Add the linear solve routines (Dgetrs, Dgels) to the lapack64 interface

cgo/lapack.go

@@ -36,6 +36,13 @@ func min(m, n int) int {
 	return n
 }
 
+func max(m, n int) int {
+	if m < n {
+		return n
+	}
+	return m
+}
+
 // checkMatrix verifies the parameters of a matrix input.
 // Copied from lapack/native. Keep in sync.
 func checkMatrix(m, n int, a []float64, lda int) {
@@ -193,6 +200,50 @@ func (impl Implementation) Dgeqrf(m, n int, a []float64, lda int, tau, work []fl
 	clapack.Dgeqrf(m, n, a, lda, tau)
 }
 
+// Dgels finds a minimum-norm solution based on the matrices A and B using the
+// QR or LQ factorization. Dgels returns false if the matrix
+// A is singular, and true if this solution was successfully found.
+//
+// The minimization problem solved depends on the input parameters.
+//
+//  1. If m >= n and trans == blas.NoTrans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+//  2. If m < n and trans == blas.NoTrans, Dgels finds the minimum norm solution of
+//     A * X = B.
+//  3. If m >= n and trans == blas.Trans, Dgels finds the minimum norm solution of
+//     A^T * X = B.
+//  4. If m < n and trans == blas.Trans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+// Note that the least-squares solutions (cases 1 and 3) perform the minimization
+// per column of B. This is not the same as finding the minimum-norm matrix.
+//
+// The matrix A is a general matrix of size m×n and is modified during this call.
+// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
+// the elements of b specify the input matrix B. B has size m×nrhs if
+// trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
+// leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,
+// this submatrix is of size n×nrhs, and of size m×nrhs otherwise.
+//
+// The C interface does not support providing temporary storage. To provide compatibility
+// with native, lwork == -1 will not run Dgeqrf but will instead write the minimum
+// work necessary to work[0]. If len(work) < lwork, Dgeqrf will panic.
+func (impl Implementation) Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool {
+	mn := min(m, n)
+	if lwork == -1 {
+		work[0] = float64(mn + max(mn, nrhs))
+		return true
+	}
+	checkMatrix(m, n, a, lda)
+	checkMatrix(mn, nrhs, b, ldb)
+	if len(work) < lwork {
+		panic(shortWork)
+	}
+	if lwork < mn+max(mn, nrhs) {
+		panic(badWork)
+	}
+	return clapack.Dgels(trans, m, n, nrhs, a, lda, b, ldb)
+}
+
 // Dgetf2 computes the LU decomposition of the m×n matrix A.
 // The LU decomposition is a factorization of a into
 //  A = P * L * U
@@ -223,7 +274,7 @@ func (Implementation) Dgetf2(m, n int, a []float64, lda int, ipiv []int) (ok boo
 }
 
 // Dgetrf computes the LU decomposition of the m×n matrix A.
-// The LU decomposition is a factorization of a into
+// The LU decomposition is a factorization of A into
 //  A = P * L * U
 // where P is a permutation matrix, L is a unit lower triangular matrix, and
 // U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored

cgo/lapack_test.go

@@ -20,6 +20,10 @@ func TestDgelq2(t *testing.T) {
 	testlapack.Dgelq2Test(t, impl)
 }
 
+func TestDgels(t *testing.T) {
+	testlapack.DgelsTest(t, impl)
+}
+
 func TestDgelqf(t *testing.T) {
 	testlapack.DgelqfTest(t, impl)
 }

lapack.go

@@ -23,9 +23,12 @@ type Complex128 interface{}
 
 // Float64 defines the public float64 LAPACK API supported by gonum/lapack.
 type Float64 interface {
+	Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
 	Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
 	Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
 	Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
+	Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool)
+	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
 }
 
 // Direct specifies the direction of the multiplication for the Householder matrix.

lapack64/lapack64.go

@@ -48,6 +48,39 @@ func Potrf(a blas64.Symmetric) (t blas64.Triangular, ok bool) {
 	return
 }
 
