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authorcnlohr <lohr85@gmail.com>2018-03-11 22:08:51 -0400
committercnlohr <lohr85@gmail.com>2018-03-11 22:08:51 -0400
commit4b0583e11983cf2446ccbda9b6115d506f781bca (patch)
tree32f1807e270cba6eb43c4fcd4a2d61de93b1f898
parent9c7823c17219c659cf12eab9cc8bb2b3f68bbc5e (diff)
downloadlibsurvive-4b0583e11983cf2446ccbda9b6115d506f781bca.tar.gz
libsurvive-4b0583e11983cf2446ccbda9b6115d506f781bca.tar.bz2
remove unneeded dep
-rw-r--r--redist/svd.h450
1 files changed, 0 insertions, 450 deletions
diff --git a/redist/svd.h b/redist/svd.h
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--- a/redist/svd.h
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-/**************************************************************************
-**
-** svd3
-**
-** Quick singular value decomposition as described by:
-** A. McAdams, A. Selle, R. Tamstorf, J. Teran and E. Sifakis,
-** "Computing the Singular Value Decomposition of 3x3 matrices
-** with minimal branching and elementary floating point operations",
-** University of Wisconsin - Madison technical report TR1690, May 2011
-**
-** OPTIMIZED CPU VERSION
-** Implementation by: Eric Jang
-**
-** 13 Apr 2014
-**
-** This file originally retrieved from:
-** https://github.com/ericjang/svd3/blob/master/svd3.h 3/26/2017
-**
-** Original licesnse is MIT per:
-** https://github.com/ericjang/svd3/blob/master/LICENSE.md
-**
-** Ported from C++ to C by Mike Turvey. All modifications also released
-** under an MIT license.
-**************************************************************************/
-
-
-#ifndef SVD3_H
-#define SVD3_H
-
-#define _gamma 5.828427124 // FOUR_GAMMA_SQUARED = sqrt(8)+3;
-#define _cstar 0.923879532 // cos(pi/8)
-#define _sstar 0.3826834323 // sin(p/8)
-#define EPSILON 1e-6
-
-#include <math.h>
-
-/* This is a novel and fast routine for the reciprocal square root of an
-IEEE float (single precision).
-http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf
-http://playstation2-linux.com/download/p2lsd/fastrsqrt.pdf
-http://www.beyond3d.com/content/articles/8/
-*/
-inline float rsqrt(float x) {
- // int ihalf = *(int *)&x - 0x00800000; // Alternative to next line,
- // float xhalf = *(float *)&ihalf; // for sufficiently large nos.
- float xhalf = 0.5f*x;
- int i = *(int *)&x; // View x as an int.
- // i = 0x5f3759df - (i >> 1); // Initial guess (traditional).
- i = 0x5f375a82 - (i >> 1); // Initial guess (slightly better).
- x = *(float *)&i; // View i as float.
- x = x*(1.5f - xhalf*x*x); // Newton step.
- // x = x*(1.5008908 - xhalf*x*x); // Newton step for a balanced error.
- return x;
-}
-
-/* This is rsqrt with an additional step of the Newton iteration, for
-increased accuracy. The constant 0x5f37599e makes the relative error
-range from 0 to -0.00000463.
-You can't balance the error by adjusting the constant. */
-inline float rsqrt1(float x) {
- float xhalf = 0.5f*x;
- int i = *(int *)&x; // View x as an int.
- i = 0x5f37599e - (i >> 1); // Initial guess.
- x = *(float *)&i; // View i as float.
- x = x*(1.5f - xhalf*x*x); // Newton step.
- x = x*(1.5f - xhalf*x*x); // Newton step again.
