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Diffstat (limited to 'jni/feature_stab/db_vlvm/db_utilities_linalg.cpp')
| -rw-r--r-- | jni/feature_stab/db_vlvm/db_utilities_linalg.cpp | 376 |
1 files changed, 376 insertions, 0 deletions
diff --git a/jni/feature_stab/db_vlvm/db_utilities_linalg.cpp b/jni/feature_stab/db_vlvm/db_utilities_linalg.cpp new file mode 100644 index 000000000..8f68b303a --- /dev/null +++ b/jni/feature_stab/db_vlvm/db_utilities_linalg.cpp @@ -0,0 +1,376 @@ +/* + * Copyright (C) 2011 The Android Open Source Project + * + * Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* $Id: db_utilities_linalg.cpp,v 1.3 2011/06/17 14:03:31 mbansal Exp $ */ + +#include "db_utilities_linalg.h" +#include "db_utilities.h" + + + +/***************************************************************** +* Lean and mean begins here * +*****************************************************************/ + +/*Cholesky-factorize symmetric positive definite 6 x 6 matrix A. Upper +part of A is used from the input. The Cholesky factor is output as +subdiagonal part in A and diagonal in d, which is 6-dimensional*/ +void db_CholeskyDecomp6x6(double A[36],double d[6]) +{ + double s,temp; + + /*[50 mult 35 add 6sqrt=85flops 6func]*/ + /*i=0*/ + s=A[0]; + d[0]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[0]); + A[6]=A[1]*temp; + A[12]=A[2]*temp; + A[18]=A[3]*temp; + A[24]=A[4]*temp; + A[30]=A[5]*temp; + /*i=1*/ + s=A[7]-A[6]*A[6]; + d[1]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[1]); + A[13]=(A[8]-A[6]*A[12])*temp; + A[19]=(A[9]-A[6]*A[18])*temp; + A[25]=(A[10]-A[6]*A[24])*temp; + A[31]=(A[11]-A[6]*A[30])*temp; + /*i=2*/ + s=A[14]-A[12]*A[12]-A[13]*A[13]; + d[2]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[2]); + A[20]=(A[15]-A[12]*A[18]-A[13]*A[19])*temp; + A[26]=(A[16]-A[12]*A[24]-A[13]*A[25])*temp; + A[32]=(A[17]-A[12]*A[30]-A[13]*A[31])*temp; + /*i=3*/ + s=A[21]-A[18]*A[18]-A[19]*A[19]-A[20]*A[20]; + d[3]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[3]); + A[27]=(A[22]-A[18]*A[24]-A[19]*A[25]-A[20]*A[26])*temp; + A[33]=(A[23]-A[18]*A[30]-A[19]*A[31]-A[20]*A[32])*temp; + /*i=4*/ + s=A[28]-A[24]*A[24]-A[25]*A[25]-A[26]*A[26]-A[27]*A[27]; + d[4]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[4]); + A[34]=(A[29]-A[24]*A[30]-A[25]*A[31]-A[26]*A[32]-A[27]*A[33])*temp; + /*i=5*/ + s=A[35]-A[30]*A[30]-A[31]*A[31]-A[32]*A[32]-A[33]*A[33]-A[34]*A[34]; + d[5]=((s>0.0)?sqrt(s):1.0); +} + +/*Cholesky-factorize symmetric positive definite n x n matrix A.Part +above diagonal of A is used from the input, diagonal of A is assumed to +be stored in d. The Cholesky factor is output as +subdiagonal part in A and diagonal in d, which is n-dimensional*/ +void db_CholeskyDecompSeparateDiagonal(double **A,double *d,int n) +{ + int i,j,k; + double s; + double temp = 0.0; + + for(i=0;i<n;i++) for(j=i;j<n;j++) + { + if(i==j) s=d[i]; + else s=A[i][j]; + for(k=i-1;k>=0;k--) s-=A[i][k]*A[j][k]; + if(i==j) + { + d[i]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[i]); + } + else A[j][i]=s*temp; + } +} + +/*Backsubstitute L%transpose(L)*x=b for x given the Cholesky decomposition +of an n x n matrix and the right hand side b. The vector b is unchanged*/ +void db_CholeskyBacksub(double *x,const double * const *A,const double *d,int n,const double *b) +{ + int i,k; + double s; + + for(i=0;i<n;i++) + { + for(s=b[i],k=i-1;k>=0;k--) s-=A[i][k]*x[k]; + x[i]=db_SafeDivision(s,d[i]); + } + for(i=n-1;i>=0;i--) + { + for(s=x[i],k=i+1;k<n;k++) s-=A[k][i]*x[k]; + x[i]=db_SafeDivision(s,d[i]); + } +} + +/*Cholesky-factorize symmetric positive definite 3 x 3 matrix A. Part +above diagonal of A is used from the input, diagonal of A is assumed to +be stored in d. The Cholesky factor is output as subdiagonal part in A +and diagonal in d, which is 3-dimensional*/ +void db_CholeskyDecomp3x3SeparateDiagonal(double A[9],double d[3]) +{ + double s,temp; + + /*i=0*/ + s=d[0]; + d[0]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[0]); + A[3]=A[1]*temp; + A[6]=A[2]*temp; + /*i=1*/ + s=d[1]-A[3]*A[3]; + d[1]=((s>0.0)?sqrt(s):1.0); + temp=db_SafeReciprocal(d[1]); + A[7]=(A[5]-A[3]*A[6])*temp; + /*i=2*/ + s=d[2]-A[6]*A[6]-A[7]*A[7]; + d[2]=((s>0.0)?sqrt(s):1.0); +} + +/*Backsubstitute L%transpose(L)*x=b for x given the Cholesky decomposition +of a 3 x 3 matrix and the right hand side b. The vector b is unchanged*/ +void db_CholeskyBacksub3x3(double x[3],const double A[9],const double d[3],const double b[3]) +{ + /*[42 mult 30 add=72flops]*/ + x[0]=db_SafeDivision(b[0],d[0]); + x[1]=db_SafeDivision((b[1]-A[3]*x[0]),d[1]); + x[2]=db_SafeDivision((b[2]-A[6]*x[0]-A[7]*x[1]),d[2]); + x[2]=db_SafeDivision(x[2],d[2]); + x[1]=db_SafeDivision((x[1]-A[7]*x[2]),d[1]); + x[0]=db_SafeDivision((x[0]-A[6]*x[2]-A[3]*x[1]),d[0]); +} + +/*Backsubstitute L%transpose(L)*x=b for x given the Cholesky decomposition +of a 6 x 6 matrix and the right hand side b. The vector b is unchanged*/ +void db_CholeskyBacksub6x6(double x[6],const double A[36],const double d[6],const double b[6]) +{ + /*[42 mult 30 add=72flops]*/ + x[0]=db_SafeDivision(b[0],d[0]); + x[1]=db_SafeDivision((b[1]-A[6]*x[0]),d[1]); + x[2]=db_SafeDivision((b[2]-A[12]*x[0]-A[13]*x[1]),d[2]); + x[3]=db_SafeDivision((b[3]-A[18]*x[0]-A[19]*x[1]-A[20]*x[2]),d[3]); + x[4]=db_SafeDivision((b[4]-A[24]*x[0]-A[25]*x[1]-A[26]*x[2]-A[27]*x[3]),d[4]); + x[5]=db_SafeDivision((b[5]-A[30]*x[0]-A[31]*x[1]-A[32]*x[2]-A[33]*x[3]-A[34]*x[4]),d[5]); + x[5]=db_SafeDivision(x[5],d[5]); + x[4]=db_SafeDivision((x[4]-A[34]*x[5]),d[4]); + x[3]=db_SafeDivision((x[3]-A[33]*x[5]-A[27]*x[4]),d[3]); + x[2]=db_SafeDivision((x[2]-A[32]*x[5]-A[26]*x[4]-A[20]*x[3]),d[2]); + x[1]=db_SafeDivision((x[1]-A[31]*x[5]-A[25]*x[4]-A[19]*x[3]-A[13]*x[2]),d[1]); + x[0]=db_SafeDivision((x[0]-A[30]*x[5]-A[24]*x[4]-A[18]*x[3]-A[12]*x[2]-A[6]*x[1]),d[0]); +} + + +void db_Orthogonalize6x7(double A[42],int orthonormalize) +{ + int i; + double ss[6]; + + /*Compute square sums of rows*/ + ss[0]=db_SquareSum7(A); + ss[1]=db_SquareSum7(A+7); + ss[2]=db_SquareSum7(A+14); + ss[3]=db_SquareSum7(A+21); + ss[4]=db_SquareSum7(A+28); + ss[5]=db_SquareSum7(A+35); + + ss[1]-=db_OrthogonalizePair7(A+7 ,A,ss[0]); + ss[2]-=db_OrthogonalizePair7(A+14,A,ss[0]); + ss[3]-=db_OrthogonalizePair7(A+21,A,ss[0]); + ss[4]-=db_OrthogonalizePair7(A+28,A,ss[0]); + ss[5]-=db_OrthogonalizePair7(A+35,A,ss[0]); + + /*Pivot on largest ss (could also be done on ss/(original_ss))*/ + i=db_MaxIndex5(ss+1); + db_OrthogonalizationSwap7(A+7,i,ss+1); + + ss[2]-=db_OrthogonalizePair7(A+14,A+7,ss[1]); + ss[3]-=db_OrthogonalizePair7(A+21,A+7,ss[1]); + ss[4]-=db_OrthogonalizePair7(A+28,A+7,ss[1]); + ss[5]-=db_OrthogonalizePair7(A+35,A+7,ss[1]); + + i=db_MaxIndex4(ss+2); + db_OrthogonalizationSwap7(A+14,i,ss+2); + + ss[3]-=db_OrthogonalizePair7(A+21,A+14,ss[2]); + ss[4]-=db_OrthogonalizePair7(A+28,A+14,ss[2]); + ss[5]-=db_OrthogonalizePair7(A+35,A+14,ss[2]); + + i=db_MaxIndex3(ss+3); + db_OrthogonalizationSwap7(A+21,i,ss+3); + + ss[4]-=db_OrthogonalizePair7(A+28,A+21,ss[3]); + ss[5]-=db_OrthogonalizePair7(A+35,A+21,ss[3]); + + i=db_MaxIndex2(ss+4); + db_OrthogonalizationSwap7(A+28,i,ss+4); + + ss[5]-=db_OrthogonalizePair7(A+35,A+28,ss[4]); + + if(orthonormalize) + { + db_MultiplyScalar7(A ,db_SafeSqrtReciprocal(ss[0])); + db_MultiplyScalar7(A+7 ,db_SafeSqrtReciprocal(ss[1])); + db_MultiplyScalar7(A+14,db_SafeSqrtReciprocal(ss[2])); + db_MultiplyScalar7(A+21,db_SafeSqrtReciprocal(ss[3])); + db_MultiplyScalar7(A+28,db_SafeSqrtReciprocal(ss[4])); + db_MultiplyScalar7(A+35,db_SafeSqrtReciprocal(ss[5])); + } +} + +void db_Orthogonalize8x9(double A[72],int orthonormalize) +{ + int i; + double ss[8]; + + /*Compute square sums of rows*/ + ss[0]=db_SquareSum9(A); + ss[1]=db_SquareSum9(A+9); + ss[2]=db_SquareSum9(A+18); + ss[3]=db_SquareSum9(A+27); + ss[4]=db_SquareSum9(A+36); + ss[5]=db_SquareSum9(A+45); + ss[6]=db_SquareSum9(A+54); + ss[7]=db_SquareSum9(A+63); + + ss[1]-=db_OrthogonalizePair9(A+9 ,A,ss[0]); + ss[2]-=db_OrthogonalizePair9(A+18,A,ss[0]); + ss[3]-=db_OrthogonalizePair9(A+27,A,ss[0]); + ss[4]-=db_OrthogonalizePair9(A+36,A,ss[0]); + ss[5]-=db_OrthogonalizePair9(A+45,A,ss[0]); + ss[6]-=db_OrthogonalizePair9(A+54,A,ss[0]); + ss[7]-=db_OrthogonalizePair9(A+63,A,ss[0]); + + /*Pivot on largest ss (could also be done on ss/(original_ss))*/ + i=db_MaxIndex7(ss+1); + db_OrthogonalizationSwap9(A+9,i,ss+1); + + ss[2]-=db_OrthogonalizePair9(A+18,A+9,ss[1]); + ss[3]-=db_OrthogonalizePair9(A+27,A+9,ss[1]); + ss[4]-=db_OrthogonalizePair9(A+36,A+9,ss[1]); + ss[5]-=db_OrthogonalizePair9(A+45,A+9,ss[1]); + ss[6]-=db_OrthogonalizePair9(A+54,A+9,ss[1]); + ss[7]-=db_OrthogonalizePair9(A+63,A+9,ss[1]); + + i=db_MaxIndex6(ss+2); + db_OrthogonalizationSwap9(A+18,i,ss+2); + + ss[3]-=db_OrthogonalizePair9(A+27,A+18,ss[2]); + ss[4]-=db_OrthogonalizePair9(A+36,A+18,ss[2]); + ss[5]-=db_OrthogonalizePair9(A+45,A+18,ss[2]); + ss[6]-=db_OrthogonalizePair9(A+54,A+18,ss[2]); + ss[7]-=db_OrthogonalizePair9(A+63,A+18,ss[2]); + + i=db_MaxIndex5(ss+3); + db_OrthogonalizationSwap9(A+27,i,ss+3); + + ss[4]-=db_OrthogonalizePair9(A+36,A+27,ss[3]); + ss[5]-=db_OrthogonalizePair9(A+45,A+27,ss[3]); + ss[6]-=db_OrthogonalizePair9(A+54,A+27,ss[3]); + ss[7]-=db_OrthogonalizePair9(A+63,A+27,ss[3]); + + i=db_MaxIndex4(ss+4); + db_OrthogonalizationSwap9(A+36,i,ss+4); + + ss[5]-=db_OrthogonalizePair9(A+45,A+36,ss[4]); + ss[6]-=db_OrthogonalizePair9(A+54,A+36,ss[4]); + ss[7]-=db_OrthogonalizePair9(A+63,A+36,ss[4]); + + i=db_MaxIndex3(ss+5); + db_OrthogonalizationSwap9(A+45,i,ss+5); + + ss[6]-=db_OrthogonalizePair9(A+54,A+45,ss[5]); + ss[7]-=db_OrthogonalizePair9(A+63,A+45,ss[5]); + + i=db_MaxIndex2(ss+6); + db_OrthogonalizationSwap9(A+54,i,ss+6); + + ss[7]-=db_OrthogonalizePair9(A+63,A+54,ss[6]); + + if(orthonormalize) + { + db_MultiplyScalar9(A ,db_SafeSqrtReciprocal(ss[0])); + db_MultiplyScalar9(A+9 ,db_SafeSqrtReciprocal(ss[1])); + db_MultiplyScalar9(A+18,db_SafeSqrtReciprocal(ss[2])); + db_MultiplyScalar9(A+27,db_SafeSqrtReciprocal(ss[3])); + db_MultiplyScalar9(A+36,db_SafeSqrtReciprocal(ss[4])); + db_MultiplyScalar9(A+45,db_SafeSqrtReciprocal(ss[5])); + db_MultiplyScalar9(A+54,db_SafeSqrtReciprocal(ss[6])); + db_MultiplyScalar9(A+63,db_SafeSqrtReciprocal(ss[7])); + } +} + +void db_NullVectorOrthonormal6x7(double x[7],const double A[42]) +{ + int i; + double omss[7]; + const double *B; + + /*Pivot by choosing row of the identity matrix + (the one corresponding to column of A with smallest square sum)*/ + omss[0]=db_SquareSum6Stride7(A); + omss[1]=db_SquareSum6Stride7(A+1); + omss[2]=db_SquareSum6Stride7(A+2); + omss[3]=db_SquareSum6Stride7(A+3); + omss[4]=db_SquareSum6Stride7(A+4); + omss[5]=db_SquareSum6Stride7(A+5); + omss[6]=db_SquareSum6Stride7(A+6); + i=db_MinIndex7(omss); + /*orthogonalize that row against all previous rows + and normalize it*/ + B=A+i; + db_MultiplyScalarCopy7(x,A,-B[0]); + db_RowOperation7(x,A+7 ,B[7]); + db_RowOperation7(x,A+14,B[14]); + db_RowOperation7(x,A+21,B[21]); + db_RowOperation7(x,A+28,B[28]); + db_RowOperation7(x,A+35,B[35]); + x[i]+=1.0; + db_MultiplyScalar7(x,db_SafeSqrtReciprocal(1.0-omss[i])); +} + +void db_NullVectorOrthonormal8x9(double x[9],const double A[72]) +{ + int i; + double omss[9]; + const double *B; + + /*Pivot by choosing row of the identity matrix + (the one corresponding to column of A with smallest square sum)*/ + omss[0]=db_SquareSum8Stride9(A); + omss[1]=db_SquareSum8Stride9(A+1); + omss[2]=db_SquareSum8Stride9(A+2); + omss[3]=db_SquareSum8Stride9(A+3); + omss[4]=db_SquareSum8Stride9(A+4); + omss[5]=db_SquareSum8Stride9(A+5); + omss[6]=db_SquareSum8Stride9(A+6); + omss[7]=db_SquareSum8Stride9(A+7); + omss[8]=db_SquareSum8Stride9(A+8); + i=db_MinIndex9(omss); + /*orthogonalize that row against all previous rows + and normalize it*/ + B=A+i; + db_MultiplyScalarCopy9(x,A,-B[0]); + db_RowOperation9(x,A+9 ,B[9]); + db_RowOperation9(x,A+18,B[18]); + db_RowOperation9(x,A+27,B[27]); + db_RowOperation9(x,A+36,B[36]); + db_RowOperation9(x,A+45,B[45]); + db_RowOperation9(x,A+54,B[54]); + db_RowOperation9(x,A+63,B[63]); + x[i]+=1.0; + db_MultiplyScalar9(x,db_SafeSqrtReciprocal(1.0-omss[i])); +} + |