Merge pull request #673 from fsantini/ErikZalm

Improvements to the auto bed leveling feature
master
alexborro 11 years ago
commit 89a304fd98

@ -367,6 +367,15 @@ const bool Z_MAX_ENDSTOP_INVERTING = true; // set to true to invert the logic of
#endif
// with accurate bed leveling, the bed is sampled in a ACCURATE_BED_LEVELING_POINTSxACCURATE_BED_LEVELING_POINTS grid and least squares solution is calculated
// Note: this feature occupies 10'206 byte
#define ACCURATE_BED_LEVELING
#ifdef ACCURATE_BED_LEVELING
// I wouldn't see a reason to go above 3 (=9 probing points on the bed)
#define ACCURATE_BED_LEVELING_POINTS 2
#endif
#endif

@ -31,6 +31,9 @@
#ifdef ENABLE_AUTO_BED_LEVELING
#include "vector_3.h"
#ifdef ACCURATE_BED_LEVELING
#include "qr_solve.h"
#endif
#endif // ENABLE_AUTO_BED_LEVELING
#include "ultralcd.h"
@ -802,6 +805,31 @@ static void axis_is_at_home(int axis) {
}
#ifdef ENABLE_AUTO_BED_LEVELING
#ifdef ACCURATE_BED_LEVELING
static void set_bed_level_equation_lsq(double *plane_equation_coefficients)
{
vector_3 planeNormal = vector_3(-plane_equation_coefficients[0], -plane_equation_coefficients[1], 1);
planeNormal.debug("planeNormal");
plan_bed_level_matrix = matrix_3x3::create_look_at(planeNormal);
//bedLevel.debug("bedLevel");
//plan_bed_level_matrix.debug("bed level before");
//vector_3 uncorrected_position = plan_get_position_mm();
//uncorrected_position.debug("position before");
vector_3 corrected_position = plan_get_position();
// corrected_position.debug("position after");
current_position[X_AXIS] = corrected_position.x;
current_position[Y_AXIS] = corrected_position.y;
current_position[Z_AXIS] = corrected_position.z;
// but the bed at 0 so we don't go below it.
current_position[Z_AXIS] = -Z_PROBE_OFFSET_FROM_EXTRUDER;
plan_set_position(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS], current_position[E_AXIS]);
}
#else
static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yFront, float z_at_xLeft_yBack) {
plan_bed_level_matrix.set_to_identity();
@ -811,11 +839,11 @@ static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yF
vector_3 xPositive = (xRightyFront - xLeftyFront).get_normal();
vector_3 yPositive = (xLeftyBack - xLeftyFront).get_normal();
vector_3 planeNormal = vector_3::cross(yPositive, xPositive).get_normal();
vector_3 planeNormal = vector_3::cross(xPositive, yPositive).get_normal();
//planeNormal.debug("planeNormal");
//yPositive.debug("yPositive");
matrix_3x3 bedLevel = matrix_3x3::create_look_at(planeNormal, yPositive);
plan_bed_level_matrix = matrix_3x3::create_look_at(planeNormal);
//bedLevel.debug("bedLevel");
//plan_bed_level_matrix.debug("bed level before");
@ -823,7 +851,6 @@ static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yF
//uncorrected_position.debug("position before");
// and set our bed level equation to do the right thing
plan_bed_level_matrix = matrix_3x3::create_inverse(bedLevel);
//plan_bed_level_matrix.debug("bed level after");
vector_3 corrected_position = plan_get_position();
@ -837,6 +864,7 @@ static void set_bed_level_equation(float z_at_xLeft_yFront, float z_at_xRight_yF
plan_set_position(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS], current_position[E_AXIS]);
}
#endif // ACCURATE_BED_LEVELING
static void run_z_probe() {
plan_bed_level_matrix.set_to_identity();
@ -1325,6 +1353,98 @@ void process_commands()
setup_for_endstop_move();
feedrate = homing_feedrate[Z_AXIS];
#ifdef ACCURATE_BED_LEVELING
int xGridSpacing = (RIGHT_PROBE_BED_POSITION - LEFT_PROBE_BED_POSITION) / (ACCURATE_BED_LEVELING_POINTS-1);
int yGridSpacing = (BACK_PROBE_BED_POSITION - FRONT_PROBE_BED_POSITION) / (ACCURATE_BED_LEVELING_POINTS-1);
// solve the plane equation ax + by + d = z
// A is the matrix with rows [x y 1] for all the probed points
// B is the vector of the Z positions
// the normal vector to the plane is formed by the coefficients of the plane equation in the standard form, which is Vx*x+Vy*y+Vz*z+d = 0
// so Vx = -a Vy = -b Vz = 1 (we want the vector facing towards positive Z
// "A" matrix of the linear system of equations
double eqnAMatrix[ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS*3];
// "B" vector of Z points
double eqnBVector[ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS];
int probePointCounter = 0;
bool zig = true;
for (int yProbe=FRONT_PROBE_BED_POSITION; yProbe <= BACK_PROBE_BED_POSITION; yProbe += yGridSpacing)
{
int xProbe, xInc;
if (zig)
{
xProbe = LEFT_PROBE_BED_POSITION;
//xEnd = RIGHT_PROBE_BED_POSITION;
xInc = xGridSpacing;
zig = false;
} else // zag
{
xProbe = RIGHT_PROBE_BED_POSITION;
//xEnd = LEFT_PROBE_BED_POSITION;
xInc = -xGridSpacing;
zig = true;
}
for (int xCount=0; xCount < ACCURATE_BED_LEVELING_POINTS; xCount++)
{
if (probePointCounter == 0)
{
// raise before probing
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], Z_RAISE_BEFORE_PROBING);
} else
{
// raise extruder
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], current_position[Z_AXIS] + Z_RAISE_BETWEEN_PROBINGS);
}
do_blocking_move_to(xProbe - X_PROBE_OFFSET_FROM_EXTRUDER, yProbe - Y_PROBE_OFFSET_FROM_EXTRUDER, current_position[Z_AXIS]);
engage_z_probe(); // Engage Z Servo endstop if available
run_z_probe();
eqnBVector[probePointCounter] = current_position[Z_AXIS];
retract_z_probe();
SERIAL_PROTOCOLPGM("Bed x: ");
SERIAL_PROTOCOL(xProbe);
SERIAL_PROTOCOLPGM(" y: ");
SERIAL_PROTOCOL(yProbe);
SERIAL_PROTOCOLPGM(" z: ");
SERIAL_PROTOCOL(current_position[Z_AXIS]);
SERIAL_PROTOCOLPGM("\n");
eqnAMatrix[probePointCounter + 0*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = xProbe;
eqnAMatrix[probePointCounter + 1*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = yProbe;
eqnAMatrix[probePointCounter + 2*ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS] = 1;
probePointCounter++;
xProbe += xInc;
}
}
clean_up_after_endstop_move();
// solve lsq problem
double *plane_equation_coefficients = qr_solve(ACCURATE_BED_LEVELING_POINTS*ACCURATE_BED_LEVELING_POINTS, 3, eqnAMatrix, eqnBVector);
SERIAL_PROTOCOLPGM("Eqn coefficients: a: ");
SERIAL_PROTOCOL(plane_equation_coefficients[0]);
SERIAL_PROTOCOLPGM(" b: ");
SERIAL_PROTOCOL(plane_equation_coefficients[1]);
SERIAL_PROTOCOLPGM(" d: ");
SERIAL_PROTOCOLLN(plane_equation_coefficients[2]);
set_bed_level_equation_lsq(plane_equation_coefficients);
free(plane_equation_coefficients);
#else // ACCURATE_BED_LEVELING not defined
// prob 1
do_blocking_move_to(current_position[X_AXIS], current_position[Y_AXIS], Z_RAISE_BEFORE_PROBING);
@ -1382,6 +1502,8 @@ void process_commands()
set_bed_level_equation(z_at_xLeft_yFront, z_at_xRight_yFront, z_at_xLeft_yBack);
#endif // ACCURATE_BED_LEVELING
st_synchronize();
// The following code correct the Z height difference from z-probe position and hotend tip position.

