Introducing the LinearCoeff method as a requirement of the PolynomialLikeVector set of objects (#15)

* Reintroduced LinearCoeff function for PolynomialLikeVector interface and got it working! (Basically)

* Added sanity test to check a corner case for the variable vector's LinearCoeff function

---------

Co-authored-by: Kwesi Rutledge <[email protected]>

Author: kwesiRutledge

symbolic/constant_matrix.go

@@ -2,6 +2,7 @@ package symbolic
 
 import (
 	"fmt"
+
 	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
 	"gonum.org/v1/gonum/mat"
 )

symbolic/constant_vector.go

@@ -101,8 +101,8 @@ Description:
 
 	This function returns a slice of the coefficients in the expression. For constants, this is always nil.
 */
-func (kv KVector) LinearCoeff() mat.Dense {
-	return ZerosMatrix(kv.Len(), kv.Len())
+func (kv KVector) LinearCoeff(wrt ...[]Variable) mat.Dense {
+	return PolynomialLikeVector_SharedLinearCoeffCalc(kv, wrt...)
 }
 
 /*

symbolic/monomial_vector.go

@@ -714,3 +714,20 @@ Description:
 func (mv MonomialVector) Power(exponent int) Expression {
 	return VectorPowerTemplate(mv, exponent)
 }
+
+/*
+LinearCoeff
+Description:
+
+	This function retrieves the "linear coefficient" of the monomial vector.
+	In math, this is extracting the matrix A such that:
+
+		mv' = L * v
+
+	where:
+	- v is the vector of variables for the monomial vector.
+	- mv' is the monomial vector mv with ONLY the terms that have degree 1
+*/
+func (mv MonomialVector) LinearCoeff(wrt ...[]Variable) mat.Dense {
+	return PolynomialLikeVector_SharedLinearCoeffCalc(mv, wrt...)
+}

symbolic/polynomial_like_matrix.go

@@ -2,6 +2,7 @@ package symbolic
 
 import (
 	"fmt"
+
 	"gonum.org/v1/gonum/mat"
 )
 

symbolic/polynomial_like_vector.go

@@ -9,6 +9,7 @@ Description:
 import (
 	"fmt"
 
+	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
 	"gonum.org/v1/gonum/mat"
 )
 
@@ -29,8 +30,8 @@ type PolynomialLikeVector interface {
 	// Variables returns the number of variables in the expression.
 	Variables() []Variable
 
-	//// Coeffs returns a slice of the coefficients in the expression
-	//LinearCoeff() mat.Dense
+	// Coeffs returns a slice of the coefficients in the expression
+	LinearCoeff(wrt ...[]Variable) mat.Dense
 
 	// Constant returns the constant additive value in the expression
 	Constant() mat.VecDense
@@ -157,3 +158,56 @@ func ToPolynomialLikeVector(e interface{}) (PolynomialLikeVector, error) {
 		)
 	}
 }
+
+/*
+PolynomialLikeVector_SharedLinearCoeffCalc
+Description:
+
+	This function retrieves the "linear coefficient" of the monomial vector.
+	In math, this is extracting the matrix A such that:
+
+		mv = L * v
+
+	where v is the vector of variables for the monomial vector.
+*/
+func PolynomialLikeVector_SharedLinearCoeffCalc(plv PolynomialLikeVector, wrt ...[]Variable) mat.Dense {
+	// Input Processing
+	err := plv.Check()
+	if err != nil {
+		panic(err)
+	}
+
+	// Check to see if the user provided a slice of variables
+	var wrtVars []Variable
+	switch len(wrt) {
+	case 0:
+		wrtVars = plv.Variables()
+	case 1:
+		wrtVars = wrt[0]
+	default:
+		panic(fmt.Errorf("Too many inputs provided to LinearCoeff() method."))
+	}
+
+	// Check the wrtVars
+	if len(wrtVars) == 0 {
+		panic(
+			smErrors.CanNotGetLinearCoeffOfConstantError{plv},
+		)
+	}
+
+	// Iterate through each monomial in the vector and extract the Linear Coefficient vector
+	// for each
+	L := mat.NewDense(plv.Len(), len(wrtVars), nil)
+
+	for ii := 0; ii < plv.Len(); ii++ {
+		mvII := plv.AtVec(ii)
+
+		// Get Coefficients for mvII and populate it
+		coeffsII := mvII.LinearCoeff(wrtVars)
+		for jj := 0; jj < len(wrtVars); jj++ {
+			L.Set(ii, jj, coeffsII.AtVec(jj))
+		}
+	}
+
+	return *L
+}

