Remove norm methods from matrix classes. To compute the norm of a ten…

src/main/java/org/flag4j/core/MatrixComparisonsMixin.java

@@ -41,12 +41,4 @@ public interface MatrixComparisonsMixin<T> {
      * @return True if this matrix is the identity matrix. Otherwise, returns false.
      */
     boolean isI();
-
-
-    /**
-     * Checks if matrices are inverses of each other.
-     * @param B Second matrix.
-     * @return True if matrix B is an inverse of this matrix. Otherwise, returns false. Otherwise, returns false.
-     */
-    boolean isInv(T B);
 }

src/main/java/org/flag4j/core/MatrixOperationsMixin.java

@@ -30,7 +30,6 @@
 import org.flag4j.dense.CVector;
 import org.flag4j.dense.Matrix;
 import org.flag4j.dense.Vector;
-import org.flag4j.linalg.decompositions.svd.SVD;
 import org.flag4j.sparse.CooCMatrix;
 import org.flag4j.sparse.CooCVector;
 import org.flag4j.sparse.CooMatrix;
@@ -1058,15 +1057,6 @@ default W stack(CooCVector b, int axis) {
     X tr();
 
 
-    /**
-     * Computes the condition number of this matrix using {@link SVD SVD}.
-     * Specifically, the condition number is computed as the maximum singular value divided by the minimum singular
-     * value of this matrix.
-     *
-     * @return The condition number of this matrix (Assuming Frobenius norm).
-     */
-    double cond();
-
     /**
      * Extracts the diagonal elements of this matrix and returns them as a vector.
      * @return A vector containing the diagonal entries of this matrix.

src/main/java/org/flag4j/core/MatrixPropertiesMixin.java

@@ -118,22 +118,6 @@ default boolean isInvertible() {
     }
 
 
-    /**
-     * Computes the L<sub>p, q</sub> norm of this matrix.
-     * @param p P value in the L<sub>p, q</sub> norm.
-     * @param q Q value in the L<sub>p, q</sub> norm.
-     * @return The L<sub>p, q</sub> norm of this matrix.
-     */
-    double norm(double p, double q);
-
-
-    /**
-     * Computes the max norm of a matrix.
-     * @return The max norm of this matrix.
-     */
-    double maxNorm();
-
-
     /**
      * Computes the rank of this matrix (i.e. the dimension of the column space of this matrix).
      * Note that here, rank is <b>NOT</b> the same as a tensor rank.

src/main/java/org/flag4j/core/TensorPropertiesMixin.java

@@ -75,28 +75,4 @@ interface TensorPropertiesMixin {
      * entry (in row-major ordering) are returned.
      */
     int[] argMax();
-
-
-    /**
-     * Computes the 2-norm of this tensor. This is equivalent to {@link #norm(double) norm(2)}.
-     * @return the 2-norm of this tensor.
-     */
-    double norm();
-
-
-    /**
-     * Computes the p-norm of this tensor.
-     * @param p The p value in the p-norm. <br>
-     *          - If p is inf, then this method computes the maximum/infinite norm.
-     * @return The p-norm of this tensor.
-     * @throws IllegalArgumentException If p is less than 1.
-     */
-    double norm(double p);
-
-
-    /**
-     * Computes the maximum/infinite norm of this tensor.
-     * @return The maximum/infinite norm of this tensor.
-     */
-    double infNorm();
 }

src/main/java/org/flag4j/core/dense_base/RealDenseTensorBase.java

@@ -136,12 +136,6 @@ public int[] argMax() {
     }
 
 
-    @Override
-    public double infNorm() {
-        return AggregateReal.maxAbs(entries);
-    }
-
-
     @Override
     public boolean isPos() {
         return RealProperties.isPos(entries);

src/main/java/org/flag4j/core/sparse_base/ComplexSparseTensorBase.java

@@ -168,12 +168,6 @@ public double maxAbs() {
     }
 
 
-    @Override
-    public double infNorm() {
-        return AggregateComplex.maxAbs(entries);
-    }
-
-
     @Override
     public boolean isZeros() {
         return ComplexProperties.isZeros(entries);

src/main/java/org/flag4j/core/sparse_base/RealSparseTensorBase.java

@@ -182,12 +182,6 @@ public double maxAbs() {
     }
 
 
-    @Override
-    public double infNorm() {
-    return AggregateReal.maxAbs(entries);
-    }
-
-
     @Override
     public boolean isPos() {
     return RealProperties.isPos(entries);

