual = Ax - b
ctx.Residual.SubVec(ctx.Residual, b)
if mat64.Norm(ctx.Residual, 2) >= settings.Tolerance {
err = iterate(method, a, b, settings, &ctx, &stats)
}
result = Result{
X: ctx.X,
Stats: stats,
Runtime: time.Since(stats.StartTime),
}
return result, err
}
func Solve(a sparse.Matrix, b, xInit []float64, settings *Settings, method Method) (result Result, err error) {
stats := Stats{
StartTime: time.Now(),
}
dim := len(xInit)
if dim == 0 {
panic("iterative: invalid dimension")
}
r, c := a.Dims()
if r != c {
panic("iterative: matrix is not square")
}
if c != dim {
panic("iterative: mismatched size of the matrix")
}
if len(b) != dim {
panic("iterative: mismatched size of the right-hand side vector")
}
if settings == nil {
settings = DefaultSettings(dim)
}
ctx := Context{
X: make([]float64, dim),
Residual: make([]float64, dim),
}
copy(ctx.X, xInit)
copy(ctx.Residual, b)
if floats.Norm(ctx.X, math.Inf(1)) > 0 {
sparse.MulMatVec(-1, false, a, ctx.X, 1, 1, ctx.Residual, 1)
stats.MatVecMultiplies++
}
if floats.Norm(ctx.Residual, 2) >= settings.Tolerance {
err = iterate(method, a, b, settings, &ctx, &stats)
}
result = Result{
X: ctx.X,
Stats: stats,
Runtime: time.Since(stats.StartTime),
}
return result, err
}
func iterate(method Method, a sparse.Matrix, b []float64, settings *Settings, ctx *Context, stats *Stats) error {
dim := len(ctx.X)
bNorm := floats.Norm(b, 2)
if bNorm == 0 {
bNorm = 1
}
request := method.Init(ctx)
for {
switch request {
case NoOperation:
case ComputeAp:
ctx.Ap = resize(ctx.Ap, dim)
sparse.MulMatVec(1, false, a, ctx.P, 1, 0, ctx.Ap, 1)
stats.MatVecMultiplies++
case SolvePreconditioner:
ctx.Z = resize(ctx.Z, dim)
copy(ctx.Z, ctx.Residual)
stats.PrecondionerSolves++
case CheckConvergence:
stats.Iterations++
stats.Residual = floats.Norm(ctx.Residual, 2) / bNorm
fmt.Println(stats.Residual)
if stats.Residual < settings.Tolerance {
return nil
}
if stats.Iterations == settings.Iterations {
return errors.New("iterative: reached iteration limit")
}
}
request = method.Iterate(ctx)
}
}
func main() {
flag.Parse()
if flag.NArg() == 0 {
log.Fatal("missing file name")
}
name := flag.Args()[0]
f, err := os.Open(name)
if err != nil {
log.Fatal(err)
}
defer f.Close()
var r io.Reader
if path.Ext(name) == ".gz" {
gz, err := gzip.NewReader(f)
if err != nil {
log.Fatal(err)
}
name = strings.TrimSuffix(name, ".gz")
r = gz
} else {
r = f
}
// blas64.Use(cgo.Implementation{})
blas64.Use(native.Implementation{})
var aDok *sparse.DOK
switch path.Ext(name) {
case ".mtx":
aDok, err = readMatrixMarket(r)
case ".rsa":
log.Fatal("reading of Harwell-Boeing format not yet implemented")
default:
log.Fatal("unknown file extension")
}
if err != nil {
log.Fatal(err)
}
a := sparse.NewCSR(aDok)
n, _ := a.Dims()
// Create the right-hand side so that the solution is [1 1 ... 1].
x := make([]float64, n)
for i := range x {
x[i] = 1
}
xVec := mat64.NewVector(n, x)
bVec := mat64.NewVector(n, make([]float64, n))
sparse.MulMatVec(bVec, 1, false, a, xVec)
result, err := iterative.Solve(a, bVec, nil, nil, &iterative.CG{})
if err != nil {
log.Fatal(err)
}
if result.X.Len() > 10 {
fmt.Println("Solution[:10]:", result.X.RawVector().Data[:10])
} else {
fmt.Println("Solution:", result.X.RawVector())
}
}