Index: trunk/psModules/src/imcombine/pmSubtractionEquation.c =================================================================== --- trunk/psModules/src/imcombine/pmSubtractionEquation.c (revision 26035) +++ trunk/psModules/src/imcombine/pmSubtractionEquation.c (revision 26893) @@ -17,5 +17,6 @@ //#define TESTING // TESTING output for debugging; may not work with threads! -#define USE_WEIGHT // Include weight (1/variance) in equation? +//#define USE_WEIGHT // Include weight (1/variance) in equation? +//#define USE_WINDOW // Include weight (1/variance) in equation? @@ -27,11 +28,15 @@ static bool calculateMatrixVector(psImage *matrix, // Least-squares matrix, updated psVector *vector, // Least-squares vector, updated + double *norm, // Normalisation, updated const psKernel *input, // Input image (target) const psKernel *reference, // Reference image (convolution source) const psKernel *weight, // Weight image + const psKernel *window, // Window image const psArray *convolutions, // Convolutions for each kernel const pmSubtractionKernels *kernels, // Kernels const psImage *polyValues, // Spatial polynomial values - int footprint // (Half-)Size of stamp + int footprint, // (Half-)Size of stamp + int normWindow, // Window (half-)size for normalisation measurement + const pmSubtractionEquationCalculationMode mode ) { @@ -51,4 +56,5 @@ // Evaluate polynomial-polynomial terms + // XXX we can skip this if we are not calculating kernel coeffs for (int iyOrder = 0, iIndex = 0; iyOrder <= spatialOrder; iyOrder++) { for (int ixOrder = 0; ixOrder <= spatialOrder - iyOrder; ixOrder++, iIndex++) { @@ -64,4 +70,18 @@ } + // initialize the matrix and vector for NOP on all coeffs. we only fill in the coeffs we + // choose to calculate + psImageInit(matrix, 0.0); + psVectorInit(vector, 1.0); + for (int i = 0; i < matrix->numCols; i++) { + matrix->data.F64[i][i] = 1.0; + } + + // the order of the elements in the matrix and vector is: + // [kernel 0, x^0 y^0][kernel 1 x^0 y^0]...[kernel N, x^0 y^0] + // [kernel 0, x^1 y^0][kernel 1 x^1 y^0]...[kernel N, x^1 y^0] + // [kernel 0, x^n y^m][kernel 1 x^n y^m]...[kernel N, x^n y^m] + // normalization + // bg 0, bg 1, bg 2 (only 0 is currently used?) for (int i = 0; i < numKernels; i++) { @@ -74,17 +94,22 @@ for (int x = - footprint; x <= footprint; x++) { double cc = iConv->kernel[y][x] * jConv->kernel[y][x]; -#ifdef USE_WEIGHT - cc *= weight->kernel[y][x]; -#endif + if (weight) { + cc *= weight->kernel[y][x]; + } + if (window) { + cc *= window->kernel[y][x]; + } sumCC += cc; } } - // Spatial variation - for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { - for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { - double value = sumCC * poly2[iTerm][jTerm]; - matrix->data.F64[iIndex][jIndex] = value; - matrix->data.F64[jIndex][iIndex] = value; + // Spatial variation of kernel coeffs + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { + for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { + double value = sumCC * poly2[iTerm][jTerm]; + matrix->data.F64[iIndex][jIndex] = value; + matrix->data.F64[jIndex][iIndex] = value; + } } } @@ -102,10 +127,16 @@ double rc = ref * conv; double c = conv; -#ifdef USE_WEIGHT - float wtVal = weight->kernel[y][x]; - ic *= wtVal; - rc *= wtVal; - c *= wtVal; -#endif + if (weight) { + float wtVal = weight->kernel[y][x]; + ic *= wtVal; + rc *= wtVal; + c *= wtVal; + } + if (window) { + float winVal = window->kernel[y][x]; + ic *= winVal; + rc *= winVal; + c *= winVal; + } sumIC += ic; sumRC += rc; @@ -117,9 +148,22 @@ double normTerm = sumRC * poly[iTerm]; double bgTerm = sumC * poly[iTerm]; - matrix->data.F64[iIndex][normIndex] = normTerm; - matrix->data.F64[normIndex][iIndex] = normTerm; - matrix->data.F64[iIndex][bgIndex] = bgTerm; - matrix->data.F64[bgIndex][iIndex] = bgTerm; - vector->data.F64[iIndex] = sumIC * poly[iTerm]; + if ((mode & PM_SUBTRACTION_EQUATION_NORM) && (mode & PM_SUBTRACTION_EQUATION_KERNELS)) { + matrix->data.F64[iIndex][normIndex] = normTerm; + matrix->data.F64[normIndex][iIndex] = normTerm; + } + if ((mode & PM_SUBTRACTION_EQUATION_BG) && (mode & PM_SUBTRACTION_EQUATION_KERNELS)) { + matrix->data.F64[iIndex][bgIndex] = bgTerm; + matrix->data.F64[bgIndex][iIndex] = bgTerm; + } + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + vector->data.F64[iIndex] = sumIC * poly[iTerm]; + if (!(mode & PM_SUBTRACTION_EQUATION_NORM)) { + // subtract norm * sumRC * poly[iTerm] + psAssert (kernels->solution1, "programming error: define solution first!"); + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + double norm = fabs(kernels->solution1->data.F64[normIndex]); // Normalisation + vector->data.F64[iIndex] -= norm * normTerm; + } + } } } @@ -130,4 +174,5 @@ double sumR = 0.0; // Sum of the reference double sumI = 0.0; // Sum of the input + double normI1 = 0.0, normI2 = 0.0; // Sum of I_1 and I_2 within the normalisation window for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { @@ -137,12 +182,26 @@ double rr = PS_SQR(ref); double one = 1.0; -#ifdef USE_WEIGHT - float wtVal = weight->kernel[y][x]; - rr *= wtVal; - ir *= wtVal; - in *= wtVal; - ref *= wtVal; - one *= wtVal; -#endif + + if (PS_SQR(x) + PS_SQR(y) <= PS_SQR(normWindow)) { + normI1 += ref; + normI2 += in; + } + + if (weight) { + float wtVal = weight->kernel[y][x]; + rr *= wtVal; + ir *= wtVal; + in *= wtVal; + ref *= wtVal; + one *= wtVal; + } + if (window) { + float winVal = window->kernel[y][x]; + rr *= winVal; + ir *= winVal; + in *= winVal; + ref *= winVal; + one *= winVal; + } sumRR += rr; sumIR += ir; @@ -152,41 +211,58 @@ } } - matrix->data.F64[normIndex][normIndex] = sumRR; - matrix->data.F64[bgIndex][bgIndex] = sum1; - matrix->data.F64[normIndex][bgIndex] = matrix->data.F64[bgIndex][normIndex] = sumR; - vector->data.F64[normIndex] = sumIR; - vector->data.F64[bgIndex] = sumI; + + *norm = normI2 / normI1; + + if (mode & PM_SUBTRACTION_EQUATION_NORM) { + matrix->data.F64[normIndex][normIndex] = sumRR; + vector->data.F64[normIndex] = sumIR; + // subtract sum over kernels * kernel solution + } + if (mode & PM_SUBTRACTION_EQUATION_BG) { + matrix->data.F64[bgIndex][bgIndex] = sum1; + vector->data.F64[bgIndex] = sumI; + } + if ((mode & PM_SUBTRACTION_EQUATION_NORM) && (mode & PM_SUBTRACTION_EQUATION_BG)) { + matrix->data.F64[normIndex][bgIndex] = sumR; + matrix->data.F64[bgIndex][normIndex] = sumR; + } + + // check for any NAN values in the result, skip if found: + for (int iy = 0; iy < matrix->numRows; iy++) { + for (int ix = 0; ix < matrix->numCols; ix++) { + if (!isfinite(matrix->data.F64[iy][ix])) { + fprintf (stderr, "WARNING: NAN in matrix\n"); + return false; + } + } + } + for (int ix = 0; ix < vector->n; ix++) { + if (!isfinite(vector->data.F64[ix])) { + fprintf (stderr, "WARNING: NAN in vector\n"); + return false; + } + } return true; } + // Calculate the least-squares matrix and vector for dual