Add Dgetrs (compute a solution based on LU factorization) and test.

Responded to PR comments

cgo/lapack.go

@@ -136,3 +136,27 @@ func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (o
 	}
 	return ok
 }
+
+// Dgetrs solves a system of equations using an LU factorization.
+// The system of equations solved is
+//  A * X = B if trans == blas.Trans
+//  A^T * X = B if trans == blas.NoTrans
+// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
+//
+// On entry b contains the elements of the matrix B. On exit, b contains the
+// elements of X, the solution to the system of equations.
+//
+// a and ipiv contain the LU factorization of A and the permutation indices as
+// computed by Dgetrf. ipiv is zero-indexed.
+func (impl Implementation) Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) {
+	checkMatrix(n, n, a, lda)
+	checkMatrix(n, nrhs, b, ldb)
+	if len(ipiv) < n {
+		panic(badIpiv)
+	}
+	ipiv32 := make([]int32, len(ipiv))
+	for i, v := range ipiv {
+		ipiv32[i] = int32(v) + 1 // Transform to one-indexed.
+	}
+	clapack.Dgetrs(trans, n, nrhs, a, lda, ipiv32, b, ldb)
+}

cgo/lapack_test.go

@@ -23,3 +23,7 @@ func TestDgetf2(t *testing.T) {
 func TestDgetrf(t *testing.T) {
 	testlapack.DgetrfTest(t, impl)
 }
+
+func TestDgetrs(t *testing.T) {
+	testlapack.DgetrsTest(t, impl)
+}

native/dgetrs.go

@@ -0,0 +1,51 @@
+package native
+
+import (
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+)
+
+// Dgetrs solves a system of equations using an LU factorization.
+// The system of equations solved is
+//  A * X = B if trans == blas.Trans
+//  A^T * X = B if trans == blas.NoTrans
+// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
+//
+// On entry b contains the elements of the matrix B. On exit, b contains the
+// elements of X, the solution to the system of equations.
+//
+// a and ipiv contain the LU factorization of A and the permutation indices as
+// computed by Dgetrf. ipiv is zero-indexed.
+func (impl Implementation) Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) {
+	checkMatrix(n, n, a, lda)
+	checkMatrix(n, nrhs, b, ldb)
+	if len(ipiv) < n {
+		panic(badIpiv)
+	}
+	if n == 0 || nrhs == 0 {
+		return
+	}
+	if trans != blas.Trans && trans != blas.NoTrans {
+		panic(badTrans)
+	}
+	bi := blas64.Implementation()
+	if trans == blas.NoTrans {
+		// Solve A * X = B.
+		impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, 1)
+		// Solve L * X = B, updating b.
+		bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit,
+			n, nrhs, 1, a, lda, b, ldb)
+		// Solve U * X = B, updating b.
+		bi.Dtrsm(blas.Left, blas.Upper, blas.NoTrans, blas.NonUnit,
+			n, nrhs, 1, a, lda, b, ldb)
+		return
+	}
+	// Solve A^T * X = B.
+	// Solve U^T * X = B, updating b.
+	bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit,
+		n, nrhs, 1, a, lda, b, ldb)
+	// Solve L^T * X = B, updating b.
+	bi.Dtrsm(blas.Left, blas.Lower, blas.Trans, blas.Unit,
+		n, nrhs, 1, a, lda, b, ldb)
+	impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, -1)
+}

native/lapack_test.go

@@ -40,6 +40,10 @@ func TestDgetrf(t *testing.T) {
 	testlapack.DgetrfTest(t, impl)
 }
 
+func TestDgetrs(t *testing.T) {
+	testlapack.DgetrsTest(t, impl)
+}
+
 func TestDlange(t *testing.T) {
 	testlapack.DlangeTest(t, impl)
 }

testlapack/dgetrs.go

@@ -0,0 +1,116 @@
+package testlapack
+
+import (
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/floats"
+)
+
+type Dgetrser interface {
+	Dgetrfer
+	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
+}
+
+func DgetrsTest(t *testing.T, impl Dgetrser) {
+	for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+		for _, test := range []struct {
+			n, nrhs, lda, ldb int
+			tol               float64
+		}{
+			{3, 3, 0, 0, 1e-14},
+			{3, 3, 0, 0, 1e-14},
+			{3, 5, 0, 0, 1e-14},
+			{3, 5, 0, 0, 1e-14},
+			{5, 3, 0, 0, 1e-14},
+			{5, 3, 0, 0, 1e-14},
+
+			{3, 3, 8, 10, 1e-14},
+			{3, 3, 8, 10, 1e-14},
+			{3, 5, 8, 10, 1e-14},
+			{3, 5, 8, 10, 1e-14},
+			{5, 3, 8, 10, 1e-14},
+			{5, 3, 8, 10, 1e-14},
+
+			{300, 300, 0, 0, 1e-10},
+			{300, 300, 0, 0, 1e-10},
+			{300, 500, 0, 0, 1e-10},
+			{300, 500, 0, 0, 1e-10},
+			{500, 300, 0, 0, 1e-10},
+			{500, 300, 0, 0, 1e-10},
+
+			{300, 300, 700, 600, 1e-10},
+			{300, 300, 700, 600, 1e-10},
+			{300, 500, 700, 600, 1e-10},
+			{300, 500, 700, 600, 1e-10},
+			{500, 300, 700, 600, 1e-10},
+			{500, 300, 700, 600, 1e-10},
+		} {
+			n := test.n
+			nrhs := test.nrhs
+			lda := test.lda
+			if lda == 0 {
+				lda = n
+			}
+			ldb := test.ldb
+			if ldb == 0 {
+				ldb = nrhs
+			}
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rand.Float64()
+			}
+			b := make([]float64, n*ldb)
+			for i := range b {
+				b[i] = rand.Float64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+			bCopy := make([]float64, len(b))
+			copy(bCopy, b)
+
+			ipiv := make([]int, n)
+			for i := range ipiv {
+				ipiv[i] = rand.Int()
+			}
+
+			// Compute the LU factorization.
+			impl.Dgetrf(n, n, a, lda, ipiv)
+			// Solve the system of equations given the result.
+			impl.Dgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb)
+
+			// Check that the system of equations holds.
+			A := blas64.General{
+				Rows:   n,
+				Cols:   n,
+				Stride: lda,
+				Data:   aCopy,
+			}
+			B := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   bCopy,
+			}
+			X := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   b,
+			}
+			tmp := blas64.General{
+				Rows:   n,
+				Cols:   nrhs,
+				Stride: ldb,
+				Data:   make([]float64, n*ldb),
+			}
+			copy(tmp.Data, bCopy)
+			blas64.Gemm(trans, blas.NoTrans, 1, A, X, 0, B)
+			if !floats.EqualApprox(tmp.Data, bCopy, test.tol) {
+				t.Errorf("Linear solve mismatch. trans = %v, n = %v, nrhs = %v, lda = %v, ldb = %v", trans, n, nrhs, lda, ldb)
+			}
+		}
+	}
+}