symbolic/polynomial_vector.go

@@ -161,47 +161,8 @@ Description:
 	The output is a matrix where element (ii,jj) of the matrix describes the coefficient
 	of variable jj (from pv.Variables()) in the polynomial at index ii.
 */
-func (pv PolynomialVector) LinearCoeff(vSlices ...[]Variable) mat.Dense {
-	// Input Processing
-	err := pv.Check()
-	if err != nil {
-		panic(err)
-	}
-
-	// Check to see if the user provided a slice of variables
-	var varSlice []Variable
-	switch len(vSlices) {
-	case 0:
-		varSlice = pv.Variables()
-	case 1:
-		varSlice = vSlices[0]
-	default:
-		panic(fmt.Errorf("Too many inputs provided to LinearCoeff() method."))
-	}
-
-	if len(varSlice) == 0 {
-		panic(
-			smErrors.CanNotGetLinearCoeffOfConstantError{Expression: pv},
-		)
-	}
-
-	// Constants
-	var linearCoeff mat.Dense = ZerosMatrix(pv.Len(), len(varSlice))
-
-	// Algorithm
-	for rowIndex := 0; rowIndex < pv.Len(); rowIndex++ {
-		// Row i of the matrix linearCoeff is the linear coefficients of the polynomial at index i
-		polynomialII := pv[rowIndex]
-		linearCoeffsII := polynomialII.LinearCoeff(varSlice)
-
-		// Convert linearCoeffsII to a slice of float64's
-		linearCoeffsIIAsSlice := make([]float64, linearCoeffsII.Len())
-		for jj := 0; jj < linearCoeffsII.Len(); jj++ {
-			linearCoeffsIIAsSlice[jj] = linearCoeffsII.AtVec(jj)
-		}
-		linearCoeff.SetRow(rowIndex, linearCoeffsIIAsSlice)
-	}
-	return linearCoeff
+func (pv PolynomialVector) LinearCoeff(wrt ...[]Variable) mat.Dense {
+	return PolynomialLikeVector_SharedLinearCoeffCalc(pv, wrt...)
 }
 
 /*

symbolic/variable_vector.go

@@ -119,8 +119,8 @@ Description:
 	Returns the matrix which is multiplied by Variables to get the current "expression".
 	For a single vector, this is an identity matrix.
 */
-func (vv VariableVector) LinearCoeff() mat.Dense {
-	return Identity(vv.Len())
+func (vv VariableVector) LinearCoeff(wrt ...[]Variable) mat.Dense {
+	return PolynomialLikeVector_SharedLinearCoeffCalc(vv, wrt...)
 }
 
 /*

testing/symbolic/constant_vector_test.go

@@ -8,12 +8,13 @@ Description:
 
 import (
 	"fmt"
+	"strings"
+	"testing"
+
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
 	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"gonum.org/v1/gonum/mat"
-	"strings"
-	"testing"
 )
 
 /*
@@ -150,11 +151,12 @@ func TestConstantVector_LinearCoeff1(t *testing.T) {
 	// Constants
 	N := 11
 	kv := symbolic.VecDenseToKVector(symbolic.OnesVector(N))
+	vv := symbolic.NewVariableVector(13)
 
 	// Test
 	for ii := 0; ii < N; ii++ {
-		for jj := 0; jj < N; jj++ {
-			if L := kv.LinearCoeff(); L.At(ii, jj) != 0 {
+		for jj := 0; jj < vv.Len(); jj++ {
+			if L := kv.LinearCoeff(vv); L.At(ii, jj) != 0 {
 				t.Errorf(
 					"Expected kv.LinearCoeff().At(%v,%v) to be 0; received %v",
 					ii, jj,

testing/symbolic/monomial_vector_test.go

@@ -2,13 +2,14 @@ package symbolic_test
 
 import (
 	"fmt"
+	"math"
+	"strings"
+	"testing"
+
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
 	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"gonum.org/v1/gonum/mat"
-	"math"
-	"strings"
-	"testing"
 )
 
