| // Copyright ©2015 The Gonum Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| package testlapack |
| |
| import ( |
| "testing" |
| |
| "golang.org/x/exp/rand" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| "gonum.org/v1/gonum/floats" |
| ) |
| |
| type Dgelser interface { |
| Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool |
| } |
| |
| func DgelsTest(t *testing.T, impl Dgelser) { |
| rnd := rand.New(rand.NewSource(1)) |
| for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} { |
| for _, test := range []struct { |
| m, n, nrhs, lda, ldb int |
| }{ |
| {3, 4, 5, 0, 0}, |
| {3, 5, 4, 0, 0}, |
| {4, 3, 5, 0, 0}, |
| {4, 5, 3, 0, 0}, |
| {5, 3, 4, 0, 0}, |
| {5, 4, 3, 0, 0}, |
| {3, 4, 5, 10, 20}, |
| {3, 5, 4, 10, 20}, |
| {4, 3, 5, 10, 20}, |
| {4, 5, 3, 10, 20}, |
| {5, 3, 4, 10, 20}, |
| {5, 4, 3, 10, 20}, |
| {3, 4, 5, 20, 10}, |
| {3, 5, 4, 20, 10}, |
| {4, 3, 5, 20, 10}, |
| {4, 5, 3, 20, 10}, |
| {5, 3, 4, 20, 10}, |
| {5, 4, 3, 20, 10}, |
| {200, 300, 400, 0, 0}, |
| {200, 400, 300, 0, 0}, |
| {300, 200, 400, 0, 0}, |
| {300, 400, 200, 0, 0}, |
| {400, 200, 300, 0, 0}, |
| {400, 300, 200, 0, 0}, |
| {200, 300, 400, 500, 600}, |
| {200, 400, 300, 500, 600}, |
| {300, 200, 400, 500, 600}, |
| {300, 400, 200, 500, 600}, |
| {400, 200, 300, 500, 600}, |
| {400, 300, 200, 500, 600}, |
| {200, 300, 400, 600, 500}, |
| {200, 400, 300, 600, 500}, |
| {300, 200, 400, 600, 500}, |
| {300, 400, 200, 600, 500}, |
| {400, 200, 300, 600, 500}, |
| {400, 300, 200, 600, 500}, |
| } { |
| m := test.m |
| n := test.n |
| nrhs := test.nrhs |
| |
| lda := test.lda |
| if lda == 0 { |
| lda = n |
| } |
| a := make([]float64, m*lda) |
| for i := range a { |
| a[i] = rnd.Float64() |
| } |
| aCopy := make([]float64, len(a)) |
| copy(aCopy, a) |
| |
| // Size of b is the same trans or no trans, because the number of rows |
| // has to be the max of (m,n). |
| mb := max(m, n) |
| nb := nrhs |
| ldb := test.ldb |
| if ldb == 0 { |
| ldb = nb |
| } |
| b := make([]float64, mb*ldb) |
| for i := range b { |
| b[i] = rnd.Float64() |
| } |
| bCopy := make([]float64, len(b)) |
| copy(bCopy, b) |
| |
| // Find optimal work length. |
| work := make([]float64, 1) |
| impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, -1) |
| |
| // Perform linear solve |
| work = make([]float64, int(work[0])) |
| lwork := len(work) |
| for i := range work { |
| work[i] = rnd.Float64() |
| } |
| impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, lwork) |
| |
| // Check that the answer is correct by comparing to the normal equations. |
| aMat := blas64.General{ |
| Rows: m, |
| Cols: n, |
| Stride: lda, |
| Data: make([]float64, len(aCopy)), |
| } |
| copy(aMat.Data, aCopy) |
| szAta := n |
| if trans == blas.Trans { |
| szAta = m |
| } |
| aTA := blas64.General{ |
| Rows: szAta, |
| Cols: szAta, |
| Stride: szAta, |
| Data: make([]float64, szAta*szAta), |
| } |
| |
| // Compute Aᵀ * A if notrans and A * Aᵀ otherwise. |
| if trans == blas.NoTrans { |
| blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, aMat, 0, aTA) |
| } else { |
| blas64.Gemm(blas.NoTrans, blas.Trans, 1, aMat, aMat, 0, aTA) |
| } |
| |
| // Multiply by X. |
| X := blas64.General{ |
| Rows: szAta, |
| Cols: nrhs, |
| Stride: ldb, |
| Data: b, |
| } |
| ans := blas64.General{ |
| Rows: aTA.Rows, |
| Cols: X.Cols, |
| Stride: X.Cols, |
| Data: make([]float64, aTA.Rows*X.Cols), |
| } |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aTA, X, 0, ans) |
| |
| B := blas64.General{ |
| Rows: szAta, |
| Cols: nrhs, |
| Stride: ldb, |
| Data: make([]float64, len(bCopy)), |
| } |
| |
| copy(B.Data, bCopy) |
| var ans2 blas64.General |
| if trans == blas.NoTrans { |
| ans2 = blas64.General{ |
| Rows: aMat.Cols, |
| Cols: B.Cols, |
| Stride: B.Cols, |
| Data: make([]float64, aMat.Cols*B.Cols), |
| } |
| } else { |
| ans2 = blas64.General{ |
| Rows: aMat.Rows, |
| Cols: B.Cols, |
| Stride: B.Cols, |
| Data: make([]float64, aMat.Rows*B.Cols), |
| } |
| } |
| |
| // Compute Aᵀ B if Trans or A * B otherwise |
| if trans == blas.NoTrans { |
| blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, B, 0, ans2) |
| } else { |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, B, 0, ans2) |
| } |
| if !floats.EqualApprox(ans.Data, ans2.Data, 1e-12) { |
| t.Errorf("Normal equations not satisfied") |
| } |
| } |
| } |
| } |