用Java求复矩阵的SVD矩阵

Question

我目前正在做一个音频信号处理项目，需要在Java中的一个复杂矩阵上使用SVD。我当前的线性代数库是Apache Commons。但它只提供实矩阵的SVD，JAMA、JBLAS、EJML、ojAlgo都不支持复杂的SVD。

我一直在用一些技巧从一个等效的实矩阵中找到SVD。然而，当我重建矩阵时，这种技术对于虚部有很大的不准确性。

    //Array2DRowFieldMatrix<Complex> A = some matrix defined earlier
    Array2DRowRealMatrix AA = new Array2DRowRealMatrix(2 * row, 2 * col);
    Complex Aentry;

    for (int c = 0; c < row; c++) {
        for (int s = 0; s < col; s++) {
            Aentry = A.getEntry(c, s);

            AA.setEntry(c, s, Aentry.getReal());
            AA.setEntry(c, col + s, -Aentry.getImaginary());
            AA.setEntry(row + c, s, Aentry.getImaginary());
            AA.setEntry(row + c, col + s, Aentry.getReal());
        }
    }

    Array2DRowRealMatrix UU, SS, VV;

    svd = new SingularValueDecomposition(AA);

    UU = (Array2DRowRealMatrix) svd.getU();
    SS = (Array2DRowRealMatrix) svd.getS();
    VV = (Array2DRowRealMatrix) svd.getV();

    double[][] tempU = new double[row][2 * row];
    double[][] tempV = new double[col][2 * row];
    double[] tempS = new double[row];

    Array2DRowFieldMatrix<Complex> U = new Array2DRowFieldMatrix<>(ComplexField.getInstance(), row, row);
    Array2DRowFieldMatrix<Complex> S = new Array2DRowFieldMatrix<>(ComplexField.getInstance(), row, row);
    Array2DRowFieldMatrix<Complex> V = new Array2DRowFieldMatrix<>(ComplexField.getInstance(), col, row);
    Array2DRowFieldMatrix<Complex> recon, diff;

    UU.copySubMatrix(row, 2 * row - 1, 0, 2 * row - 1, tempU);
    VV.copySubMatrix(col, 2 * col - 1, 0, 2 * row - 1, tempV);

    for (int i = 0; i < row; i++) {
        for (int j = 0; j < row; j++) {
            U.setEntry(i, j, new Complex(tempU[i][2 * j], tempU[i][2 * j + 1]));
        }
    }

    for (int i = 0; i < col; i++) {
        for (int j = 0; j < row; j++) {
            V.setEntry(i, j, new Complex(tempV[i][2 * j], tempV[i][2 * j + 1]));
        }
    }

    for (int i = 0; i < row; i++) {
        tempS[i] = SS.getEntry(i * row, i * row);
        if (tempS[i] == 0) {
            tempS[i] = EPSILON;
        }
    }

    for (int i = 0; i < row; i++) {
        for (int j = 0; j < row; j++) {
            if (i != j) {
                S.setEntry(i, j, Complex.ZERO);
            }
        }

        S.setEntry(i, i, new Complex(tempS[i]));
    }

    recon = (Array2DRowFieldMatrix<Complex>)U.multiply(S).multiply(conjugate(V).transpose());

Answer 1

如果您可以使用本机库，那么jeigen是一个选项