@ -942,7 +942,7 @@ vector_3 plan_get_position() {
//position.debug("in plan_get position");
//plan_bed_level_matrix.debug("in plan_get bed_level");
matrix_3x3 inverse = matrix_3x3::create_inverse(plan_bed_level_matrix);
matrix_3x3 inverse = matrix_3x3::transpose(plan_bed_level_matrix);
//inverse.debug("in plan_get inverse");
position.apply_rotation(inverse);
//position.debug("after rotation");

@ -0,0 +1,1932 @@
#include "qr_solve.h"
#ifdef ACCURATE_BED_LEVELING
#include <stdlib.h>
#include <math.h>
#include <time.h>
//# include "r8lib.h"
int i4_min ( int i1, int i2 )
/******************************************************************************/
/*
Purpose:
I4_MIN returns the smaller of two I4's.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
29 August 2006
Author:
John Burkardt
Parameters:
Input, int I1, I2, two integers to be compared.
Output, int I4_MIN, the smaller of I1 and I2.
*/
{
int value;
if ( i1 < i2 )
{
value = i1;
}
else
{
value = i2;
}
return value;
}
double r8_epsilon ( void )
/******************************************************************************/
/*
Purpose:
R8_EPSILON returns the R8 round off unit.
Discussion:
R8_EPSILON is a number R which is a power of 2 with the property that,
to the precision of the computer's arithmetic,
1 < 1 + R
but
1 = ( 1 + R / 2 )
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
01 September 2012
Author:
John Burkardt
Parameters:
Output, double R8_EPSILON, the R8 round-off unit.
*/
{
const double value = 2.220446049250313E-016;
return value;
}
double r8_max ( double x, double y )
/******************************************************************************/
/*
Purpose:
R8_MAX returns the maximum of two R8's.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 May 2006
Author:
John Burkardt
Parameters:
Input, double X, Y, the quantities to compare.
Output, double R8_MAX, the maximum of X and Y.
*/
{
double value;
if ( y < x )
{
value = x;
}
else
{
value = y;
}
return value;
}
double r8_abs ( double x )
/******************************************************************************/
/*
Purpose:
R8_ABS returns the absolute value of an R8.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 May 2006
Author:
John Burkardt
Parameters:
Input, double X, the quantity whose absolute value is desired.
Output, double R8_ABS, the absolute value of X.
*/
{
double value;
if ( 0.0 <= x )
{
value = + x;
}
else
{
value = - x;
}
return value;
}
double r8_sign ( double x )
/******************************************************************************/
/*
Purpose:
R8_SIGN returns the sign of an R8.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
08 May 2006
Author:
John Burkardt
Parameters:
Input, double X, the number whose sign is desired.
Output, double R8_SIGN, the sign of X.
*/
{
double value;
if ( x < 0.0 )
{
value = - 1.0;
}
else
{
value = + 1.0;
}
return value;
}
double r8mat_amax ( int m, int n, double a[] )
/******************************************************************************/
/*
Purpose:
R8MAT_AMAX returns the maximum absolute value entry of an R8MAT.
Discussion:
An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
in column-major order.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 September 2012
Author:
John Burkardt
Parameters:
Input, int M, the number of rows in A.
Input, int N, the number of columns in A.
Input, double A[M*N], the M by N matrix.
Output, double R8MAT_AMAX, the maximum absolute value entry of A.
*/
{
int i;
int j;
double value;
value = r8_abs ( a[0+0*m] );
for ( j = 0; j < n; j++ )
{
for ( i = 0; i < m; i++ )
{
if ( value < r8_abs ( a[i+j*m] ) )
{
value = r8_abs ( a[i+j*m] );
}
}
}
return value;
}
double *r8mat_copy_new ( int m, int n, double a1[] )
/******************************************************************************/
/*
Purpose:
R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.
Discussion:
An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
in column-major order.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
26 July 2008
Author:
John Burkardt
Parameters:
Input, int M, N, the number of rows and columns.
Input, double A1[M*N], the matrix to be copied.
Output, double R8MAT_COPY_NEW[M*N], the copy of A1.
*/
{
double *a2;
int i;
int j;
a2 = ( double * ) malloc ( m * n * sizeof ( double ) );
for ( j = 0; j < n; j++ )
{
for ( i = 0; i < m; i++ )
{
a2[i+j*m] = a1[i+j*m];
}
}
return a2;
}
/******************************************************************************/
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy )
/******************************************************************************/
/*
Purpose:
DAXPY computes constant times a vector plus a vector.
Discussion:
This routine uses unrolled loops for increments equal to one.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Basic Linear Algebra Subprograms for Fortran Usage,
Algorithm 539,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input, int N, the number of elements in DX and DY.
Input, double DA, the multiplier of DX.
Input, double DX[*], the first vector.
Input, int INCX, the increment between successive entries of DX.
Input/output, double DY[*], the second vector.
On output, DY[*] has been replaced by DY[*] + DA * DX[*].
Input, int INCY, the increment between successive entries of DY.
*/
{
int i;
int ix;
int iy;
int m;
if ( n <= 0 )
{
return;
}
if ( da == 0.0 )
{
return;
}
/*
Code for unequal increments or equal increments
not equal to 1.
*/
if ( incx != 1 || incy != 1 )
{
if ( 0 <= incx )
{
ix = 0;
}
else
{
ix = ( - n + 1 ) * incx;
}
if ( 0 <= incy )
{
iy = 0;
}
else
{
iy = ( - n + 1 ) * incy;
}
for ( i = 0; i < n; i++ )
{
dy[iy] = dy[iy] + da * dx[ix];
ix = ix + incx;
iy = iy + incy;
}
}
/*
Code for both increments equal to 1.
*/
else
{
m = n % 4;
for ( i = 0; i < m; i++ )
{
dy[i] = dy[i] + da * dx[i];
}
for ( i = m; i < n; i = i + 4 )
{
dy[i ] = dy[i ] + da * dx[i ];
dy[i+1] = dy[i+1] + da * dx[i+1];
dy[i+2] = dy[i+2] + da * dx[i+2];
dy[i+3] = dy[i+3] + da * dx[i+3];
}
}
return;
}
/******************************************************************************/
double ddot ( int n, double dx[], int incx, double dy[], int incy )
/******************************************************************************/
/*
Purpose:
DDOT forms the dot product of two vectors.
Discussion:
This routine uses unrolled loops for increments equal to one.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Basic Linear Algebra Subprograms for Fortran Usage,
Algorithm 539,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input, int N, the number of entries in the vectors.
Input, double DX[*], the first vector.
Input, int INCX, the increment between successive entries in DX.
Input, double DY[*], the second vector.
Input, int INCY, the increment between successive entries in DY.
Output, double DDOT, the sum of the product of the corresponding
entries of DX and DY.
*/
{
double dtemp;
int i;
int ix;
int iy;
int m;
dtemp = 0.0;
if ( n <= 0 )
{
return dtemp;
}
/*
Code for unequal increments or equal increments
not equal to 1.
*/
if ( incx != 1 || incy != 1 )
{
if ( 0 <= incx )
{
ix = 0;
}
else
{
ix = ( - n + 1 ) * incx;
}
if ( 0 <= incy )
{
iy = 0;
}
else
{
iy = ( - n + 1 ) * incy;
}
for ( i = 0; i < n; i++ )
{
dtemp = dtemp + dx[ix] * dy[iy];
ix = ix + incx;
iy = iy + incy;
}
}
/*
Code for both increments equal to 1.
*/
else
{
m = n % 5;
for ( i = 0; i < m; i++ )
{
dtemp = dtemp + dx[i] * dy[i];
}
for ( i = m; i < n; i = i + 5 )
{
dtemp = dtemp + dx[i ] * dy[i ]
+ dx[i+1] * dy[i+1]
+ dx[i+2] * dy[i+2]
+ dx[i+3] * dy[i+3]
+ dx[i+4] * dy[i+4];
}
}
return dtemp;
}
/******************************************************************************/
double dnrm2 ( int n, double x[], int incx )
/******************************************************************************/
/*
Purpose:
DNRM2 returns the euclidean norm of a vector.
Discussion:
DNRM2 ( X ) = sqrt ( X' * X )
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Basic Linear Algebra Subprograms for Fortran Usage,
Algorithm 539,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input, int N, the number of entries in the vector.
Input, double X[*], the vector whose norm is to be computed.
Input, int INCX, the increment between successive entries of X.
Output, double DNRM2, the Euclidean norm of X.
*/
{
double absxi;
int i;
int ix;
double norm;
double scale;
double ssq;
double value;
if ( n < 1 || incx < 1 )
{
norm = 0.0;
}
else if ( n == 1 )
{
norm = r8_abs ( x[0] );
}
else
{
scale = 0.0;
ssq = 1.0;
ix = 0;
for ( i = 0; i < n; i++ )
{
if ( x[ix] != 0.0 )
{
absxi = r8_abs ( x[ix] );
if ( scale < absxi )
{
ssq = 1.0 + ssq * ( scale / absxi ) * ( scale / absxi );
scale = absxi;
}
else
{
ssq = ssq + ( absxi / scale ) * ( absxi / scale );
}
}
ix = ix + incx;
}
norm = scale * sqrt ( ssq );
}
return norm;
}
/******************************************************************************/
void dqrank ( double a[], int lda, int m, int n, double tol, int *kr,
int jpvt[], double qraux[] )
/******************************************************************************/
/*
Purpose:
DQRANK computes the QR factorization of a rectangular matrix.
Discussion:
This routine is used in conjunction with DQRLSS to solve
overdetermined, underdetermined and singular linear systems
in a least squares sense.
DQRANK uses the LINPACK subroutine DQRDC to compute the QR
factorization, with column pivoting, of an M by N matrix A.
The numerical rank is determined using the tolerance TOL.
Note that on output, ABS ( A(1,1) ) / ABS ( A(KR,KR) ) is an estimate
of the condition number of the matrix of independent columns,
and of R. This estimate will be <= 1/TOL.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
21 April 2012
Author:
C version by John Burkardt.
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
Parameters:
Input/output, double A[LDA*N]. On input, the matrix whose
decomposition is to be computed. On output, the information from DQRDC.
The triangular matrix R of the QR factorization is contained in the
upper triangle and information needed to recover the orthogonal
matrix Q is stored below the diagonal in A and in the vector QRAUX.
Input, int LDA, the leading dimension of A, which must
be at least M.
Input, int M, the number of rows of A.
Input, int N, the number of columns of A.
Input, double TOL, a relative tolerance used to determine the
numerical rank. The problem should be scaled so that all the elements
of A have roughly the same absolute accuracy, EPS. Then a reasonable
value for TOL is roughly EPS divided by the magnitude of the largest
element.
Output, int *KR, the numerical rank.
Output, int JPVT[N], the pivot information from DQRDC.
Columns JPVT(1), ..., JPVT(KR) of the original matrix are linearly
independent to within the tolerance TOL and the remaining columns
are linearly dependent.
Output, double QRAUX[N], will contain extra information defining
the QR factorization.
*/
{
int i;
int j;
int job;
int k;
double *work;
for ( i = 0; i < n; i++ )
{
jpvt[i] = 0;
}
work = ( double * ) malloc ( n * sizeof ( double ) );
job = 1;
dqrdc ( a, lda, m, n, qraux, jpvt, work, job );
*kr = 0;
k = i4_min ( m, n );
for ( j = 0; j < k; j++ )
{
if ( r8_abs ( a[j+j*lda] ) <= tol * r8_abs ( a[0+0*lda] ) )
{
return;
}
*kr = j + 1;
}
free ( work );
return;
}
/******************************************************************************/
void dqrdc ( double a[], int lda, int n, int p, double qraux[], int jpvt[],
double work[], int job )
/******************************************************************************/
/*
Purpose:
DQRDC computes the QR factorization of a real rectangular matrix.
Discussion:
DQRDC uses Householder transformations.
Column pivoting based on the 2-norms of the reduced columns may be
performed at the user's option.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 June 2005
Author:
C version by John Burkardt.
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
LINPACK User's Guide,
SIAM, (Society for Industrial and Applied Mathematics),
3600 University City Science Center,
Philadelphia, PA, 19104-2688.
ISBN 0-89871-172-X
Parameters:
Input/output, double A(LDA,P). On input, the N by P matrix
whose decomposition is to be computed. On output, A contains in
its upper triangle the upper triangular matrix R of the QR
factorization. Below its diagonal A contains information from
which the orthogonal part of the decomposition can be recovered.
Note that if pivoting has been requested, the decomposition is not that
of the original matrix A but that of A with its columns permuted
as described by JPVT.
Input, int LDA, the leading dimension of the array A. LDA must
be at least N.
Input, int N, the number of rows of the matrix A.
Input, int P, the number of columns of the matrix A.
Output, double QRAUX[P], contains further information required
to recover the orthogonal part of the decomposition.
Input/output, integer JPVT[P]. On input, JPVT contains integers that
control the selection of the pivot columns. The K-th column A(*,K) of A
is placed in one of three classes according to the value of JPVT(K).
> 0, then A(K) is an initial column.
= 0, then A(K) is a free column.
< 0, then A(K) is a final column.
Before the decomposition is computed, initial columns are moved to
the beginning of the array A and final columns to the end. Both
initial and final columns are frozen in place during the computation
and only free columns are moved. At the K-th stage of the
reduction, if A(*,K) is occupied by a free column it is interchanged
with the free column of largest reduced norm. JPVT is not referenced
if JOB == 0. On output, JPVT(K) contains the index of the column of the
original matrix that has been interchanged into the K-th column, if
pivoting was requested.
Workspace, double WORK[P]. WORK is not referenced if JOB == 0.
Input, int JOB, initiates column pivoting.
0, no pivoting is done.
nonzero, pivoting is done.
*/
{
int j;
int jp;
int l;
int lup;
int maxj;
double maxnrm;
double nrmxl;
int pl;
int pu;
int swapj;
double t;
double tt;
pl = 1;
pu = 0;
/*
If pivoting is requested, rearrange the columns.
*/
if ( job != 0 )
{
for ( j = 1; j <= p; j++ )
{
swapj = ( 0 < jpvt[j-1] );
if ( jpvt[j-1] < 0 )
{
jpvt[j-1] = -j;
}
else
{
jpvt[j-1] = j;
}
if ( swapj )
{
if ( j != pl )
{
dswap ( n, a+0+(pl-1)*lda, 1, a+0+(j-1), 1 );
}
jpvt[j-1] = jpvt[pl-1];
jpvt[pl-1] = j;
pl = pl + 1;
}
}
pu = p;
for ( j = p; 1 <= j; j-- )
{
if ( jpvt[j-1] < 0 )
{
jpvt[j-1] = -jpvt[j-1];
if ( j != pu )
{
dswap ( n, a+0+(pu-1)*lda, 1, a+0+(j-1)*lda, 1 );
jp = jpvt[pu-1];
jpvt[pu-1] = jpvt[j-1];
jpvt[j-1] = jp;
}
pu = pu - 1;
}
}
}
/*
Compute the norms of the free columns.
*/
for ( j = pl; j <= pu; j++ )
{
qraux[j-1] = dnrm2 ( n, a+0+(j-1)*lda, 1 );
}
for ( j = pl; j <= pu; j++ )
{
work[j-1] = qraux[j-1];
}
/*
Perform the Householder reduction of A.
*/
lup = i4_min ( n, p );
for ( l = 1; l <= lup; l++ )
{
/*
Bring the column of largest norm into the pivot position.
*/
if ( pl <= l && l < pu )
{
maxnrm = 0.0;
maxj = l;
for ( j = l; j <= pu; j++ )
{
if ( maxnrm < qraux[j-1] )
{
maxnrm = qraux[j-1];
maxj = j;
}
}
if ( maxj != l )
{
dswap ( n, a+0+(l-1)*lda, 1, a+0+(maxj-1)*lda, 1 );
qraux[maxj-1] = qraux[l-1];
work[maxj-1] = work[l-1];
jp = jpvt[maxj-1];
jpvt[maxj-1] = jpvt[l-1];
jpvt[l-1] = jp;
}
}
/*
Compute the Householder transformation for column L.
*/
qraux[l-1] = 0.0;
if ( l != n )
{
nrmxl = dnrm2 ( n-l+1, a+l-1+(l-1)*lda, 1 );
if ( nrmxl != 0.0 )
{
if ( a[l-1+(l-1)*lda] != 0.0 )
{
nrmxl = nrmxl * r8_sign ( a[l-1+(l-1)*lda] );
}
dscal ( n-l+1, 1.0 / nrmxl, a+l-1+(l-1)*lda, 1 );
a[l-1+(l-1)*lda] = 1.0 + a[l-1+(l-1)*lda];
/*
Apply the transformation to the remaining columns, updating the norms.
*/
for ( j = l + 1; j <= p; j++ )
{
t = -ddot ( n-l+1, a+l-1+(l-1)*lda, 1, a+l-1+(j-1)*lda, 1 )
/ a[l-1+(l-1)*lda];
daxpy ( n-l+1, t, a+l-1+(l-1)*lda, 1, a+l-1+(j-1)*lda, 1 );
if ( pl <= j && j <= pu )
{
if ( qraux[j-1] != 0.0 )
{
tt = 1.0 - pow ( r8_abs ( a[l-1+(j-1)*lda] ) / qraux[j-1], 2 );
tt = r8_max ( tt, 0.0 );
t = tt;
tt = 1.0 + 0.05 * tt * pow ( qraux[j-1] / work[j-1], 2 );
if ( tt != 1.0 )
{
qraux[j-1] = qraux[j-1] * sqrt ( t );
}
else
{
qraux[j-1] = dnrm2 ( n-l, a+l+(j-1)*lda, 1 );
work[j-1] = qraux[j-1];
}
}
}
}
/*
Save the transformation.
*/
qraux[l-1] = a[l-1+(l-1)*lda];
a[l-1+(l-1)*lda] = -nrmxl;
}
}
}
return;
}
/******************************************************************************/
int dqrls ( double a[], int lda, int m, int n, double tol, int *kr, double b[],
double x[], double rsd[], int jpvt[], double qraux[], int itask )
/******************************************************************************/
/*
Purpose:
DQRLS factors and solves a linear system in the least squares sense.
Discussion:
The linear system may be overdetermined, underdetermined or singular.
The solution is obtained using a QR factorization of the
coefficient matrix.
DQRLS can be efficiently used to solve several least squares
problems with the same matrix A. The first system is solved
with ITASK = 1. The subsequent systems are solved with
ITASK = 2, to avoid the recomputation of the matrix factors.
The parameters KR, JPVT, and QRAUX must not be modified
between calls to DQRLS.
DQRLS is used to solve in a least squares sense
overdetermined, underdetermined and singular linear systems.
The system is A*X approximates B where A is M by N.
B is a given M-vector, and X is the N-vector to be computed.
A solution X is found which minimimzes the sum of squares (2-norm)
of the residual, A*X - B.
The numerical rank of A is determined using the tolerance TOL.
DQRLS uses the LINPACK subroutine DQRDC to compute the QR
factorization, with column pivoting, of an M by N matrix A.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
10 September 2012
Author:
C version by John Burkardt.
Reference:
David Kahaner, Cleve Moler, Steven Nash,
Numerical Methods and Software,
Prentice Hall, 1989,
ISBN: 0-13-627258-4,
LC: TA345.K34.
Parameters:
Input/output, double A[LDA*N], an M by N matrix.
On input, the matrix whose decomposition is to be computed.
In a least squares data fitting problem, A(I,J) is the
value of the J-th basis (model) function at the I-th data point.
On output, A contains the output from DQRDC. The triangular matrix R
of the QR factorization is contained in the upper triangle and
information needed to recover the orthogonal matrix Q is stored
below the diagonal in A and in the vector QRAUX.
Input, int LDA, the leading dimension of A.
Input, int M, the number of rows of A.
Input, int N, the number of columns of A.
Input, double TOL, a relative tolerance used to determine the
numerical rank. The problem should be scaled so that all the elements
of A have roughly the same absolute accuracy EPS. Then a reasonable
value for TOL is roughly EPS divided by the magnitude of the largest
element.
Output, int *KR, the numerical rank.
Input, double B[M], the right hand side of the linear system.
Output, double X[N], a least squares solution to the linear
system.
Output, double RSD[M], the residual, B - A*X. RSD may
overwrite B.
Workspace, int JPVT[N], required if ITASK = 1.
Columns JPVT(1), ..., JPVT(KR) of the original matrix are linearly
independent to within the tolerance TOL and the remaining columns
are linearly dependent. ABS ( A(1,1) ) / ABS ( A(KR,KR) ) is an estimate
of the condition number of the matrix of independent columns,
and of R. This estimate will be <= 1/TOL.
Workspace, double QRAUX[N], required if ITASK = 1.
Input, int ITASK.
1, DQRLS factors the matrix A and solves the least squares problem.
2, DQRLS assumes that the matrix A was factored with an earlier
call to DQRLS, and only solves the least squares problem.
Output, int DQRLS, error code.
0: no error
-1: LDA < M (fatal error)
-2: N < 1 (fatal error)
-3: ITASK < 1 (fatal error)
*/
{
int ind;
if ( lda < m )
{
/*fprintf ( stderr, "\n" );
fprintf ( stderr, "DQRLS - Fatal error!\n" );
fprintf ( stderr, " LDA < M.\n" );*/
ind = -1;
return ind;
}
if ( n <= 0 )
{
/*fprintf ( stderr, "\n" );
fprintf ( stderr, "DQRLS - Fatal error!\n" );
fprintf ( stderr, " N <= 0.\n" );*/
ind = -2;
return ind;
}
if ( itask < 1 )
{
/*fprintf ( stderr, "\n" );
fprintf ( stderr, "DQRLS - Fatal error!\n" );
fprintf ( stderr, " ITASK < 1.\n" );*/
ind = -3;
return ind;
}
ind = 0;
/*
Factor the matrix.
*/
if ( itask == 1 )
{
dqrank ( a, lda, m, n, tol, kr, jpvt, qraux );
}
/*
Solve the least-squares problem.
*/
dqrlss ( a, lda, m, n, *kr, b, x, rsd, jpvt, qraux );
return ind;
}
/******************************************************************************/
void dqrlss ( double a[], int lda, int m, int n, int kr, double b[], double x[],
double rsd[], int jpvt[], double qraux[] )
/******************************************************************************/
/*
Purpose:
DQRLSS solves a linear system in a least squares sense.
Discussion:
DQRLSS must be preceeded by a call to DQRANK.
The system is to be solved is
A * X = B
where
A is an M by N matrix with rank KR, as determined by DQRANK,
B is a given M-vector,
X is the N-vector to be computed.
A solution X, with at most KR nonzero components, is found which
minimizes the 2-norm of the residual (A*X-B).
Once the matrix A has been formed, DQRANK should be
called once to decompose it. Then, for each right hand
side B, DQRLSS should be called once to obtain the
solution and residual.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
10 September 2012
Author:
C version by John Burkardt
Parameters:
Input, double A[LDA*N], the QR factorization information
from DQRANK. The triangular matrix R of the QR factorization is
contained in the upper triangle and information needed to recover
the orthogonal matrix Q is stored below the diagonal in A and in
the vector QRAUX.
Input, int LDA, the leading dimension of A, which must
be at least M.
Input, int M, the number of rows of A.
Input, int N, the number of columns of A.
Input, int KR, the rank of the matrix, as estimated by DQRANK.
Input, double B[M], the right hand side of the linear system.
Output, double X[N], a least squares solution to the
linear system.
Output, double RSD[M], the residual, B - A*X. RSD may
overwite B.
Input, int JPVT[N], the pivot information from DQRANK.
Columns JPVT[0], ..., JPVT[KR-1] of the original matrix are linearly
independent to within the tolerance TOL and the remaining columns
are linearly dependent.
Input, double QRAUX[N], auxiliary information from DQRANK
defining the QR factorization.
*/
{
int i;
int info;
int j;
int job;
int k;
double t;
if ( kr != 0 )
{
job = 110;
info = dqrsl ( a, lda, m, kr, qraux, b, rsd, rsd, x, rsd, rsd, job );
}
for ( i = 0; i < n; i++ )
{
jpvt[i] = - jpvt[i];
}
for ( i = kr; i < n; i++ )
{
x[i] = 0.0;
}
for ( j = 1; j <= n; j++ )
{
if ( jpvt[j-1] <= 0 )
{
k = - jpvt[j-1];
jpvt[j-1] = k;
while ( k != j )
{
t = x[j-1];
x[j-1] = x[k-1];
x[k-1] = t;
jpvt[k-1] = -jpvt[k-1];
k = jpvt[k-1];
}
}
}
return;
}
/******************************************************************************/
int dqrsl ( double a[], int lda, int n, int k, double qraux[], double y[],
double qy[], double qty[], double b[], double rsd[], double ab[], int job )
/******************************************************************************/
/*
Purpose:
DQRSL computes transformations, projections, and least squares solutions.
Discussion:
DQRSL requires the output of DQRDC.
For K <= min(N,P), let AK be the matrix
AK = ( A(JPVT[0]), A(JPVT(2)), ..., A(JPVT(K)) )
formed from columns JPVT[0], ..., JPVT(K) of the original
N by P matrix A that was input to DQRDC. If no pivoting was
done, AK consists of the first K columns of A in their
original order. DQRDC produces a factored orthogonal matrix Q
and an upper triangular matrix R such that
AK = Q * (R)
(0)
This information is contained in coded form in the arrays
A and QRAUX.
The parameters QY, QTY, B, RSD, and AB are not referenced
if their computation is not requested and in this case
can be replaced by dummy variables in the calling program.
To save storage, the user may in some cases use the same
array for different parameters in the calling sequence. A
frequently occuring example is when one wishes to compute
any of B, RSD, or AB and does not need Y or QTY. In this
case one may identify Y, QTY, and one of B, RSD, or AB, while
providing separate arrays for anything else that is to be
computed.
Thus the calling sequence
dqrsl ( a, lda, n, k, qraux, y, dum, y, b, y, dum, 110, info )
will result in the computation of B and RSD, with RSD
overwriting Y. More generally, each item in the following
list contains groups of permissible identifications for
a single calling sequence.
1. (Y,QTY,B) (RSD) (AB) (QY)
2. (Y,QTY,RSD) (B) (AB) (QY)
3. (Y,QTY,AB) (B) (RSD) (QY)
4. (Y,QY) (QTY,B) (RSD) (AB)
5. (Y,QY) (QTY,RSD) (B) (AB)
6. (Y,QY) (QTY,AB) (B) (RSD)
In any group the value returned in the array allocated to
the group corresponds to the last member of the group.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 June 2005
Author:
C version by John Burkardt.
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
LINPACK User's Guide,
SIAM, (Society for Industrial and Applied Mathematics),
3600 University City Science Center,
Philadelphia, PA, 19104-2688.
ISBN 0-89871-172-X
Parameters:
Input, double A[LDA*P], contains the output of DQRDC.
Input, int LDA, the leading dimension of the array A.
Input, int N, the number of rows of the matrix AK. It must
have the same value as N in DQRDC.
Input, int K, the number of columns of the matrix AK. K
must not be greater than min(N,P), where P is the same as in the
calling sequence to DQRDC.
Input, double QRAUX[P], the auxiliary output from DQRDC.
Input, double Y[N], a vector to be manipulated by DQRSL.
Output, double QY[N], contains Q * Y, if requested.
Output, double QTY[N], contains Q' * Y, if requested.
Output, double B[K], the solution of the least squares problem
minimize norm2 ( Y - AK * B),
if its computation has been requested. Note that if pivoting was
requested in DQRDC, the J-th component of B will be associated with
column JPVT(J) of the original matrix A that was input into DQRDC.
Output, double RSD[N], the least squares residual Y - AK * B,
if its computation has been requested. RSD is also the orthogonal
projection of Y onto the orthogonal complement of the column space
of AK.
Output, double AB[N], the least squares approximation Ak * B,
if its computation has been requested. AB is also the orthogonal
projection of Y onto the column space of A.
Input, integer JOB, specifies what is to be computed. JOB has
the decimal expansion ABCDE, with the following meaning:
if A != 0, compute QY.
if B != 0, compute QTY.
if C != 0, compute QTY and B.
if D != 0, compute QTY and RSD.
if E != 0, compute QTY and AB.
Note that a request to compute B, RSD, or AB automatically triggers
the computation of QTY, for which an array must be provided in the
calling sequence.
Output, int DQRSL, is zero unless the computation of B has
been requested and R is exactly singular. In this case, INFO is the
index of the first zero diagonal element of R, and B is left unaltered.
*/
{
int cab;
int cb;
int cqty;
int cqy;
int cr;
int i;
int info;
int j;
int jj;
int ju;
double t;
double temp;
/*
Set INFO flag.
*/
info = 0;
/*
Determine what is to be computed.
*/
cqy = ( job / 10000 != 0 );
cqty = ( ( job % 10000 ) != 0 );
cb = ( ( job % 1000 ) / 100 != 0 );
cr = ( ( job % 100 ) / 10 != 0 );
cab = ( ( job % 10 ) != 0 );
ju = i4_min ( k, n-1 );
/*
Special action when N = 1.
*/
if ( ju == 0 )
{
if ( cqy )
{
qy[0] = y[0];
}
if ( cqty )
{
qty[0] = y[0];
}
if ( cab )
{
ab[0] = y[0];
}
if ( cb )
{
if ( a[0+0*lda] == 0.0 )
{
info = 1;
}
else
{
b[0] = y[0] / a[0+0*lda];
}
}
if ( cr )
{
rsd[0] = 0.0;
}
return info;
}
/*
Set up to compute QY or QTY.
*/
if ( cqy )
{
for ( i = 1; i <= n; i++ )
{
qy[i-1] = y[i-1];
}
}
if ( cqty )
{
for ( i = 1; i <= n; i++ )
{
qty[i-1] = y[i-1];
}
}
/*
Compute QY.
*/
if ( cqy )
{
for ( jj = 1; jj <= ju; jj++ )
{
j = ju - jj + 1;
if ( qraux[j-1] != 0.0 )
{
temp = a[j-1+(j-1)*lda];
a[j-1+(j-1)*lda] = qraux[j-1];
t = -ddot ( n-j+1, a+j-1+(j-1)*lda, 1, qy+j-1, 1 ) / a[j-1+(j-1)*lda];
daxpy ( n-j+1, t, a+j-1+(j-1)*lda, 1, qy+j-1, 1 );
a[j-1+(j-1)*lda] = temp;
}
}
}
/*
Compute Q'*Y.
*/
if ( cqty )
{
for ( j = 1; j <= ju; j++ )
{
if ( qraux[j-1] != 0.0 )
{
temp = a[j-1+(j-1)*lda];
a[j-1+(j-1)*lda] = qraux[j-1];
t = -ddot ( n-j+1, a+j-1+(j-1)*lda, 1, qty+j-1, 1 ) / a[j-1+(j-1)*lda];
daxpy ( n-j+1, t, a+j-1+(j-1)*lda, 1, qty+j-1, 1 );
a[j-1+(j-1)*lda] = temp;
}
}
}
/*
Set up to compute B, RSD, or AB.
