Working implementation of blocked QR

Improved function documentation

Fixed dlarfb and dlarft and added full tests

Added dgelq2

Working Dgels

Fix many comments and tests

Many PR comment responses

Responded to more PR comments

Many PR comments

native/general.go

@@ -4,20 +4,57 @@
 
 package native
 
-import "github.com/gonum/lapack"
+import (
+	"math"
 
+	"github.com/gonum/lapack"
+)
+
+// Implementation is the native Go implementation of LAPACK routines. It
+// is built on top of calls to the return of blas64.Implementation(), so while
+// this code is in pure Go, the underlying BLAS implementation may not be.
 type Implementation struct{}
 
 var _ lapack.Float64 = Implementation{}
 
 const (
-	badUplo = "lapack: illegal triangle"
-	nLT0    = "lapack: n < 0"
-	badLdA  = "lapack: index of a out of range"
+	badDirect     = "lapack: bad direct"
+	badLdA        = "lapack: index of a out of range"
+	badSide       = "lapack: bad side"
+	badStore      = "lapack: bad store"
+	badTau        = "lapack: tau has insufficient length"
+	badTrans      = "lapack: bad trans"
+	badUplo       = "lapack: illegal triangle"
+	badWork       = "lapack: insufficient working memory"
+	badWorkStride = "lapack: insufficient working array stride"
+	negDimension  = "lapack: negative matrix dimension"
+	nLT0          = "lapack: n < 0"
+	shortWork     = "lapack: working array shorter than declared"
 )
 
-func blockSize() int {
-	return 64
+// checkMatrix verifies the parameters of a matrix input.
+func checkMatrix(m, n int, a []float64, lda int) {
+	if m < 0 {
+		panic("lapack: has negative number of rows")
+	}
+	if m < 0 {
+		panic("lapack: has negative number of columns")
+	}
+	if lda < n {
+		panic("lapack: stride less than number of columns")
+	}
+	if len(a) < (m-1)*lda+n {
+		panic("lapack: insufficient matrix slice length")
+	}
+}
+
+func checkVector(n int, v []float64, inc int) {
+	if n < 0 {
+		panic("lapack: negative matrix length")
+	}
+	if (inc > 0 && (n-1)*inc >= len(v)) || (inc < 0 && (1-n)*inc >= len(v)) {
+		panic("lapack: insufficient vector slice length")
+	}
 }
 
 func min(a, b int) int {
@@ -33,3 +70,23 @@ func max(a, b int) int {
 	}
 	return b
 }
+
+// dlamch is a function in fortran, but since go forces IEEE-754 these are all
+// fixed values. Probably a way to get them as constants.
+// TODO(btracey): Is there a better way to find the smallest number such that 1+E > 1
+
+var dlamchE, dlamchS, dlamchP float64
+
+func init() {
+	onePlusEps := math.Nextafter(1, math.Inf(1))
+	eps := (math.Nextafter(1, math.Inf(1)) - 1) * 0.5
+	dlamchE = eps
+	sfmin := math.SmallestNonzeroFloat64
+	small := 1 / math.MaxFloat64
+	if small >= sfmin {
+		sfmin = small * onePlusEps
+	}
+	dlamchS = sfmin
+	radix := 2.0
+	dlamchP = radix * eps
+}