solveValidation = function solveValidation(m, b, copy) {
    // matrix size
    var size = m.size(); // validate matrix dimensions

    if (size.length !== 2) {
      throw new RangeError('Matrix must be two dimensional (size: ' + string.format(size) + ')');
    } // rows & columns


    var rows = size[0];
    var columns = size[1]; // validate rows & columns

    if (rows !== columns) {
      throw new RangeError('Matrix must be square (size: ' + string.format(size) + ')');
    } // vars


    var data, i, bdata; // check b is matrix

    if (type.isMatrix(b)) {
      // matrix size
      var msize = b.size(); // vector

      if (msize.length === 1) {
        // check vector length
        if (msize[0] !== rows) {
          throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
        } // create data array


        data = []; // matrix data (DenseMatrix)

        bdata = b._data; // loop b data

        for (i = 0; i < rows; i++) {
          // row array
          data[i] = [bdata[i]];
        } // return Dense Matrix


        return new DenseMatrix({
          data: data,
          size: [rows, 1],
          datatype: b._datatype
        });
      } // two dimensions


      if (msize.length === 2) {
        // array must be a column vector
        if (msize[0] !== rows || msize[1] !== 1) {
          throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
        } // check matrix type


        if (type.isDenseMatrix(b)) {
          // check a copy is needed
          if (copy) {
            // create data array
            data = []; // matrix data (DenseMatrix)

            bdata = b._data; // loop b data

            for (i = 0; i < rows; i++) {
              // row array
              data[i] = [bdata[i][0]];
            } // return Dense Matrix


            return new DenseMatrix({
              data: data,
              size: [rows, 1],
              datatype: b._datatype
            });
          } // b is already a column vector


          return b;
        } // create data array


        data = [];

        for (i = 0; i < rows; i++) {
          data[i] = [0];
        } // sparse matrix arrays


        var values = b._values;
        var index = b._index;
        var ptr = b._ptr; // loop values in column 0

        for (var k1 = ptr[1], k = ptr[0]; k < k1; k++) {
          // row
          i = index[k]; // add to data

          data[i][0] = values[k];
        } // return Dense Matrix


        return new DenseMatrix({
          data: data,
          size: [rows, 1],
          datatype: b._datatype
        });
      } // throw error


      throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
    } // check b is array


    if (isArray(b)) {
      // size
      var asize = array.size(b); // check matrix dimensions, vector

      if (asize.length === 1) {
        // check vector length
        if (asize[0] !== rows) {
          throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
        } // create data array


        data = []; // loop b

        for (i = 0; i < rows; i++) {
          // row array
          data[i] = [b[i]];
        } // return Dense Matrix


        return new DenseMatrix({
          data: data,
          size: [rows, 1]
        });
      }

      if (asize.length === 2) {
        // array must be a column vector
        if (asize[0] !== rows || asize[1] !== 1) {
          throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
        } // create data array


        data = []; // loop b data

        for (i = 0; i < rows; i++) {
          // row array
          data[i] = [b[i][0]];
        } // return Dense Matrix


        return new DenseMatrix({
          data: data,
          size: [rows, 1]
        });
      } // throw error


      throw new RangeError('Dimension mismatch. Matrix columns must match vector length.');
    }
  }
Validates matrix and column vector b for backward/forward substitution algorithms.

@param {Matrix} m            An N x N matrix
@param {Array | Matrix} b    A column vector
@param {Boolean} copy        Return a copy of vector b

@return {DenseMatrix}        Dense column vector b