*/
if ( cb )
{
for ( i = 1; i <= k; i++ )
{
b[i-1] = qty[i-1];
}
}
if ( cab )
{
for ( i = 1; i <= k; i++ )
{
ab[i-1] = qty[i-1];
}
}
if ( cr && k < n )
{
for ( i = k+1; i <= n; i++ )
{
rsd[i-1] = qty[i-1];
}
}
if ( cab && k+1 <= n )
{
for ( i = k+1; i <= n; i++ )
{
ab[i-1] = 0.0;
}
}
if ( cr )
{
for ( i = 1; i <= k; i++ )
{
rsd[i-1] = 0.0;
}
}
/*
Compute B.
*/
if ( cb )
{
for ( jj = 1; jj <= k; jj++ )
{
j = k - jj + 1;
if ( a[j-1+(j-1)*lda] == 0.0 )
{
info = j;
break;
}
b[j-1] = b[j-1] / a[j-1+(j-1)*lda];
if ( j != 1 )
{
t = -b[j-1];
daxpy ( j-1, t, a+0+(j-1)*lda, 1, b, 1 );
}
}
}
/*
Compute RSD or AB as required.
*/
if ( cr || cab )
{
for ( jj = 1; jj <= ju; jj++ )
{
j = ju - jj + 1;
if ( qraux[j-1] != 0.0 )
{
temp = a[j-1+(j-1)*lda];
a[j-1+(j-1)*lda] = qraux[j-1];
if ( cr )
{
t = -ddot ( n-j+1, a+j-1+(j-1)*lda, 1, rsd+j-1, 1 )
/ a[j-1+(j-1)*lda];
daxpy ( n-j+1, t, a+j-1+(j-1)*lda, 1, rsd+j-1, 1 );
}
if ( cab )
{
t = -ddot ( n-j+1, a+j-1+(j-1)*lda, 1, ab+j-1, 1 )
/ a[j-1+(j-1)*lda];
daxpy ( n-j+1, t, a+j-1+(j-1)*lda, 1, ab+j-1, 1 );
}
a[j-1+(j-1)*lda] = temp;
}
}
}
return info;
}
/******************************************************************************/
/******************************************************************************/
void dscal ( int n, double sa, double x[], int incx )
/******************************************************************************/
/*
Purpose:
DSCAL scales a vector by a constant.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Basic Linear Algebra Subprograms for Fortran Usage,
Algorithm 539,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input, int N, the number of entries in the vector.
Input, double SA, the multiplier.
Input/output, double X[*], the vector to be scaled.
Input, int INCX, the increment between successive entries of X.
*/
{
int i;
int ix;
int m;
if ( n <= 0 )
{
}
else if ( incx == 1 )
{
m = n % 5;
for ( i = 0; i < m; i++ )
{
x[i] = sa * x[i];
}
for ( i = m; i < n; i = i + 5 )
{
x[i] = sa * x[i];
x[i+1] = sa * x[i+1];
x[i+2] = sa * x[i+2];
x[i+3] = sa * x[i+3];
x[i+4] = sa * x[i+4];
}
}
else
{
if ( 0 <= incx )
{
ix = 0;
}
else
{
ix = ( - n + 1 ) * incx;
}
for ( i = 0; i < n; i++ )
{
x[ix] = sa * x[ix];
ix = ix + incx;
}
}
return;
}
/******************************************************************************/
void dswap ( int n, double x[], int incx, double y[], int incy )
/******************************************************************************/
/*
Purpose:
DSWAP interchanges two vectors.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Basic Linear Algebra Subprograms for Fortran Usage,
Algorithm 539,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input, int N, the number of entries in the vectors.
Input/output, double X[*], one of the vectors to swap.
Input, int INCX, the increment between successive entries of X.
Input/output, double Y[*], one of the vectors to swap.
Input, int INCY, the increment between successive elements of Y.
*/
{
int i;
int ix;
int iy;
int m;
double temp;
if ( n <= 0 )
{
}
else if ( incx == 1 && incy == 1 )
{
m = n % 3;
for ( i = 0; i < m; i++ )
{
temp = x[i];
x[i] = y[i];
y[i] = temp;
}
for ( i = m; i < n; i = i + 3 )
{
temp = x[i];
x[i] = y[i];
y[i] = temp;
temp = x[i+1];
x[i+1] = y[i+1];
y[i+1] = temp;
temp = x[i+2];
x[i+2] = y[i+2];
y[i+2] = temp;
}
}
else
{
if ( 0 <= incx )
{
ix = 0;
}
else
{
ix = ( - n + 1 ) * incx;
}
if ( 0 <= incy )
{
iy = 0;
}
else
{
iy = ( - n + 1 ) * incy;
}
for ( i = 0; i < n; i++ )
{
temp = x[ix];
x[ix] = y[iy];
y[iy] = temp;
ix = ix + incx;
iy = iy + incy;
}
}
return;
}
/******************************************************************************/
/******************************************************************************/
double *qr_solve ( int m, int n, double a[], double b[] )
/******************************************************************************/
/*
Purpose:
QR_SOLVE solves a linear system in the least squares sense.
Discussion:
If the matrix A has full column rank, then the solution X should be the
unique vector that minimizes the Euclidean norm of the residual.
If the matrix A does not have full column rank, then the solution is
not unique; the vector X will minimize the residual norm, but so will
various other vectors.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
Reference:
David Kahaner, Cleve Moler, Steven Nash,
Numerical Methods and Software,
Prentice Hall, 1989,
ISBN: 0-13-627258-4,
LC: TA345.K34.
Parameters:
Input, int M, the number of rows of A.
Input, int N, the number of columns of A.
Input, double A[M*N], the matrix.
Input, double B[M], the right hand side.
Output, double QR_SOLVE[N], the least squares solution.
