maths.f90 File Reference

This module contains all mathematics support routines. More...

Go to the source code of this file.

Data Types
interface	maths::cross_product
	Calculates the vector cross product of two vectors. More...
interface	maths::crossproduct
	Calculates the vector cross product of two vectors. More...
interface	maths::d_cross_product
	Calculates the the vector cross product of A*B in C and the N derivatives, D_C, of the vector cross product given the derivatives D_A and D_B of A and B. More...
interface	maths::dcrossproduct
	Calculates the the vector cross product of a x b in c and the n derivatives, dc, of the vector cross product given the derivatives da and db of a and b. More...
interface	maths::determinant
	Returns the determinant of a matrix. More...
interface	maths::edp
	Calculates the elliptic integral of the second kind - E(m). More...
interface	maths::eigenvalue
	Returns the eigenvalues of a matrix. More...
interface	maths::eigenvector
	Returns the eigenvectors of a matrix. More...
interface	maths::i0
	Calculates the modified Bessel function of the first kind of order 0 using the approximation of Abromowitz and Stegun. More...
interface	maths::i1
	Calculates the modified Bessel function of the first kind of order 1 using the approximation of Abromowitz and Stegun. More...
interface	maths::invert
	Returns the inverse of a matrix. More...
interface	maths::k0
	Calculates the modified Bessel function of the second kind of order 0 using the approximation of Abromowitz and Stegun. More...
interface	maths::k1
	Calculates the modified Bessel function of the second kind of order 1 using the approximation of Abromowitz and Stegun. More...
interface	maths::kdp
	Calculates the elliptic integral of the first kind - K(m). More...
interface	maths::identitymatrix
	Returns the identity matrix. More...
interface	maths::l2norm
	Returns the L2 norm of a vector. More...
interface	maths::matrix_product
	Calculates and returns the matrix-product A*B in the matrix C. More...
interface	maths::matrixproduct
	Calculates and returns the matrix-product A*B in the matrix C. More...
interface	maths::matrixtransposeproduct
	Calculates and returns the matrix-transpose product A^T*B in the matrix C. More...
interface	maths::matrixproducttranspose
	Calculates and returns the matrix-product-transpose A*B^T in the matrix C. More...
interface	maths::matrix_transpose
	Returns the transpose of a matrix A in A^T. More...
interface	maths::matrixtranspose
	Returns the transpose of a matrix A in A^T. More...
interface	maths::matrix_vector_product
	Calculates and returns the matrix-vector-product A*b in the vector c. More...
interface	maths::matrixvectorproduct
	Calculates and returns the matrix-vector-product A*b in the vector c. More...
interface	maths::matrixtransposevectorproduct
	Calculates and returns the matrix-transpose vector-product A^T*b in the vector c. More...
interface	maths::normalise
	Normalises a vector. More...
interface	maths::norm_cross_product
	Calculates the normalised vector cross product of two vectors. More...
interface	maths::normcrossproduct
	Calculates the normalised vector cross product of two vectors. More...
interface	maths::solve_small_linear_system
	Solves a small linear system Ax=b. More...
interface	maths::solvesmalllinearsystem
	Solves a small linear system Ax=b. More...
interface	maths::coth
	Returns hyperbolic cotangent of argument. More...

Modules
module	maths
	This module contains all mathematics support routines.

Functions/Subroutines
subroutine	maths::crossproductintg (a, b, c, err, error,)
	Calculates and returns the vector cross-product of the integer vectors a x b in c. More...
subroutine	maths::crossproductsp (a, b, c, err, error,)
	Calculates and returns the vector cross-product of the single precision vectors a x b in c. More...
subroutine	maths::crossproductdp (a, b, c, err, error,)
	Calculates and returns the vector cross-product of the double precision vectors a x b in c. More...
subroutine	maths::dcrossproductintg (n, a, b, c, da, db, dc, err, error,)
	Calculates the the vector cross product of a x b in c and the n derivatives, dc, of the vector cross product given the derivatives da and db of a and b for integer vectors. More...
subroutine	maths::dcrossproductsp (n, a, b, c, da, db, dc, err, error,)
	Calculates the the vector cross product of a x b in c and the n derivatives, dc, of the vector cross product given the derivatives da and db of a and b for single precision vectors. More...
subroutine	maths::dcrossproductdp (n, a, b, c, da, db, dc, err, error,)
	Calculates the the vector cross product of a x b in c and the n derivatives, dc, of the vector cross product given the derivatives da and db of a and b for double precision vectors. More...
subroutine	maths::matrixvectorproductsp (A, b, c, err, error,)
	Calculates and returns the matrix-vector product of the single precision vector A*b in c. More...
subroutine	maths::matrixvectorproductdp (A, b, c, err, error,)
	Calculates and returns the matrix-vector product of the double precision vectir A*b in c. More...
subroutine	maths::matrixtransposevectorproductsp (A, b, c, err, error,)
	Calculates and returns the matrix-transpose vector product of the single precision vector A^T*b in c. More...
subroutine	maths::matrixtransposevectorproductdp (A, b, c, err, error,)
	Calculates and returns the matrix-transpose vector product of the double precision vector A^T*b in c. More...
integer(intg) function	maths::determinantfullintg (A, err, error)
	Returns the determinant of a full integer matrix A. More...
real(sp) function	maths::determinantfullsp (A, err, error)
	Returns the determinant of a full single precision matrix A. More...
real(dp) function	maths::determinantfulldp (A, err, error)
	Returns the determinant of a full double precision matrix A. More...
pure real(dp) function	maths::edpdp (x)
	Calculates the elliptic integral of the second kind - E(m), for a double precision argument. More...
pure real(sp) function	maths::edpsp (x)
	Calculates the elliptic integral of the second kind - E(m), for a single precision argument. More...
subroutine	maths::eigenvaluefullsp (A, eValues, err, error,)
	Returns the eigenvalues of a full single precision matrix A. More...
subroutine	maths::eigenvaluefulldp (A, eValues, err, error,)
	Returns the eigenvalues of a full double precision matrix A. More...
subroutine	maths::eigenvectorfullsp (A, eValue, eVector, err, error,)
	Returns the normalised eigenvector of a full single precision symmetric matrix A that corresponds to the eigenvalue eValue. More...
subroutine	maths::eigenvectorfulldp (A, eValue, eVector, err, error,)
	Returns the normalised eigenvector of a full double precision symmetric matrix A that corresponds to the eigenvalue eValue. More...
pure real(dp) function	maths::i0dp (x)
	Calculates the modified Bessel function of the first kind of order 0 using the approximation of Abromowitz and Stegun, for a double precision argument. More...
pure real(sp) function	maths::i0sp (x)
	Calculates the modified Bessel function of the first kind of order 0 using the approximation of Abromowitz and Stegun, for a single precision argument. More...
pure real(dp) function	maths::i1dp (x)
	Calculates the modified Bessel function of the first kind of order 1 using the approximation of Abromowitz and Stegun, for a double precision argument. More...
pure real(sp) function	maths::i1sp (x)
	Calculates the modified Bessel function of the first kind of order 1 using the approximation of Abromowitz and Stegun, for a single precision argument. More...
subroutine	maths::identitymatrixsp (A, err, error,)
	Returns an identity matrix. More...
subroutine	maths::identitymatrixdp (A, err, error,)
	Returns an identity matrix. More...
subroutine	maths::invertfullsp (A, B, det, err, error,)
	Inverts a full single precision matrix A to give matrix B and returns the determinant of A in det. More...
subroutine	maths::invertfulldp (A, B, det, err, error,)
	Inverts a full double precision matrix A to give matrix B and returns the determinant of A in det. More...
pure real(dp) function	maths::k0dp (x)
	Calculates the modified Bessel function of the second kind of order 1 using the approximation of Abromowitz and Stegun, for a double precision argument. More...
pure real(sp) function	maths::k0sp (x)
	Calculates the modified Bessel function of the second kind of order 0 using the approximation of Abromowitz and Stegun, for a single precision argument. More...
pure real(dp) function	maths::k1dp (x)
	Calculates the modified Bessel function of the second kind of order 1 using the approximation of Abromowitz and Stegun, for a double precision argument. More...
pure real(sp) function	maths::k1sp (x)
	Calculates the modified Bessel function of the second kind of order 1 using the approximation of Abromowitz and Stegun, for a single precision argument. More...
pure real(dp) function	maths::kdpdp (x)
	Calculates the elliptic integral of the first kind - K(m), for a double precision argument. More...
pure real(sp) function	maths::kdpsp (x)
	Calculates the elliptic integral of the first kind - K(m), for a single precision argument. More...
pure real(sp) function	maths::l2normsp (a)
	Returns the L2-norm of the single precision vector a. More...
real(dp) function	maths::l2normdp (A)
	Returns the L2-norm of the double precision vector a. More...
subroutine	maths::matrixproductsp (A, B, C, err, error,)
	Calculates and returns the matrix-product of the single precision matrix A*B in C for single precision arguments. More...
subroutine	maths::matrixproductdp (A, B, C, err, error,)
	Calculates and returns the matrix-product of the double precision matrix A*B in C. More...
subroutine	maths::matrixtransposeproductsp (A, B, C, err, error,)
	Calculates and returns the matrix-transpose product of the single precision matrix A^T*B in C for single precision arguments. More...
subroutine	maths::matrixtransposeproductdp (A, B, C, err, error,)
	Calculates and returns the matrix-transpose product of the double precision matrix A^T*B in C for double precision arguments. More...
subroutine	maths::matrixproducttransposesp (A, B, C, err, error,)
	Calculates and returns the matrix-product-transpose of the single precision matrix A*B^T in C for single precision arguments. More...
subroutine	maths::matrixproducttransposedp (A, B, C, err, error,)
	Calculates and returns the matrix-product-transpose of the double precision matrix A*B^T in C. More...
subroutine	maths::matrixtransposesp (A, AT, err, error,)
	Returns the transpose of a single precision matrix A in AT. More...
subroutine	maths::matrixtransposedp (A, AT, err, error,)
	Returns the transpose of a double precision matrix A in AT. More...
real(sp) function, dimension(size(a, 1))	maths::normalisesp (a, err, error)
	Normalises a real single precision vector a. More...
real(dp) function, dimension(size(a, 1))	maths::normalisedp (a, err, error)
	Normalises a real double precision vector a. More...
subroutine	maths::normcrossproductsp (a, b, c, err, error,)
	Calculates and returns the normalised vector cross-prouct of the single precision vectors a x b in c. More...
subroutine	maths::normcrossproductdp (a, b, c, err, error,)
	Calculates and returns the normalised vector cross-prouct of the double precision vectors a x b in c. More...
subroutine	maths::solvesmalllinearsystemsp (A, x, b, err, error,)
	Finds the solution to a small single precision linear system Ax=b. More...
subroutine	maths::solvesmalllinearsystemdp (A, x, b, err, error,)
	Finds the solution to a small double precision linear system Ax=b. More...
real(sp) function	maths::cothsp (a)
	Calculates single precision hyperbolic cotangent function. More...
real(dp) function	maths::cothdp (a)
	Calculates double precision hyperbolic cotangent function. More...
subroutine, public	maths::spline_cubic_set (n, t, y, ibcbeg, ybcbeg, ibcend, ybcend, ypp, err, error,)
	Calculates second derivatives of a cubic spline function for a tabulated function y(x). Call spline_cubic_val to evaluate at t values. algorithm adapted from John Burkhardt's spline_cubic_set routine from the SPLINE package (http://people.sc.fsu.edu/~jburkardt/f_src/spline/spline.html) More...
subroutine, public	maths::s3_fs (a1, a2, a3, n, b, x, err, error,)
	S3_FS factors and solves a tridiagonal linear system. algorithm adapted from John Burkhardt's s3_fs routine from the SPLINE package (http://people.sc.fsu.edu/~jburkardt/f_src/spline/spline.html) More...
subroutine, public	maths::spline_cubic_val (n, t, y, ypp, tval, yval, ypval, yppval, err, error,)
	Evaluates a cubic spline at a specified point. First call spline_cubic_set to calculate derivatives algorithm adapted from John Burkhardt's spline_cubic_val routine from the SPLINE package (http://people.sc.fsu.edu/~jburkardt/f_src/spline/spline.html) More...

Detailed Description

This module contains all mathematics support routines.

Author

Chris Bradley

LICENSE

Version: MPL 1.1/GPL 2.0/LGPL 2.1

The contents of this file are subject to the Mozilla Public License Version 1.1 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.mozilla.org/MPL/

Software distributed under the License is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License for the specific language governing rights and limitations under the License.

The Original Code is OpenCMISS

The Initial Developer of the Original Code is University of Auckland, Auckland, New Zealand, the University of Oxford, Oxford, United Kingdom and King's College, London, United Kingdom. Portions created by the University of Auckland, the University of Oxford and King's College, London are Copyright (C) 2007-2010 by the University of Auckland, the University of Oxford and King's College, London. All Rights Reserved.

Contributor(s): Kumar Mithraratne

Alternatively, the contents of this file may be used under the terms of either the GNU General Public License Version 2 or later (the "GPL"), or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), in which case the provisions of the GPL or the LGPL are applicable instead of those above. If you wish to allow use of your version of this file only under the terms of either the GPL or the LGPL, and not to allow others to use your version of this file under the terms of the MPL, indicate your decision by deleting the provisions above and replace them with the notice and other provisions required by the GPL or the LGPL. If you do not delete the provisions above, a recipient may use your version of this file under the terms of any one of the MPL, the GPL or the LGPL.

Definition in file maths.f90.