 /*
@@ -1842,3 +1843,42 @@ func TestMonomialVector_Power2(t *testing.T) {
 		)
 	}
 }
+
+/*
+TestMonomialVector_LinearCoeff1
+Description:
+
+	Tests that the LinearCoeff1 method properly returns a matrix of all zeros,
+	when called on a monomial vector containing ALL monomials with degree > 1.
+*/
+func TestMonomialVector_LinearCoeff1(t *testing.T) {
+	// Setup
+	n := 11
+	x1 := symbolic.NewVariable()
+	x2 := symbolic.NewVariable()
+
+	var mSlice []symbolic.Monomial
+	for ii := 0; ii < n; ii++ {
+		// Assemble Monomial slice
+		mSlice = append(
+			mSlice,
+			symbolic.Monomial{
+				Coefficient:     3.14,
+				VariableFactors: []symbolic.Variable{x1, x2},
+				Exponents:       []int{1, ii + 1},
+			},
+		)
+	}
+
+	// Create monomial vector
+	mv0 := symbolic.MonomialVector(mSlice)
+
+	// Find LinearCoeff
+	L0 := mv0.LinearCoeff()
+
+	// Compare all elements to zeros
+	ZerosMat1 := symbolic.ZerosMatrix(n, 2)
+	if !mat.EqualApprox(&L0, &ZerosMat1, 0.001) {
+		t.Errorf("The two matrices are not equal!")
+	}
+}

testing/symbolic/polynomial_vector_test.go

@@ -7,10 +7,11 @@ Description:
 */
 
 import (
-	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
-	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"strings"
 	"testing"
+
+	"github.com/MatProGo-dev/SymbolicMath.go/smErrors"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 )
 
 /*
@@ -525,7 +526,7 @@ func TestPolynomialVector_LinearCoeff1(t *testing.T) {
 TestPolynomialVector_LinearCoeff2
 Description:
 
-	This test verifies that the LinearCoeff method panics when a polynomial of all
+	This test verifies that the LinearCoeff method DOES NOT PANIC when a polynomial of all
 	constants is provided to the method.
 */
 func TestPolynomialVector_LinearCoeff2(t *testing.T) {

testing/symbolic/variable_vector_test.go

@@ -157,6 +157,77 @@ func TestVariableVector_LinearCoeff1(t *testing.T) {
 	}
 }
 
+/*
+TestVariableVector_LinearCoeff2
+Description:
+
+	Verifies that the LinearCoeff method returns a non-square matrix when it is a
+	LONG vector composed of only 2 different variables.
+*/
+func TestVariableVector_LinearCoeff2(t *testing.T) {
+	// Constants
+	N := 111
+	vv := symbolic.NewVariableVector(2)
+	var vvSlice2 []symbolic.Variable
+	for ii := 0; ii < N; ii++ {
+		if ii%2 == 0 {
+			vvSlice2 = append(vvSlice2, vv[0])
+		} else {
+			vvSlice2 = append(vvSlice2, vv[1])
+		}
+	}
+	vv2 := symbolic.VariableVector(vvSlice2)
+
+	// Test
+	L2 := vv2.LinearCoeff()
+
+	// Compare dimensions
+	nRows, nCols := L2.Dims()
+	if nRows != N {
+		t.Errorf("Expeected L2 to contain %v rows; received %v", N, nRows)
+	}
+
+	if nCols != 2 {
+		t.Errorf("Expected L2 to contain %v rows; received %v", 2, nCols)
+	}
+
+	// Check the elements
+	for ii := 0; ii < nRows; ii++ {
+		if ii%2 == 0 {
+			if L2.At(ii, 0) != 1 {
+				t.Errorf(
+					"Expected vv.LinearCoeff().At(%v,%v) to be 1; received %v",
+					ii, 0,
+					L2.At(ii, 0),
+				)
+			}
+			if L2.At(ii, 1) != 0 {
+				t.Errorf(
+					"Expected vv.LinearCoeff().At(%v,%v) to be 0; received %v",
+					ii, 1,
+					L2.At(ii, 1),
+				)
+			}
+			continue
+		} else {
+			if L2.At(ii, 0) != 0 {
+				t.Errorf(
+					"Expected vv.LinearCoeff().At(%v,%v) to be 0; received %v",
+					ii, 0,
+					L2.At(ii, 0),
+				)
+			}
+			if L2.At(ii, 1) != 1 {
+				t.Errorf(
+					"Expected vv.LinearCoeff().At(%v,%v) to be 1; received %v",
+					ii, 1,
+					L2.At(ii, 1),
+				)
+			}
+		}
+	}
+}
+
 /*
 TestVariableVector_Plus1
 Description: