diff Problems/private/myblas.h @ 51:217a33ac374e

(none)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Problems/private/myblas.h	Mon Mar 14 16:52:27 2011 +0000
@@ -0,0 +1,492 @@
+/**************************************************************************
+ *
+ * File name: myblas.h
+ *
+ * Ron Rubinstein
+ * Computer Science Department
+ * Technion, Haifa 32000 Israel
+ * ronrubin@cs
+ *
+ * Version: 1.1
+ * Last updated: 17.8.2009
+ *
+ * A collection of basic linear algebra functions, in the spirit of the
+ * BLAS/LAPACK libraries.
+ *
+ *************************************************************************/
+
+
+
+#ifndef __MY_BLAS_H__
+#define __MY_BLAS_H__
+
+
+#include "mex.h"
+#include <math.h>
+
+
+
+/**************************************************************************
+ * Squared value.
+ **************************************************************************/
+#define SQR(X) ((X)*(X))
+
+
+
+/**************************************************************************
+ * Matrix-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A*x
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   x - vector of length m
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void mat_vec(double alpha, double A[], double x[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Matrix-transpose-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A'*x
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   x - vector of length n
+ *   y - output vector of length m
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void matT_vec(double alpha, double A[], double x[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Sparse-matrix-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A*x
+ *
+ * where A is a sparse matrix.
+ *
+ * Parameters:
+ *   pr,ir,jc - sparse representation of the matrix A, of size n x m
+ *   x - vector of length m
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void mat_sp_vec(double alpha, double pr[], mwIndex ir[], mwIndex jc[], double x[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Sparse-matrix-transpose-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A'*x
+ *
+ * where A is a sparse matrix.
+ *
+ * Parameters:
+ *   pr,ir,jc - sparse representation of the matrix A, of size n x m
+ *   x - vector of length m
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void matT_sp_vec(double alpha, double pr[], mwIndex ir[], mwIndex jc[], double x[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Matrix-sparse-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A*x
+ *
+ * where A is a matrix and x is a sparse vector.
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   pr,ir,jc - sparse representation of the vector x, of length m
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void mat_vec_sp(double alpha, double A[], double pr[], mwIndex ir[], mwIndex jc[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Matrix-transpose-sparse-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A'*x
+ *
+ * where A is a matrix and x is a sparse vector.
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   pr,ir,jc - sparse representation of the vector x, of length n
+ *   y - output vector of length m
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void matT_vec_sp(double alpha, double A[], double pr[], mwIndex ir[], mwIndex jc[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Sparse-matrix-sparse-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A*x
+ *
+ * where A is a sparse matrix and x is a sparse vector.
+ *
+ * Parameters:
+ *   pr,ir,jc - sparse representation of the matrix A, of size n x m
+ *   prx,irx,jcx - sparse representation of the vector x (of length m)
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void mat_sp_vec_sp(double alpha, double pr[], mwIndex ir[], mwIndex jc[], double prx[], mwIndex irx[], mwIndex jcx[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Sparse-matrix-transpose-sparse-vector multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*A'*x
+ *
+ * where A is a sparse matrix and x is a sparse vector.
+ *
+ * Importnant note: this function is provided for completeness, but is NOT efficient.
+ * If possible, convert x to non-sparse representation and use matT_vec_sp instead.
+ *
+ * Parameters:
+ *   pr,ir,jc - sparse representation of the matrix A, of size n x m
+ *   prx,irx,jcx - sparse representation of the vector x (of length n)
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n, m - dimensions of A
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void matT_sp_vec_sp(double alpha, double pr[], mwIndex ir[], mwIndex jc[], double prx[], mwIndex irx[], mwIndex jcx[], double y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Matrix-matrix multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   X := alpha*A*B
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   B - matrix of size m X k
+ *   X - output matrix of size n X k
+ *   alpha - real constant
+ *   n, m, k - dimensions of A, B
+ *
+ * Note: This function re-writes the contents of X.
+ *
+ **************************************************************************/
+void mat_mat(double alpha, double A[], double B[], double X[], mwSize n, mwSize m, mwSize k);
+
+
+
+/**************************************************************************
+ * Matrix-transpose-matrix multiplication. 
+ *
+ * Computes an operation of the form:
+ *
+ *   X := alpha*A*B
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   B - matrix of size m X k
+ *   X - output matrix of size n X k
+ *   alpha - real constant
+ *   n, m, k - dimensions of A, B
+ *
+ * Note: This function re-writes the contents of X.
+ *
+ **************************************************************************/
+void matT_mat(double alpha, double A[], double B[], double X[], mwSize n, mwSize m, mwSize k);
+
+
+
+/**************************************************************************
+ * Tensor-matrix multiplication. 
+ *
+ * This function accepts a 3-D tensor A of size n X m X k
+ * and a 2-D matrix B of size l X k.
+ * The function computes the 3-D tensor X of size n X m X l, where
+ *
+ *   X(i,j,:) = B*A(i,j,:)
+ *
+ * for all i,j.
+ *
+ * Parameters:
+ *   A - tensor of size n X m X k
+ *   B - matrix of size l X k
+ *   X - output tensor of size n X m X l
+ *   alpha - real constant
+ *   n, m, k, l - dimensions of A, B
+ *
+ * Note: This function re-writes the contents of X.
+ *
+ **************************************************************************/
+void tens_mat(double alpha, double A[], double B[], double X[], mwSize n, mwSize m, mwSize k, mwSize l);
+
+
+
+/**************************************************************************
+ * Tensor-matrix-transpose multiplication. 
+ *
+ * This function accepts a 3-D tensor A of size n X m X k
+ * and a 2-D matrix B of size k X l.
+ * The function computes the 3-D tensor X of size n X m X l, where
+ *
+ *   X(i,j,:) = B'*A(i,j,:)
+ *
+ * for all i,j.
+ *
+ * Parameters:
+ *   A - tensor of size n X m X k
+ *   B - matrix of size k X l
+ *   X - output tensor of size n X m X l
+ *   alpha - real constant
+ *   n, m, k, l - dimensions of A, B
+ *
+ * Note: This function re-writes the contents of X.
+ *
+ **************************************************************************/
+void tens_matT(double alpha, double A[], double B[], double X[], mwSize n, mwSize m, mwSize k, mwSize l);
+
+
+
+/**************************************************************************
+ * Vector-vector sum.
+ *
+ * Computes an operation of the form:
+ *
+ *   y := alpha*x + y
+ *
+ * Parameters:
+ *   x - vector of length n
+ *   y - output vector of length n
+ *   alpha - real constant
+ *   n - length of x,y
+ *
+ * Note: This function re-writes the contents of y.
+ *
+ **************************************************************************/
+void vec_sum(double alpha, double x[], double y[], mwSize n);
+
+
+
+/**************************************************************************
+ * Triangular back substitution.
+ *
+ * Solve the set of linear equations
+ *
+ *   T*x = b
+ *
+ * where T is lower or upper triangular.
+ *
+ * Parameters:
+ *   ul - 'U' for upper triangular, 'L' for lower triangular
+ *   A  - matrix of size n x m containing T
+ *   b  - vector of length k
+ *   x  - output vector of length k
+ *   n  - size of first dimension of A
+ *   k  - the size of the equation set, k<=n,m
+ *
+ * Note:
+ *   The matrix A can be of any size n X m, as long as n,m >= k. 
+ *   Only the lower/upper triangle of the submatrix A(1:k,1:k) defines the
+ *   matrix T (depending on the parameter ul).
+ *
+ **************************************************************************/
+void backsubst(char ul, double A[], double b[], double x[], mwSize n, mwSize k);
+
+
+
+/**************************************************************************
+ * Solve a set of equations using a Cholesky decomposition.
+ *
+ * Solve the set of linear equations
+ *
+ *   M*x = b
+ *
+ * where M is positive definite with a known Cholesky decomposition:
+ * either M=L*L' (L lower triangular) or M=U'*U (U upper triangular).
+ *
+ * Parameters:
+ *   ul - 'U' for upper triangular, 'L' for lower triangular decomposition
+ *   A  - matrix of size n x m with the Cholesky decomposition of M
+ *   b  - vector of length k
+ *   x  - output vector of length k
+ *   n  - size of first dimension of A
+ *   k  - the size of the equation set, k<=n,m
+ *
+ * Note:
+ *   The matrix A can be of any size n X m, as long as n,m >= k. 
+ *   Only the lower/upper triangle of the submatrix A(1:k,1:k) is used as
+ *   the Cholesky decomposition of M (depending on the parameter ul).
+ *
+ **************************************************************************/
+void cholsolve(char ul, double A[], double b[], double x[], mwSize n, mwSize k);
+
+
+
+/**************************************************************************
+ * Maximum absolute value.
+ *
+ * Returns the index of the coefficient with maximal absolute value in a vector.
+ *
+ * Parameters:
+ *   x - vector of length n
+ *   n - length of x
+ *
+ **************************************************************************/
+mwIndex maxabs(double x[], mwSize n);
+
+
+
+/**************************************************************************
+ * Maximum vector element.
+ *
+ * Returns the index of the maximal coefficient in a vector.
+ *
+ * Parameters:
+ *   x - vector of length n
+ *   n - length of x
+ *
+ **************************************************************************/
+mwIndex maxpos(double x[], mwSize n);
+
+
+
+/**************************************************************************
+ * Vector-vector dot product.
+ *
+ * Computes an operation of the form:
+ *
+ *   c = a'*b
+ *
+ * Parameters:
+ *   a, b - vectors of length n
+ *   n - length of a,b
+ *
+ * Returns: The dot product c.
+ *
+ **************************************************************************/
+double dotprod(double a[], double b[], mwSize n);
+
+
+
+/**************************************************************************
+ * Indexed vector assignment.
+ *
+ * Perform a permutation assignment of the form
+ *
+ *   y = x(ind)
+ *
+ * where ind is an array of indices to x.
+ *
+ * Parameters:
+ *   y - output vector of length k
+ *   x - input vector of arbitrary length
+ *   ind - array of indices into x (indices begin at 0)
+ *   k - length of the array ind
+ *
+ **************************************************************************/
+void vec_assign(double y[], double x[], mwIndex ind[], mwSize k);
+
+
+
+/**************************************************************************
+ * Matrix transpose.
+ *
+ * Computes Y := X'
+ *
+ * Parameters:
+ *   X - input matrix of size n X m
+ *   Y - output matrix of size m X n
+ *   n, m - dimensions of X
+ *
+ **************************************************************************/
+void transpose(double X[], double Y[], mwSize n, mwSize m);
+
+
+
+/**************************************************************************
+ * Print a matrix.
+ *
+ * Parameters:
+ *   A - matrix of size n X m
+ *   n, m - dimensions of A
+ *   matname - name of matrix to display
+ *
+ **************************************************************************/
+void printmat(double A[], int n, int m, char* matname);
+
+
+
+/**************************************************************************
+ * Print a sparse matrix.
+ *
+ * Parameters:
+ *   A - sparse matrix of type double
+ *   matname - name of matrix to display
+ *
+ **************************************************************************/
+void printspmat(mxArray *A, char* matname);
+
+
+#endif
+