+// Gels finds a minimum-norm solution based on the matrices A and B using the
+// QR or LQ factorization. Dgels returns false if the matrix
+// A is singular, and true if this solution was successfully found.
+//
+// The minimization problem solved depends on the input parameters.
+//
+//  1. If m >= n and trans == blas.NoTrans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+//  2. If m < n and trans == blas.NoTrans, Dgels finds the minimum norm solution of
+//     A * X = B.
+//  3. If m >= n and trans == blas.Trans, Dgels finds the minimum norm solution of
+//     A^T * X = B.
+//  4. If m < n and trans == blas.Trans, Dgels finds X such that || A*X - B||_2
+//     is minimized.
+// Note that the least-squares solutions (cases 1 and 3) perform the minimization
+// per column of B. This is not the same as finding the minimum-norm matrix.
+//
+// The matrix A is a general matrix of size m×n and is modified during this call.
+// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
+// the elements of b specify the input matrix B. B has size m×nrhs if
+// trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
+// leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,
+// this submatrix is of size n×nrhs, and of size m×nrhs otherwise.
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= max(m,n) + max(m,n,nrhs), and this function will panic
+// otherwise. A longer work will enable blocked algorithms to be called.
+// In the special case that lwork == -1, work[0] will be set to the optimal working
+// length.
+func Gels(trans blas.Transpose, a blas64.General, b blas64.General, work []float64, lwork int) {
+	lapack64.Dgels(trans, a.Rows, a.Cols, b.Cols, a.Data, a.Stride, b.Data, b.Stride, work, lwork)
+}
+
 // Geqrf computes the QR factorization of the m×n matrix A using a blocked
 // algorithm. A is modified to contain the information to construct Q and R.
 // The upper triangle of a contains the matrix R. The lower triangular elements
@@ -93,3 +126,39 @@ func Geqrf(a blas64.General, tau, work []float64, lwork int) {
 func Gelqf(a blas64.General, tau, work []float64, lwork int) {
 	lapack64.Dgelqf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
 }
+
+// Getrf computes the LU decomposition of the m×n matrix A.
+// The LU decomposition is a factorization of A into
+//  A = P * L * U
+// where P is a permutation matrix, L is a unit lower triangular matrix, and
+// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
+// in place into a.
+//
+// ipiv is a permutation vector. It indicates that row i of the matrix was
+// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
+// otherwise. ipiv is zero-indexed.
+//
+// Dgetrf is the blocked version of the algorithm.
+//
+// Dgetrf returns whether the matrix A is singular. The LU decomposition will
+// be computed regardless of the singularity of A, but division by zero
+// will occur if the false is returned and the result is used to solve a
+// system of equations.
+func Getrf(a blas64.General, ipiv []int) bool {
+	return lapack64.Dgetrf(a.Rows, a.Cols, a.Data, a.Stride, ipiv)
+}
+
+// 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 Getrf. ipiv is zero-indexed.
+func Getrs(trans blas.Transpose, a blas64.General, b blas64.General, ipiv []int) {
+	lapack64.Dgetrs(trans, a.Cols, b.Cols, a.Data, a.Stride, ipiv, b.Data, b.Stride)
+}

native/dgels.go

@@ -9,7 +9,7 @@ import (
 	"github.com/gonum/lapack"
 )
 
-// Dgels finds a minimum-norm solution based on the matrices a and b using the
+// Dgels finds a minimum-norm solution based on the matrices A and B using the
 // QR or LQ factorization. Dgels returns false if the matrix
 // A is singular, and true if this solution was successfully found.
 //
@@ -26,8 +26,8 @@ import (
 // Note that the least-squares solutions (cases 1 and 3) perform the minimization
 // per column of B. This is not the same as finding the minimum-norm matrix.
 //
-// The matrix a is a general matrix of size m×n and is modified during this call.
-// The input matrix b is of size max(m,n)×nrhs, and serves two purposes. On entry,
+// The matrix A is a general matrix of size m×n and is modified during this call.
+// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
 // the elements of b specify the input matrix B. B has size m×nrhs if
 // trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
 // leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,

native/dgetrf.go

@@ -5,8 +5,8 @@ import (
 	"github.com/gonum/blas/blas64"
 )
 
-// Dgetrf computes the LU decomposition of the m×n matrix a.
-// The LU decomposition is a factorization of a into
+// Dgetrf computes the LU decomposition of the m×n matrix A.
+// The LU decomposition is a factorization of A into
 //  A = P * L * U
 // where P is a permutation matrix, L is a unit lower triangular matrix, and
 // U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored