gov.nist.math.jampack.Norm Maven / Gradle / Ivy

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package gov.nist.math.jampack;

/**
 * Norm computes norms of matrices.
 * 
 * Comments: At this point only the Frobenius norm is calculated. Later the 1,
 * 2, and infinity norms will be added.
 * 
 * @version Pre-alpha
 * @author G. W. Stewart
 */
public final class Norm {

    /**
     * Computes the Frobenius norm of a the submatrix (ii1:ii2, jj1,jj2) of a
     * Zmat.
     * 
     * @param A
     *            The zmat
     * @param ii1
     *            The lower row index
     * @param ii2
     *            The upper row index
     * @param jj1
     *            The lower column index
     * @param jj2
     *            The upper column index
     * @return The Frobenius norm of A(ii1:ii2, jj1:jj2)
     */
    public static double fro(Zmat A, int ii1, int ii2, int jj1, int jj2) {
        int i, i1, i2, j, j1, j2;
        double fac, nrm, scale;

        i1 = ii1 - 1;
        i2 = ii2 - 1;
        j1 = jj1 - 1;
        j2 = jj2 - 1;

        scale = 0.0;
        for (i = i1; i <= i2; i++) {
            for (j = j1; j <= j2; j++) {
                scale = Math.max(scale, Math.abs(A.re[i][j]) + Math.abs(A.im[i][j]));
            }
        }
        if (scale == 0.0) {
            return 0.0;
        }
        if (scale < 1.0) {
            scale = scale * 1.0e20;
        }
        scale = 1.0 / scale;
        nrm = 0.0;
        for (i = i1; i <= i2; i++) {
            for (j = j1; j <= j2; j++) {
                fac = scale * A.re[i][j];
                nrm = nrm + fac * fac;
                fac = scale * A.im[i][j];
                nrm = nrm + fac * fac;
            }
        }
        return Math.sqrt(nrm) / scale;
    }

    /**
     * Computes the Frobenius norm of a Zmat.
     * 
     * @param A
     *            The Zmat
     * @return The Frobenius norm of A
     */
    public static double fro(Zmat A) {
        return Norm.fro(A, 1, A.rx, 1, A.cx);
    }

    /**
     * Computes the Frobenius norm of a Z1.
     * 
     * @param u
     *            The Z1
     * @return The Frobenius norm of u
     */
    public static double fro(Z1 u) {
        int i;
        double fac, nrm, scale;

        int n = u.n;

        scale = 0.0;
        for (i = 0; i < n; i++) {
            scale = Math.max(scale, Math.abs(u.re[i]) + Math.abs(u.im[i]));
        }
        if (scale == 0.0) {
            return 0.0;
        }
        if (scale < 1.0) {
            scale = scale * 1.0e20;
        }
        scale = 1.0 / scale;
        nrm = 0.0;

        for (i = 0; i < n; i++) {
            fac = scale * u.re[i];
            nrm = nrm + fac * fac;
            fac = scale * u.im[i];
            nrm = nrm + fac * fac;
        }

        return Math.sqrt(nrm) / scale;
    }

    /**
     * Computes the Frobenius norm of a Zdiagmat.
     * 
     * @param D
     *            The Zdiagmat
     * @return The Frobenius norm of D
     */
    public static double fro(Zdiagmat D) {
        int i;
        double fac, nrm, scale;

        int n = D.order;

        scale = 0.0;
        for (i = 0; i < n; i++) {
            scale = Math.max(scale, Math.abs(D.re[i]) + Math.abs(D.im[i]));
        }
        if (scale == 0.0) {
            return 0.0;
        }
        if (scale < 1.0) {
            scale = scale * 1.0e20;
        }
        scale = 1.0 / scale;
        nrm = 0.0;

        for (i = 0; i < n; i++) {
            fac = scale * D.re[i];
            nrm = nrm + fac * fac;
            fac = scale * D.im[i];
            nrm = nrm + fac * fac;
        }

        return Math.sqrt(nrm) / scale;
    }
}