convolution -static bool calculateDualMatrixVector(psImage *matrix1, // Least-squares matrix, updated - psVector *vector1, // Least-squares vector, updated - psImage *matrix2, // Least-squares matrix, updated - psVector *vector2, // Least-squares vector, updated - psImage *matrixX, // Cross-matrix +static bool calculateDualMatrixVector(psImage *matrix, // Least-squares matrix, updated + psVector *vector, // Least-squares vector, updated + double *norm, // Normalisation, updated const psKernel *image1, // Image 1 const psKernel *image2, // Image 2 const psKernel *weight, // Weight image + const psKernel *window, // Window image const psArray *convolutions1, // Convolutions of image 1 for each kernel const psArray *convolutions2, // Convolutions of image 2 for each kernel const pmSubtractionKernels *kernels, // Kernels const psImage *polyValues, // Spatial polynomial values - int footprint // (Half-)Size of stamp + int footprint, // (Half-)Size of stamp + int normWindow, // Window (half-)size for normalisation measurement + const pmSubtractionEquationCalculationMode mode ) { - // A_ij = A_i A_j - // B_ij = B_i B_j - // C_ij = A_i B_j - // d_i = A_i I_2 - // e_i = B_i I_2 - - // A_i = I_1 * k_i - // B_i = I_2 * k_i - - // Background: A_i = 1.0 - // Normalisation: A_i = I_1 - int numKernels = kernels->num; // Number of kernels int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation @@ -196,4 +272,19 @@ double poly[numPoly]; // Polynomial terms double poly2[numPoly][numPoly]; // Polynomial-polynomial values + + int numBackground = PM_SUBTRACTION_POLYTERMS(kernels->bgOrder); // Number of background terms + int numParams = numKernels * numPoly + 1 + numBackground; // Number of regular parameters + int numParams2 = numKernels * numPoly; // Number of additional parameters for dual + int numDual = numParams + numParams2; // Total number of parameters for dual + + psAssert(matrix && + matrix->type.type == PS_TYPE_F64 && + matrix->numCols == numDual && + matrix->numRows == numDual, + "Least-squares matrix is bad."); + psAssert(vector && + vector->type.type == PS_TYPE_F64 && + vector->n == numDual, + "Least-squares vector is bad."); // Evaluate polynomial-polynomial terms @@ -212,4 +303,12 @@ + // initialize the matrix and vector for NOP on all coeffs. we only fill in the coeffs we + // choose to calculate + psImageInit(matrix, 0.0); + psVectorInit(vector, 1.0); + for (int i = 0; i < matrix->numCols; i++) { + matrix->data.F64[i][i] = 1.0; + } + for (int i = 0; i < numKernels; i++) { psKernel *iConv1 = convolutions1->data[i]; // Convolution 1 for index i @@ -219,7 +318,7 @@ psKernel *jConv2 = convolutions2->data[j]; // Convolution 2 for index j - double sumAA = 0.0; // Sum of convolution products for matrix A - double sumBB = 0.0; // Sum of convolution products for matrix B - double sumAB = 0.0; // Sum of convolution products for matrix C + double sumAA = 0.0; // Sum of convolution products between image 1 + double sumBB = 0.0; // Sum of convolution products between image 2 + double sumAB = 0.0; // Sum of convolution products across images 1 and 2 for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { @@ -227,10 +326,16 @@ double bb = iConv2->kernel[y][x] * jConv2->kernel[y][x]; double ab = iConv1->kernel[y][x] * jConv2->kernel[y][x]; -#ifdef USE_WEIGHT - float wtVal = weight->kernel[y][x]; - aa *= wtVal; - bb *= wtVal; - ab *= wtVal; -#endif + if (weight) { + float wtVal = weight->kernel[y][x]; + aa *= wtVal; + bb *= wtVal; + ab *= wtVal; + } + if (window) { + float wtVal = window->kernel[y][x]; + aa *= wtVal; + bb *= wtVal; + ab *= wtVal; + } sumAA += aa; sumBB += bb; @@ -239,15 +344,21 @@ } - // Spatial variation - for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { - for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { - double aa = sumAA * poly2[iTerm][jTerm]; - double bb = sumBB * poly2[iTerm][jTerm]; - double ab = sumAB * poly2[iTerm][jTerm]; - matrix1->data.F64[iIndex][jIndex] = aa; - matrix1->data.F64[jIndex][iIndex] = aa; - matrix2->data.F64[iIndex][jIndex] = bb; - matrix2->data.F64[jIndex][iIndex] = bb; - matrixX->data.F64[iIndex][jIndex] = ab; + // Spatial variation of kernel coeffs + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { + for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { + double aa = sumAA * poly2[iTerm][jTerm]; + double bb = sumBB * poly2[iTerm][jTerm]; + double ab = sumAB * poly2[iTerm][jTerm]; + + matrix->data.F64[iIndex][jIndex] = aa; + matrix->data.F64[jIndex][iIndex] = aa; + + matrix->data.F64[iIndex + numParams][jIndex + numParams] = bb; + matrix->data.F64[jIndex + numParams][iIndex + numParams] = bb; + + matrix->data.F64[iIndex][jIndex + numParams] = ab; + matrix->data.F64[jIndex + numParams][iIndex] = ab; + } } } @@ -259,32 +370,37 @@ for (int x = - footprint; x <= footprint; x++) { double ab = iConv1->kernel[y][x] * jConv2->kernel[y][x]; -#ifdef USE_WEIGHT - ab *= weight->kernel[y][x]; -#endif + if (weight) { + ab *= weight->kernel[y][x]; + } + if (window) { + ab *= window->kernel[y][x]; + } sumAB += ab; } } - // Spatial variation - for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { - for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { - double ab = sumAB * poly2[iTerm][jTerm]; - matrixX->data.F64[iIndex][jIndex] = ab; - } - } - } - - double sumAI2 = 0.0; // Sum of A.I_2 products (for vector 1) - double sumBI2 = 0.0; // Sum of B.I_2 products (for vector 2) - double sumAI1 = 0.0; // Sum of A.I_1 products (for matrix 1, normalisation) - double sumA = 0.0; // Sum of A (for matrix 1, background) - double sumBI1 = 0.0; // Sum of B.I_1 products (for matrix X, normalisation) - double sumB = 0.0; // Sum of B products (for matrix X, background) - double sumI2 = 0.0; // Sum of I_2 (for vector 1, background) - double sumI1I2 = 0.0; // Sum of I_1.I_2 (for vector 1, normalisation) + // Spatial variation of kernel coeffs + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + for (int iTerm = 0, iIndex = i; iTerm < numPoly; iTerm++, iIndex += numKernels) { + for (int jTerm = 0, jIndex = j; jTerm < numPoly; jTerm++, jIndex += numKernels) { + double ab = sumAB * poly2[iTerm][jTerm]; + matrix->data.F64[iIndex][jIndex + numParams] = ab; + matrix->data.F64[jIndex + numParams][iIndex] = ab; + } + } + } + } + + double sumAI2 = 0.0; // Sum of A.I_2 products (for vector) + double sumBI2 = 0.0; // Sum of B.I_2 products (for vector) + double sumAI1 = 0.0; // Sum of A.I_1 products (for matrix, normalisation) + double sumA = 0.0; // Sum of A (for matrix, background) + double sumBI1 = 0.0; // Sum of B.I_1 products (for matrix, normalisation) + double sumB = 0.0; // Sum of B products (for matrix, background) + double sumI2 = 0.0; // Sum of I_2 (for vector, background) for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - float a = iConv1->kernel[y][x]; - float b = iConv2->kernel[y][x]; + double a = iConv1->kernel[y][x]; + double