- return x;
-}
-
-inline float accurateSqrt(float x)
-{
- return x * rsqrt1(x);
-}
-
-inline void condSwap(bool c, float *X, float *Y)
-{
- // used in step 2
- float Z = *X;
- *X = c ? *Y : *X;
- *Y = c ? Z : *Y;
-}
-
-inline void condNegSwap(bool c, float *X, float *Y)
-{
- // used in step 2 and 3
- float Z = -*X;
- *X = c ? *Y : *X;
- *Y = c ? Z : *Y;
-}
-
-// matrix multiplication M = A * B
-inline void multAB(float a11, float a12, float a13,
- float a21, float a22, float a23,
- float a31, float a32, float a33,
- //
- float b11, float b12, float b13,
- float b21, float b22, float b23,
- float b31, float b32, float b33,
- //
- float *m11, float *m12, float *m13,
- float *m21, float *m22, float *m23,
- float *m31, float *m32, float *m33)
-{
-
- *m11 = a11*b11 + a12*b21 + a13*b31; *m12 = a11*b12 + a12*b22 + a13*b32; *m13 = a11*b13 + a12*b23 + a13*b33;
- *m21 = a21*b11 + a22*b21 + a23*b31; *m22 = a21*b12 + a22*b22 + a23*b32; *m23 = a21*b13 + a22*b23 + a23*b33;
- *m31 = a31*b11 + a32*b21 + a33*b31; *m32 = a31*b12 + a32*b22 + a33*b32; *m33 = a31*b13 + a32*b23 + a33*b33;
-}
-
-// matrix multiplication M = Transpose[A] * B
-inline void multAtB(float a11, float a12, float a13,
- float a21, float a22, float a23,
- float a31, float a32, float a33,
- //
- float b11, float b12, float b13,
- float b21, float b22, float b23,
- float b31, float b32, float b33,
- //
- float *m11, float *m12, float *m13,
- float *m21, float *m22, float *m23,
- float *m31, float *m32, float *m33)
-{
- *m11 = a11*b11 + a21*b21 + a31*b31; *m12 = a11*b12 + a21*b22 + a31*b32; *m13 = a11*b13 + a21*b23 + a31*b33;
- *m21 = a12*b11 + a22*b21 + a32*b31; *m22 = a12*b12 + a22*b22 + a32*b32; *m23 = a12*b13 + a22*b23 + a32*b33;
- *m31 = a13*b11 + a23*b21 + a33*b31; *m32 = a13*b12 + a23*b22 + a33*b32; *m33 = a13*b13 + a23*b23 + a33*b33;
-}
-
-inline void quatToMat3(const float * qV,
- float *m11, float *m12, float *m13,
- float *m21, float *m22, float *m23,
- float *m31, float *m32, float *m33
-)
-{
- float w = qV[3];
- float x = qV[0];
- float y = qV[1];
- float z = qV[2];
-
- float qxx = x*x;
- float qyy = y*y;
- float qzz = z*z;
- float qxz = x*z;
- float qxy = x*y;
- float qyz = y*z;
- float qwx = w*x;
- float qwy = w*y;
- float qwz = w*z;
-
- *m11 = 1 - 2 * (qyy + qzz); *m12 = 2 * (qxy - qwz); *m13 = 2 * (qxz + qwy);
- *m21 = 2 * (qxy + qwz); *m22 = 1 - 2 * (qxx + qzz); *m23 = 2 * (qyz - qwx);
- *m31 = 2 * (qxz - qwy); *m32 = 2 * (qyz + qwx); *m33 = 1 - 2 * (qxx + qyy);
-}
-
-inline void approximateGivensQuaternion(float a11, float a12, float a22, float *ch, float *sh)
-{
- /*
- * Given givens angle computed by approximateGivensAngles,
- * compute the corresponding rotation quaternion.