src/main/java/org/flag4j/dense/CMatrix.java

@@ -32,13 +32,16 @@
 import org.flag4j.core.dense_base.ComplexDenseTensorBase;
 import org.flag4j.core.dense_base.DenseMatrixMixin;
 import org.flag4j.io.PrintOptions;
-import org.flag4j.linalg.Invert;
+import org.flag4j.linalg.MatrixNorms;
 import org.flag4j.linalg.decompositions.svd.ComplexSVD;
 import org.flag4j.operations.MatrixMultiplyDispatcher;
 import org.flag4j.operations.TransposeDispatcher;
 import org.flag4j.operations.common.complex.ComplexOperations;
 import org.flag4j.operations.common.real.RealProperties;
-import org.flag4j.operations.dense.complex.*;
+import org.flag4j.operations.dense.complex.ComplexDenseDeterminant;
+import org.flag4j.operations.dense.complex.ComplexDenseEquals;
+import org.flag4j.operations.dense.complex.ComplexDenseProperties;
+import org.flag4j.operations.dense.complex.ComplexDenseSetOperations;
 import org.flag4j.operations.dense.real_complex.RealComplexDenseElemDiv;
 import org.flag4j.operations.dense.real_complex.RealComplexDenseElemMult;
 import org.flag4j.operations.dense.real_complex.RealComplexDenseEquals;
@@ -530,26 +533,6 @@ public boolean isCloseToI() {
     }
 
 
-    /**
-     * Checks if matrices are inverses of each other.
-     *
-     * @param B Second matrix.
-     * @return True if matrix B is an inverse (approximately) of this matrix. Otherwise, returns false. Otherwise, returns false.
-     */
-    @Override
-    public boolean isInv(CMatrix B) {
-        boolean result;
-
-        if(!this.isSquare() || !B.isSquare() || !shape.equals(B.shape)) {
-            result = false;
-        } else {
-            result = this.mult(B).isCloseToI();
-        }
-
-        return result;
-    }
-
-
     /**
      * Flattens a matrix to have a single row. To flatten matrix to a single column, see {@link #flatten(int)}.
      *
@@ -3350,48 +3333,6 @@ public CNumber tr() {
     }
 
 
-    /**
-     * Computes the condition number of this matrix using the 2-norm.
-     * Specifically, the condition number is computed as the norm of this matrix multiplied by the norm
-     * of the inverse of this matrix.
-     *
-     * @return The condition number of this matrix (Assuming 2-norm). This value may be
-     * {@link Double#POSITIVE_INFINITY infinite}.
-     */
-    @Override
-    public double cond() {
-        return cond(2);
-    }
-
-
-    /**
-     * Computes the condition number of this matrix using a specified norm. The condition number of a matrix is defined
-     * as the norm of a matrix multiplied by the norm of the inverse of the matrix.
-     * @param p Specifies the order of the norm to be used when computing the condition number.
-     *          Common {@code p} values include:<br>
-     *          - {@code p} = {@link Double#POSITIVE_INFINITY}, {@link #infNorm()}.<br>
-     *          - {@code p} = 2, The standard matrix 2-norm (the largest singular value).<br>
-     *          - {@code p} = -2, The Smallest singular value.<br>
-     *          - {@code p} = 1, Maximum absolute row sum.<br>
-     * @return The condition number of this matrix using the specified norm. This value may be
-     * {@link Double#POSITIVE_INFINITY infinite}.
-     */
-    // TODO Pull up to matrix mixin
-    public double cond(double p) {
-        double cond;
-
-        if(p==2 || p==-2) {
-            // Compute the singular value decomposition of the matrix.
-            Vector s = new ComplexSVD(false).decompose(this).getS().getDiag();
-            cond = p==2 ? s.max()/s.min() : s.min()/s.max();
-        } else {
-            cond = norm(p)*Invert.inv(this).norm(p);
-        }
-
-        return cond;
-    }
-
-
     /**
      * Extracts the diagonal elements of this matrix and returns them as a vector.
      * @return A vector containing the diagonal entries of this matrix.
@@ -3589,30 +3530,6 @@ public boolean isSingular() {
     }
 
 
-    /**
-     * Computes the L<sub>p, q</sub> norm of this matrix.
-     *
-     * @param p P value in the L<sub>p, q</sub> norm.
-     * @param q Q value in the L<sub>p, q</sub> norm.
-     * @return The L<sub>p, q</sub> norm of this matrix.
-     */
-    @Override
-    public double norm(double p, double q) {
-        return ComplexDenseOperations.matrixNormLpq(entries, shape, p, q);
-    }
-
-
-    /**
-     * Computes the max norm of a matrix.
-     *
-     * @return The max norm of this matrix.
-     */
-    @Override
-    public double maxNorm() {
-        return ComplexDenseOperations.matrixMaxNorm(entries);
-    }
-
-
     /**
      * Computes the rank of this matrix (i.e. the dimension of the column space of this matrix).
      * Note that here, rank is <b>NOT</b> the same as a tensor rank.
@@ -3624,7 +3541,9 @@ public int matrixRank() {
         Matrix S = new ComplexSVD(false).decompose(this).getS();
         int stopIdx = Math.min(numRows, numCols);
 
