lapack/testlapack: test Dpbtf2 like Dpbtrf

lapack/testlapack/dpbtf2.go

@@ -5,6 +5,8 @@
 package testlapack
 
 import (
+	"fmt"
+	"math"
 	"testing"
 
 	"golang.org/x/exp/rand"
@@ -13,40 +15,81 @@ import (
 )
 
 type Dpbtf2er interface {
-	Dpbtf2(ul blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
-	Dpotrfer
+	Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
 }
 
+// Dpbtf2Test tests Dpbtf2 on random symmetric positive definite band matrices
+// by checking that the Cholesky factors multiply back to the original matrix.
 func Dpbtf2Test(t *testing.T, impl Dpbtf2er) {
-	// Test random symmetric banded matrices against the full version.
+	// TODO(vladimir-ch): include expected-failure test case.
 	rnd := rand.New(rand.NewSource(1))
-
-	for _, n := range []int{5, 10, 20} {
-		for _, kb := range []int{0, 1, 3, n - 1} {
-			for _, ldoff := range []int{0, 4} {
-				for _, ul := range []blas.Uplo{blas.Upper, blas.Lower} {
-					ldab := kb + 1 + ldoff
-					band, sym := randSymBand(ul, n, kb, ldab, rnd)
-
-					// Compute the Cholesky decomposition of the symmetric matrix.
-					ok := impl.Dpotrf(ul, sym.N, sym.Data, sym.Stride)
-					if !ok {
-						panic("bad test: symmetric cholesky decomp failed")
-					}
-
-					// Compute the Cholesky decomposition of the banded matrix.
-					ok = impl.Dpbtf2(band.Uplo, band.N, band.K, band.Data, band.Stride)
-					if !ok {
-						t.Errorf("SymBand cholesky decomp failed")
-					}
-
-					// Compare the result to the Symmetric decomposition.
-					sb := symBandToSym(ul, band.Data, n, kb, ldab)
-					if !equalApproxSymmetric(sym, sb, 1e-10) {
-						t.Errorf("chol mismatch banded and sym. n = %v, kb = %v, ldoff = %v", n, kb, ldoff)
-					}
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20} {
+		for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} {
+			for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+				for _, ldab := range []int{kd + 1, kd + 1 + 7} {
+					dpbtf2Test(t, impl, rnd, uplo, n, kd, ldab)
 				}
 			}
 		}
 	}
 }
+
+func dpbtf2Test(t *testing.T, impl Dpbtf2er, rnd *rand.Rand, uplo blas.Uplo, n, kd int, ldab int) {
+	const tol = 1e-12
+
+	name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,ldab=%v", string(uplo), n, kd, ldab)
+
+	// Allocate a band matrix and fill it with random numbers.
+	ab := make([]float64, n*ldab)
+	for i := range ab {
+		ab[i] = rnd.NormFloat64()
+	}
+	// Make sure that the matrix U or L has a sufficiently positive diagonal.
+	switch uplo {
+	case blas.Upper:
+		for i := 0; i < n; i++ {
+			ab[i*ldab] = 2 + rnd.Float64()
+		}
+	case blas.Lower:
+		for i := 0; i < n; i++ {
+			ab[i*ldab+kd] = 2 + rnd.Float64()
+		}
+	}
+	// Compute U^T*U or L*L^T. The resulting (symmetric) matrix A will be positive definite.
+	dsbmm(uplo, n, kd, ab, ldab)
+
+	// Compute the Cholesky decomposition of A.
+	abFac := make([]float64, len(ab))
+	copy(abFac, ab)
+	ok := impl.Dpbtf2(uplo, n, kd, abFac, ldab)
+	if !ok {
+		t.Fatalf("%v: bad test matrix, Dpbtf2 failed", name)
+	}
+
+	if n == 0 {
+		return
+	}
+
+	// Reconstruct an symmetric band matrix from the U^T*U or L*L^T factorization, overwriting abFac.
+	dsbmm(uplo, n, kd, abFac, ldab)
+
+	// Compute and check the max-norm distance between the reconstructed and original matrix A.
+	var diff float64
+	switch uplo {
+	case blas.Upper:
+		for i := 0; i < n; i++ {
+			for j := 0; j < min(kd+1, n-i); j++ {
+				diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
+			}
+		}
+	case blas.Lower:
+		for i := 0; i < n; i++ {
+			for j := max(0, kd-i); j < kd+1; j++ {
+				diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
+			}
+		}
+	}
+	if diff > tol {
+		t.Errorf("%v: unexpected result, diff=%v", name, diff)
+	}
+}