- */
- *ch = 2 * (a11 - a22);
- *sh = a12;
- bool b = _gamma* (*sh)*(*sh) < (*ch)*(*ch);
- // fast rsqrt function suffices
- // rsqrt2 (https://code.google.com/p/lppython/source/browse/algorithm/HDcode/newCode/rsqrt.c?r=26)
- // is even faster but results in too much error
- float w = rsqrt((*ch)*(*ch) + (*sh)*(*sh));
- *ch = b ? w*(*ch) : (float)_cstar;
- *sh = b ? w*(*sh) : (float)_sstar;
-}
-
-inline void jacobiConjugation(const int x, const int y, const int z,
- float *s11,
- float *s21, float *s22,
- float *s31, float *s32, float *s33,
- float * qV)
-{
- float ch, sh;
- approximateGivensQuaternion(*s11, *s21, *s22, &ch, &sh);
-
- float scale = ch*ch + sh*sh;
- float a = (ch*ch - sh*sh) / scale;
- float b = (2 * sh*ch) / scale;
-
- // make temp copy of S
- float _s11 = *s11;
- float _s21 = *s21; float _s22 = *s22;
- float _s31 = *s31; float _s32 = *s32; float _s33 = *s33;
-
- // perform conjugation S = Q'*S*Q
- // Q already implicitly solved from a, b
- *s11 = a*(a*_s11 + b*_s21) + b*(a*_s21 + b*_s22);
- *s21 = a*(-b*_s11 + a*_s21) + b*(-b*_s21 + a*_s22); *s22 = -b*(-b*_s11 + a*_s21) + a*(-b*_s21 + a*_s22);
- *s31 = a*_s31 + b*_s32; *s32 = -b*_s31 + a*_s32; *s33 = _s33;
-
- // update cumulative rotation qV
- float tmp[3];
- tmp[0] = qV[0] * sh;
- tmp[1] = qV[1] * sh;
- tmp[2] = qV[2] * sh;
- sh *= qV[3];
-
- qV[0] *= ch;
- qV[1] *= ch;
- qV[2] *= ch;
- qV[3] *= ch;
-
- // (x,y,z) corresponds to ((0,1,2),(1,2,0),(2,0,1))
- // for (p,q) = ((0,1),(1,2),(0,2))
- qV[z] += sh;
- qV[3] -= tmp[z]; // w
- qV[x] += tmp[y];
- qV[y] -= tmp[x];
-
- // re-arrange matrix for next iteration
- _s11 = *s22;
- _s21 = *s32; _s22 = *s33;
- _s31 = *s21; _s32 = *s31; _s33 = *s11;
- *s11 = _s11;
- *s21 = _s21; *s22 = _s22;
- *s31 = _s31; *s32 = _s32; *s33 = _s33;
-
-}
-
-inline float dist2(float x, float y, float z)
-{
- return x*x + y*y + z*z;
-}
-
-// finds transformation that diagonalizes a symmetric matrix
-inline void jacobiEigenanlysis( // symmetric matrix
- float *s11,
- float *s21, float *s22,
- float *s31, float *s32, float *s33,
- // quaternion representation of V
- float * qV)
-{
- qV[3] = 1; qV[0] = 0; qV[1] = 0; qV[2] = 0; // follow same indexing convention as GLM
- for (int i = 0; i<4; i++)
- {
- // we wish to eliminate the maximum off-diagonal element
- // on every iteration, but cycling over all 3 possible rotations
- // in fixed order (p,q) = (1,2) , (2,3), (1,3) still retains
- // asymptotic convergence
- jacobiConjugation(0, 1, 2, s11, s21, s22, s31, s32, s33, qV); // p,q = 0,1
- jacobiConjugation(1, 2, 0, s11, s21, s22, s31, s32, s33, qV); // p,q = 1,2
- jacobiConjugation(2, 0, 1, s11, s21, s22, s31, s32, s33, qV); // p,q = 0,2
- }
-}
-
-
-inline void sortSingularValues(// matrix that we want to decompose
- float *b11, float *b12, float *b13,
- float *b21, float *b22, float *b23,
- float *b31, float *b32, float *b33,
- // sort V simultaneously
- float *v11, float *v12, float *v13,
- float *v21, float *v22, float *v23,
