Add dependencies for code generator

vendor/gonum.org/v1/gonum/lapack/gonum/dlaqp2.go

@@ -0,0 +1,127 @@
+// Copyright ©2017 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 (
+	"math"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+// Dlaqp2 computes a QR factorization with column pivoting of the block A[offset:m, 0:n]
+// of the m×n matrix A. The block A[0:offset, 0:n] is accordingly pivoted, but not factorized.
+//
+// On exit, the upper triangle of block A[offset:m, 0:n] is the triangular factor obtained.
+// The elements in block A[offset:m, 0:n] below the diagonal, together with tau, represent
+// the orthogonal matrix Q as a product of elementary reflectors.
+//
+// offset is number of rows of the matrix A that must be pivoted but not factorized.
+// offset must not be negative otherwise Dlaqp2 will panic.
+//
+// On exit, jpvt holds the permutation that was applied; the jth column of A*P was the
+// jpvt[j] column of A. jpvt must have length n, otherwise Dlaqp2 will panic.
+//
+// On exit tau holds the scalar factors of the elementary reflectors. It must have length
+// at least min(m-offset, n) otherwise Dlaqp2 will panic.
+//
+// vn1 and vn2 hold the partial and complete column norms respectively. They must have length n,
+// otherwise Dlaqp2 will panic.
+//
+// work must have length n, otherwise Dlaqp2 will panic.
+//
+// Dlaqp2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlaqp2(m, n, offset int, a []float64, lda int, jpvt []int, tau, vn1, vn2, work []float64) {
+	switch {
+	case m < 0:
+		panic(mLT0)
+	case n < 0:
+		panic(nLT0)
+	case offset < 0:
+		panic(offsetLT0)
+	case offset > m:
+		panic(offsetGTM)
+	case lda < max(1, n):
+		panic(badLdA)
+	}
+
+	// Quick return if possible.
+	if m == 0 || n == 0 {
+		return
+	}
+
+	mn := min(m-offset, n)
+	switch {
+	case len(a) < (m-1)*lda+n:
+		panic(shortA)
+	case len(jpvt) != n:
+		panic(badLenJpvt)
+	case len(tau) < mn:
+		panic(shortTau)
+	case len(vn1) < n:
+		panic(shortVn1)
+	case len(vn2) < n:
+		panic(shortVn2)
+	case len(work) < n:
+		panic(shortWork)
+	}
+
+	tol3z := math.Sqrt(dlamchE)
+
+	bi := blas64.Implementation()
+
+	// Compute factorization.
+	for i := 0; i < mn; i++ {
+		offpi := offset + i
+
+		// Determine ith pivot column and swap if necessary.
+		p := i + bi.Idamax(n-i, vn1[i:], 1)
+		if p != i {
+			bi.Dswap(m, a[p:], lda, a[i:], lda)
+			jpvt[p], jpvt[i] = jpvt[i], jpvt[p]
+			vn1[p] = vn1[i]
+			vn2[p] = vn2[i]
+		}
+
+		// Generate elementary reflector H_i.
+		if offpi < m-1 {
+			a[offpi*lda+i], tau[i] = impl.Dlarfg(m-offpi, a[offpi*lda+i], a[(offpi+1)*lda+i:], lda)
+		} else {
+			tau[i] = 0
+		}
+
+		if i < n-1 {
+			// Apply H_i^T to A[offset+i:m, i:n] from the left.
+			aii := a[offpi*lda+i]
+			a[offpi*lda+i] = 1
+			impl.Dlarf(blas.Left, m-offpi, n-i-1, a[offpi*lda+i:], lda, tau[i], a[offpi*lda+i+1:], lda, work)
+			a[offpi*lda+i] = aii
+		}
+
+		// Update partial column norms.
+		for j := i + 1; j < n; j++ {
+			if vn1[j] == 0 {
+				continue
+			}
+
+			// The following marked lines follow from the
+			// analysis in Lapack Working Note 176.
+			r := math.Abs(a[offpi*lda+j]) / vn1[j] // *
+			temp := math.Max(0, 1-r*r)             // *
+			r = vn1[j] / vn2[j]                    // *
+			temp2 := temp * r * r                  // *
+			if temp2 < tol3z {
+				var v float64
+				if offpi < m-1 {
+					v = bi.Dnrm2(m-offpi-1, a[(offpi+1)*lda+j:], lda)
+				}
+				vn1[j] = v
+				vn2[j] = v
+			} else {
+				vn1[j] *= math.Sqrt(temp) // *
+			}
+		}
+	}
+}