-        double tol = 2.0*Math.max(numRows, numCols)* Flag4jConstants.EPS_F64*norm(); // Tolerance for determining if a singular value should be considered zero.
+        double tol = 2.0*Math.max(numRows, numCols)* Flag4jConstants.EPS_F64*MatrixNorms.norm(this); // Tolerance for determining if a
+        // singular
+        // value should be considered zero.
         int rank = 0;
 
         for(int i=0; i<stopIdx; i++) {
@@ -3715,54 +3634,6 @@ public CNumber get(int... indices) {
     }
 
 
-    /**
-     * Computes the 2-norm of this tensor. This is equivalent to {@link #norm(double) norm(2)}.
-     *
-     * @return the 2-norm of this tensor.
-     */
-    @Override
-    public double norm() {
-        return ComplexDenseOperations.matrixNormL2(entries, shape);
-    }
-
-
-    /**
-     * Computes the p-norm of this tensor.
-     *
-     * @param p The p value in the p-norm. <br>
-     *          - If p is inf, then this method computes the maximum/infinite norm.
-     * @return The p-norm of this tensor.
-     * @throws IllegalArgumentException If p is less than 1.
-     */
-    @Override
-    public double norm(double p) {
-        double norm;
-
-        if(Double.isInfinite(p)) {
-            if(p > 0) {
-                norm = maxNorm();
-            } else {
-                norm = minAbs();
-            }
-        } else {
-            norm = ComplexDenseOperations.matrixNormLp(entries, shape, p);
-        }
-
-        return norm;
-    }
-
-
-    /**
-     * Computes the maximum/infinite norm of this tensor.
-     *
-     * @return The maximum/infinite norm of this tensor.
-     */
-    @Override
-    public double infNorm() {
-        return ComplexDenseOperations.matrixInfNorm(entries, shape);
-    }
-
-
     /**
      * Gets row of matrix formatted as a human-readable String. Helper method for {@link #toString} method.
      * @param i Index of row to get.

src/main/java/org/flag4j/dense/CVector.java

@@ -30,7 +30,7 @@
 import org.flag4j.core.dense_base.ComplexDenseTensorBase;
 import org.flag4j.core.dense_base.DenseVectorMixin;
 import org.flag4j.io.PrintOptions;
-import org.flag4j.operations.common.real.VectorNorms;
+import org.flag4j.linalg.VectorNorms;
 import org.flag4j.operations.dense.complex.ComplexDenseVectorOperations;
 import org.flag4j.operations.dense.real_complex.RealComplexDenseElemDiv;
 import org.flag4j.operations.dense.real_complex.RealComplexDenseElemMult;
@@ -365,42 +365,6 @@ protected Vector makeRealTensor(Shape shape, double[] entries) {
     }
 
 
-    /**
-     * Computes the 2-norm of this tensor. This is equivalent to {@link #norm(double) norm(2)}.
-     *
-     * @return the 2-norm of this tensor.
-     */
-    @Override
-    public double norm() {
-        return VectorNorms.norm(entries);
-    }
-
-
-    /**
-     * Computes the p-norm of this tensor. Warning, if p is large in absolute value, overflow errors may occur.
-     *
-     * @param p The p value in the p-norm. <br>
-     *          - If p is {@link Double#POSITIVE_INFINITY}, then this method computes the maximum/infinite norm.<br>
-     *          - If p is {@link Double#NEGATIVE_INFINITY}, then this method computes the minimum norm.
-     * @return The p-norm of this tensor.
-     */
-    @Override
-    public double norm(double p) {
-        return VectorNorms.norm(entries, p);
-    }
-
-
-    /**
-     * Computes the maximum/infinite norm of this tensor.
-     *
-     * @return The maximum/infinite norm of this tensor.
-     */
-    @Override
-    public double infNorm() {
-        return maxAbs();
-    }
-
-
     /**
      * Extends a vector a specified number of times to a matrix.
      *
@@ -891,7 +855,7 @@ public CNumber inner(CooVector b) {
      */
     @Override
     public CVector normalize() {
-        double norm = this.norm();
+        double norm = VectorNorms.norm(this);
         return norm==0 ? new CVector(size) : this.div(norm);
     }