- float *v31, float *v32, float *v33)
-{
- float rho1 = dist2(*b11, *b21, *b31);
- float rho2 = dist2(*b12, *b22, *b32);
- float rho3 = dist2(*b13, *b23, *b33);
- bool c;
- c = rho1 < rho2;
- condNegSwap(c, b11, b12); condNegSwap(c, v11, v12);
- condNegSwap(c, b21, b22); condNegSwap(c, v21, v22);
- condNegSwap(c, b31, b32); condNegSwap(c, v31, v32);
- condSwap(c, &rho1, &rho2);
- c = rho1 < rho3;
- condNegSwap(c, b11, b13); condNegSwap(c, v11, v13);
- condNegSwap(c, b21, b23); condNegSwap(c, v21, v23);
- condNegSwap(c, b31, b33); condNegSwap(c, v31, v33);
- condSwap(c, &rho1, &rho3);
- c = rho2 < rho3;
- condNegSwap(c, b12, b13); condNegSwap(c, v12, v13);
- condNegSwap(c, b22, b23); condNegSwap(c, v22, v23);
- condNegSwap(c, b32, b33); condNegSwap(c, v32, v33);
-}
-
-
-void QRGivensQuaternion(float a1, float a2, float *ch, float *sh)
-{
- // a1 = pivot point on diagonal
- // a2 = lower triangular entry we want to annihilate
- float epsilon = (float)EPSILON;
- float rho = accurateSqrt(a1*a1 + a2*a2);
-
- *sh = rho > epsilon ? a2 : 0;
- *ch = fabsf(a1) + fmaxf(rho, epsilon);
- bool b = a1 < 0;
- condSwap(b, sh, ch);
- float w = rsqrt((*ch)*(*ch) + (*sh)*(*sh));
- *ch *= w;
- *sh *= w;
-}
-
-
-inline void QRDecomposition(// matrix that we want to decompose
- float b11, float b12, float b13,
- float b21, float b22, float b23,
- float b31, float b32, float b33,
- // output Q
- float *q11, float *q12, float *q13,
- float *q21, float *q22, float *q23,
- float *q31, float *q32, float *q33,
- // output R
- float *r11, float *r12, float *r13,
- float *r21, float *r22, float *r23,
- float *r31, float *r32, float *r33)
-{
- float ch1, sh1, ch2, sh2, ch3, sh3;
- float a, b;
-
- // first givens rotation (ch,0,0,sh)
- QRGivensQuaternion(b11, b21, &ch1, &sh1);
- a = 1 - 2 * sh1*sh1;
- b = 2 * ch1*sh1;
- // apply B = Q' * B
- *r11 = a*b11 + b*b21; *r12 = a*b12 + b*b22; *r13 = a*b13 + b*b23;
- *r21 = -b*b11 + a*b21; *r22 = -b*b12 + a*b22; *r23 = -b*b13 + a*b23;
- *r31 = b31; *r32 = b32; *r33 = b33;
-
- // second givens rotation (ch,0,-sh,0)
- QRGivensQuaternion(*r11, *r31, &ch2, &sh2);
- a = 1 - 2 * sh2*sh2;
- b = 2 * ch2*sh2;
- // apply B = Q' * B;
- b11 = a*(*r11) + b*(*r31); b12 = a*(*r12) + b*(*r32); b13 = a*(*r13) + b*(*r33);
- b21 = *r21; b22 = *r22; b23 = *r23;
- b31 = -b*(*r11) + a*(*r31); b32 = -b*(*r12) + a*(*r32); b33 = -b*(*r13) + a*(*r33);
-
- // third givens rotation (ch,sh,0,0)
- QRGivensQuaternion(b22, b32, &ch3, &sh3);
- a = 1 - 2 * sh3*sh3;
- b = 2 * ch3*sh3;
- // R is now set to desired value
- *r11 = b11; *r12 = b12; *r13 = b13;
- *r21 = a*b21 + b*b31; *r22 = a*b22 + b*b32; *r23 = a*b23 + b*b33;
- *r31 = -b*b21 + a*b31; *r32 = -b*b22 + a*b32; *r33 = -b*b23 + a*b33;
-
- // construct the cumulative rotation Q=Q1 * Q2 * Q3
- // the number of floating point operations for three quaternion multiplications
- // is more or less comparable to the explicit form of the joined matrix.
- // certainly more memory-efficient!
