lapack/gonum: add Dlauu2 and Dlauum

lapack/gonum/dlauu2.go

@@ -0,0 +1,61 @@
+// Copyright ©2018 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 gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlauu2 computes the product
+//  U * U^T  if uplo is blas.Upper
+//  L^T * L  if uplo is blas.Lower
+// where U or L is stored in the upper or lower triangular part of A.
+// Only the upper or lower triangle of the result is stored, overwriting
+// the corresponding factor in A.
+func (impl Implementation) Dlauu2(uplo blas.Uplo, n int, a []float64, lda int) {
+	switch {
+	case uplo != blas.Upper && uplo != blas.Lower:
+		panic(badUplo)
+	case n < 0:
+		panic(nLT0)
+	case lda < max(1, n):
+		panic(badLdA)
+	case len(a) < (n-1)*lda+n:
+		panic("lapack: a has insufficient length")
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		return
+	}
+
+	bi := blas64.Implementation()
+	if uplo == blas.Upper {
+		// Compute the product U*U^T.
+		for i := 0; i < n; i++ {
+			aii := a[i*lda+i]
+			if i < n-1 {
+				a[i*lda+i] = bi.Ddot(n-i, a[i*lda+i:], 1, a[i*lda+i:], 1)
+				bi.Dgemv(blas.NoTrans, i, n-i-1, 1, a[i+1:], lda, a[i*lda+i+1:], 1,
+					aii, a[i:], lda)
+			} else {
+				bi.Dscal(i+1, aii, a[i:], lda)
+			}
+		}
+	} else {
+		// Compute the product L^T*L.
+		for i := 0; i < n; i++ {
+			aii := a[i*lda+i]
+			if i < n-1 {
+				a[i*lda+i] = bi.Ddot(n-i, a[i*lda+i:], lda, a[i*lda+i:], lda)
+				bi.Dgemv(blas.Trans, n-i-1, i, 1, a[(i+1)*lda:], lda, a[(i+1)*lda+i:], lda,
+					aii, a[i*lda:], 1)
+			} else {
+				bi.Dscal(i+1, aii, a[i*lda:], 1)
+			}
+		}
+	}
+}

lapack/gonum/dlauum.go

@@ -0,0 +1,79 @@
+// Copyright ©2018 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 gonum
+
+import (
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlauum computes the product
+//  U * U^T  if uplo is blas.Upper
+//  L^T * L  if uplo is blas.Lower
+// where U or L is stored in the upper or lower triangular part of A.
+// Only the upper or lower triangle of the result is stored, overwriting
+// the corresponding factor in A.
+func (impl Implementation) Dlauum(uplo blas.Uplo, n int, a []float64, lda int) {
+	switch {
+	case uplo != blas.Upper && uplo != blas.Lower:
+		panic(badUplo)
+	case n < 0:
+		panic(nLT0)
+	case lda < max(1, n):
+		panic(badLdA)
+	case len(a) < (n-1)*lda+n:
+		panic("lapack: a has insufficient length")
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		return
+	}
+
+	// Determine the block size.
+	opts := "U"
+	if uplo == blas.Lower {
+		opts = "L"
+	}
+	nb := impl.Ilaenv(1, "DLAUUM", opts, n, -1, -1, -1)
+
+	if nb <= 1 || n <= nb {
+		// Use unblocked code.
+		impl.Dlauu2(uplo, n, a, lda)
+		return
+	}
+
+	// Use blocked code.
+	bi := blas64.Implementation()
+	if uplo == blas.Upper {
+		// Compute the product U*U^T.
+		for i := 0; i < n; i += nb {
+			ib := min(nb, n-i)
+			bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.NonUnit,
+				i, ib, 1, a[i*lda+i:], lda, a[i:], lda)
+			impl.Dlauu2(blas.Upper, ib, a[i*lda+i:], lda)
+			if n-i-ib > 0 {
+				bi.Dgemm(blas.NoTrans, blas.Trans, i, ib, n-i-ib,
+					1, a[i+ib:], lda, a[i*lda+i+ib:], lda, 1, a[i:], lda)
+				bi.Dsyrk(blas.Upper, blas.NoTrans, ib, n-i-ib,
+					1, a[i*lda+i+ib:], lda, 1, a[i*lda+i:], lda)
+			}
+		}
+	} else {
+		// Compute the product L^T*L.
+		for i := 0; i < n; i += nb {
+			ib := min(nb, n-i)
+			bi.Dtrmm(blas.Left, blas.Lower, blas.Trans, blas.NonUnit,
+				ib, i, 1, a[i*lda+i:], lda, a[i*lda:], lda)
+			impl.Dlauu2(blas.Lower, ib, a[i*lda+i:], lda)
+			if n-i-ib > 0 {
+				bi.Dgemm(blas.Trans, blas.NoTrans, ib, i, n-i-ib,
+					1, a[(i+ib)*lda+i:], lda, a[(i+ib)*lda:], lda, 1, a[i*lda:], lda)
+				bi.Dsyrk(blas.Lower, blas.Trans, ib, n-i-ib,
+					1, a[(i+ib)*lda+i:], lda, 1, a[i*lda+i:], lda)
+			}
+		}
+	}
+}