*/
{
double *a_qr;
int ind;
int itask;
int *jpvt;
int kr;
int lda;
double *qraux;
double *r;
double tol;
double *x;
a_qr = r8mat_copy_new ( m, n, a );
lda = m;
tol = r8_epsilon ( ) / r8mat_amax ( m, n, a_qr );
x = ( double * ) malloc ( n * sizeof ( double ) );
jpvt = ( int * ) malloc ( n * sizeof ( int ) );
qraux = ( double * ) malloc ( n * sizeof ( double ) );
r = ( double * ) malloc ( m * sizeof ( double ) );
itask = 1;
ind = dqrls ( a_qr, lda, m, n, tol, &kr, b, x, r, jpvt, qraux, itask );
free ( a_qr );
free ( jpvt );
free ( qraux );
free ( r );
return x;
}
/******************************************************************************/
#endif

@ -0,0 +1,22 @@
#include "Configuration.h"
#ifdef ACCURATE_BED_LEVELING
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy );
double ddot ( int n, double dx[], int incx, double dy[], int incy );
double dnrm2 ( int n, double x[], int incx );
void dqrank ( double a[], int lda, int m, int n, double tol, int *kr,
int jpvt[], double qraux[] );
void dqrdc ( double a[], int lda, int n, int p, double qraux[], int jpvt[],
double work[], int job );
int dqrls ( double a[], int lda, int m, int n, double tol, int *kr, double b[],
double x[], double rsd[], int jpvt[], double qraux[], int itask );
void dqrlss ( double a[], int lda, int m, int n, int kr, double b[], double x[],
double rsd[], int jpvt[], double qraux[] );
int dqrsl ( double a[], int lda, int n, int k, double qraux[], double y[],
double qy[], double qty[], double b[], double rsd[], double ab[], int job );
void dscal ( int n, double sa, double x[], int incx );
void dswap ( int n, double x[], int incx, double y[], int incy );
double *qr_solve ( int m, int n, double a[], double b[] );
#endif

@ -127,57 +127,32 @@ void matrix_3x3::set_to_identity()
matrix[6] = 0; matrix[7] = 0; matrix[8] = 1;
}
matrix_3x3 matrix_3x3::create_look_at(vector_3 target, vector_3 up)
matrix_3x3 matrix_3x3::create_look_at(vector_3 target)
{
// There are lots of examples of look at code on the internet that don't do all these noramize and also find the position
// through several dot products. The problem with them is that they have a bit of error in that all the vectors arn't normal and need to be.
vector_3 z_row = vector_3(-target.x, -target.y, -target.z).get_normal();
vector_3 x_row = vector_3::cross(up, z_row).get_normal();
vector_3 y_row = vector_3::cross(z_row, x_row).get_normal();
vector_3 z_row = target.get_normal();
vector_3 x_row = vector_3(1, 0, -target.x/target.z).get_normal();
vector_3 y_row = vector_3(0, 1, -target.y/target.z).get_normal();
//x_row.debug("x_row");
//y_row.debug("y_row");
//z_row.debug("z_row");
// x_row.debug("x_row");
// y_row.debug("y_row");
// z_row.debug("z_row");
matrix_3x3 rot = matrix_3x3::create_from_rows(vector_3(x_row.x, y_row.x, z_row.x),
vector_3(x_row.y, y_row.y, z_row.y),
vector_3(x_row.z, y_row.z, z_row.z));
//rot.debug("rot");
// create the matrix already correctly transposed
matrix_3x3 rot = matrix_3x3::create_from_rows(x_row, y_row, z_row);
// rot.debug("rot");
return rot;
}
matrix_3x3 matrix_3x3::create_inverse(matrix_3x3 original)
{
//original.debug("original");
float* A = original.matrix;
float determinant =
+ A[0 * 3 + 0] * (A[1 * 3 + 1] * A[2 * 3 + 2] - A[2 * 3 + 1] * A[1 * 3 + 2])
- A[0 * 3 + 1] * (A[1 * 3 + 0] * A[2 * 3 + 2] - A[1 * 3 + 2] * A[2 * 3 + 0])
+ A[0 * 3 + 2] * (A[1 * 3 + 0] * A[2 * 3 + 1] - A[1 * 3 + 1] * A[2 * 3 + 0]);
matrix_3x3 inverse;
inverse.matrix[0 * 3 + 0] = +(A[1 * 3 + 1] * A[2 * 3 + 2] - A[2 * 3 + 1] * A[1 * 3 + 2]) / determinant;
inverse.matrix[0 * 3 + 1] = -(A[0 * 3 + 1] * A[2 * 3 + 2] - A[0 * 3 + 2] * A[2 * 3 + 1]) / determinant;
inverse.matrix[0 * 3 + 2] = +(A[0 * 3 + 1] * A[1 * 3 + 2] - A[0 * 3 + 2] * A[1 * 3 + 1]) / determinant;
inverse.matrix[1 * 3 + 0] = -(A[1 * 3 + 0] * A[2 * 3 + 2] - A[1 * 3 + 2] * A[2 * 3 + 0]) / determinant;
inverse.matrix[1 * 3 + 1] = +(A[0 * 3 + 0] * A[2 * 3 + 2] - A[0 * 3 + 2] * A[2 * 3 + 0]) / determinant;
inverse.matrix[1 * 3 + 2] = -(A[0 * 3 + 0] * A[1 * 3 + 2] - A[1 * 3 + 0] * A[0 * 3 + 2]) / determinant;
inverse.matrix[2 * 3 + 0] = +(A[1 * 3 + 0] * A[2 * 3 + 1] - A[2 * 3 + 0] * A[1 * 3 + 1]) / determinant;
inverse.matrix[2 * 3 + 1] = -(A[0 * 3 + 0] * A[2 * 3 + 1] - A[2 * 3 + 0] * A[0 * 3 + 1]) / determinant;
inverse.matrix[2 * 3 + 2] = +(A[0 * 3 + 0] * A[1 * 3 + 1] - A[1 * 3 + 0] * A[0 * 3 + 1]) / determinant;
vector_3 row0 = vector_3(inverse.matrix[0 * 3 + 0], inverse.matrix[0 * 3 + 1], inverse.matrix[0 * 3 + 2]);
vector_3 row1 = vector_3(inverse.matrix[1 * 3 + 0], inverse.matrix[1 * 3 + 1], inverse.matrix[1 * 3 + 2]);
vector_3 row2 = vector_3(inverse.matrix[2 * 3 + 0], inverse.matrix[2 * 3 + 1], inverse.matrix[2 * 3 + 2]);
row0.normalize();
row1.normalize();
row2.normalize();
inverse = matrix_3x3::create_from_rows(row0, row1, row2);
//inverse.debug("inverse");
return inverse;
matrix_3x3 matrix_3x3::transpose(matrix_3x3 original)
{
matrix_3x3 new_matrix;
new_matrix.matrix[0] = original.matrix[0]; new_matrix.matrix[1] = original.matrix[3]; new_matrix.matrix[2] = original.matrix[6];
new_matrix.matrix[3] = original.matrix[1]; new_matrix.matrix[4] = original.matrix[4]; new_matrix.matrix[5] = original.matrix[7];
new_matrix.matrix[6] = original.matrix[2]; new_matrix.matrix[7] = original.matrix[5]; new_matrix.matrix[8] = original.matrix[8];
return new_matrix;
}
void matrix_3x3::debug(char* title)

@ -47,8 +47,8 @@ struct matrix_3x3
float matrix[9];
static matrix_3x3 create_from_rows(vector_3 row_0, vector_3 row_1, vector_3 row_2);
static matrix_3x3 create_look_at(vector_3 target, vector_3 up);
static matrix_3x3 create_inverse(matrix_3x3 original);
static matrix_3x3 create_look_at(vector_3 target);
static matrix_3x3 transpose(matrix_3x3 original);
void set_to_identity();

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