- float sh12 = sh1*sh1;
- float sh22 = sh2*sh2;
- float sh32 = sh3*sh3;
-
- *q11 = (-1 + 2 * sh12)*(-1 + 2 * sh22);
- *q12 = 4 * ch2*ch3*(-1 + 2 * sh12)*sh2*sh3 + 2 * ch1*sh1*(-1 + 2 * sh32);
- *q13 = 4 * ch1*ch3*sh1*sh3 - 2 * ch2*(-1 + 2 * sh12)*sh2*(-1 + 2 * sh32);
-
- *q21 = 2 * ch1*sh1*(1 - 2 * sh22);
- *q22 = -8 * ch1*ch2*ch3*sh1*sh2*sh3 + (-1 + 2 * sh12)*(-1 + 2 * sh32);
- *q23 = -2 * ch3*sh3 + 4 * sh1*(ch3*sh1*sh3 + ch1*ch2*sh2*(-1 + 2 * sh32));
-
- *q31 = 2 * ch2*sh2;
- *q32 = 2 * ch3*(1 - 2 * sh22)*sh3;
- *q33 = (-1 + 2 * sh22)*(-1 + 2 * sh32);
-}
-
-void svd(// input A
- float a11, float a12, float a13,
- float a21, float a22, float a23,
- float a31, float a32, float a33,
- // output U
- float *u11, float *u12, float *u13,
- float *u21, float *u22, float *u23,
- float *u31, float *u32, float *u33,
- // output S
- float *s11, float *s12, float *s13,
- float *s21, float *s22, float *s23,
- float *s31, float *s32, float *s33,
- // output V
- float *v11, float *v12, float *v13,
- float *v21, float *v22, float *v23,
- float *v31, float *v32, float *v33)
-{
- // normal equations matrix
- float ATA11, ATA12, ATA13;
- float ATA21, ATA22, ATA23;
- float ATA31, ATA32, ATA33;
-
- multAtB(a11, a12, a13, a21, a22, a23, a31, a32, a33,
- a11, a12, a13, a21, a22, a23, a31, a32, a33,
- &ATA11, &ATA12, &ATA13, &ATA21, &ATA22, &ATA23, &ATA31, &ATA32, &ATA33);
-
- // symmetric eigenalysis
- float qV[4];
- jacobiEigenanlysis(&ATA11, &ATA21, &ATA22, &ATA31, &ATA32, &ATA33, qV);
- quatToMat3(qV, v11, v12, v13, v21, v22, v23, v31, v32, v33);
-
- float b11, b12, b13;
- float b21, b22, b23;
- float b31, b32, b33;
- multAB(a11, a12, a13, a21, a22, a23, a31, a32, a33,
- *v11, *v12, *v13, *v21, *v22, *v23, *v31, *v32, *v33,
- &b11, &b12, &b13, &b21, &b22, &b23, &b31, &b32, &b33);
-
- // sort singular values and find V
- sortSingularValues(&b11, &b12, &b13, &b21, &b22, &b23, &b31, &b32, &b33,
- v11, v12, v13, v21, v22, v23, v31, v32, v33);
-
- // QR decomposition
- QRDecomposition(b11, b12, b13, b21, b22, b23, b31, b32, b33,
- u11, u12, u13, u21, u22, u23, u31, u32, u33,
- s11, s12, s13, s21, s22, s23, s31, s32, s33
- );
-}
-
-/// polar decomposition can be reconstructed trivially from SVD result
-// A = UP
-void pd(float a11, float a12, float a13,
- float a21, float a22, float a23,
- float a31, float a32, float a33,
- // output U
- float *u11, float *u12, float *u13,
- float *u21, float *u22, float *u23,
- float *u31, float *u32, float *u33,
- // output P
- float *p11, float *p12, float *p13,
- float *p21, float *p22, float *p23,
- float *p31, float *p32, float *p33)
-{
- float w11, w12, w13, w21, w22, w23, w31, w32, w33;
- float s11, s12, s13, s21, s22, s23, s31, s32, s33;
- float v11, v12, v13, v21, v22, v23, v31, v32, v33;
-
- svd(a11, a12, a13, a21, a22, a23, a31, a32, a33,
- &w11, &w12, &w13, &w21, &w22, &w23, &w31, &w32, &w33,
- &s11, &s12, &s13, &s21, &s22, &s23, &s31, &s32, &s33,
- &v11, &v12, &v13, &v21, &v22, &v23, &v31, &v32, &v33);
-
- // P = VSV'
- float t11, t12, t13, t21, t22, t23, t31, t32, t33;
- multAB(v11, v12, v13, v21, v22, v23, v31, v32, v33,
- s11, s12, s13, s21, s22, s23, s31, s32, s33,
- &t11, &t12, &t13, &t21, &t22, &t23, &t31, &t32, &t33);
-
- multAB(t11, t12, t13, t21, t22, t23, t31, t32, t33,
- v11, v21, v31, v12, v22, v32, v13, v23, v33,
- p11, p12, p13, p21, p22, p23, p31, p32, p33);
-
- // U = WV'
- multAB(w11, w12, w13, w21, w22, w23, w31, w32, w33,
- v11, v21, v31, v12, v22, v32, v13, v23, v33,
- u11, u12, u13, u21, u22, u23, u31, u32, u33);
-}
-
-#endif \ No newline at end of file