b = iConv2->kernel[y][x]; float i1 = image1->kernel[y][x]; float i2 = image2->kernel[y][x]; @@ -294,18 +410,25 @@ double ai1 = a * i1; double bi1 = b * i1; - double i1i2 = i1 * i2; - -#ifdef USE_WEIGHT - float wtVal = weight->kernel[y][x]; - ai2 *= wtVal; - bi2 *= wtVal; - ai1 *= wtVal; - bi1 *= wtVal; - i1i2 *= wtVal; - a *= wtVal; - b *= wtVal; - i2 *= wtVal; -#endif - + + if (weight) { + float wtVal = weight->kernel[y][x]; + ai2 *= wtVal; + bi2 *= wtVal; + ai1 *= wtVal; + bi1 *= wtVal; + a *= wtVal; + b *= wtVal; + i2 *= wtVal; + } + if (window) { + float wtVal = window->kernel[y][x]; + ai2 *= wtVal; + bi2 *= wtVal; + ai1 *= wtVal; + bi1 *= wtVal; + a *= wtVal; + b *= wtVal; + i2 *= wtVal; + } sumAI2 += ai2; sumBI2 += bi2; @@ -315,5 +438,4 @@ sumB += b; sumI2 += i2; - sumI1I2 += i1i2; } } @@ -323,28 +445,45 @@ double bi2 = sumBI2 * poly[iTerm]; double ai1 = sumAI1 * poly[iTerm]; - double a = sumA * poly[iTerm]; + double a = sumA * poly[iTerm]; double bi1 = sumBI1 * poly[iTerm]; - double b = sumB * poly[iTerm]; - - matrix1->data.F64[iIndex][normIndex] = ai1; - matrix1->data.F64[normIndex][iIndex] = ai1; - matrix1->data.F64[iIndex][bgIndex] = a; - matrix1->data.F64[bgIndex][iIndex] = a; - vector1->data.F64[iIndex] = ai2; - vector2->data.F64[iIndex] = bi2; - matrixX->data.F64[iIndex][normIndex] = bi1; - matrixX->data.F64[iIndex][bgIndex] = b; - } - } - - double sumI1 = 0.0; // Sum of I_1 (for matrix 1, background-normalisation) - double sumI1I1 = 0.0; // Sum of I_1^2 (for matrix 1, normalisation-normalisation) - double sum1 = 0.0; // Sum of 1 (for matrix 1, background-background) - double sumI2 = 0.0; // Sum of I_2 (for vector 1, background) - double sumI1I2 = 0.0; // Sum of I_1.I_2 (for vector 1, normalisation) + double b = sumB * poly[iTerm]; + + if ((mode & PM_SUBTRACTION_EQUATION_NORM) && (mode & PM_SUBTRACTION_EQUATION_KERNELS)) { + matrix->data.F64[iIndex][normIndex] = ai1; + matrix->data.F64[normIndex][iIndex] = ai1; + matrix->data.F64[iIndex + numParams][normIndex] = bi1; + matrix->data.F64[normIndex][iIndex + numParams] = bi1; + } + if ((mode & PM_SUBTRACTION_EQUATION_BG) && (mode & PM_SUBTRACTION_EQUATION_KERNELS)) { + matrix->data.F64[iIndex][bgIndex] = a; + matrix->data.F64[bgIndex][iIndex] = a; + matrix->data.F64[iIndex + numParams][bgIndex] = b; + matrix->data.F64[bgIndex][iIndex + numParams] = b; + } + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + vector->data.F64[iIndex] = ai2; + vector->data.F64[iIndex + numParams] = bi2; + if (!(mode & PM_SUBTRACTION_EQUATION_NORM)) { + // subtract norm * sumRC * poly[iTerm] + psAssert (kernels->solution1, "programming error: define solution first!"); + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + double norm = fabs(kernels->solution1->data.F64[normIndex]); // Normalisation + vector->data.F64[iIndex] -= norm * ai1; + vector->data.F64[iIndex + numParams] -= norm * bi1; + } + } + } + } + + double sumI1 = 0.0; // Sum of I_1 (for matrix, background-normalisation) + double sumI1I1 = 0.0; // Sum of I_1^2 (for matrix, normalisation-normalisation) + double sum1 = 0.0; // Sum of 1 (for matrix, background-background) + double sumI2 = 0.0; // Sum of I_2 (for vector, background) + double sumI1I2 = 0.0; // Sum of I_1.I_2 (for vector, normalisation) + double normI1 = 0.0, normI2 = 0.0; // Sum of I_1 and I_2 within the normalisation window for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - float i1 = image1->kernel[y][x]; - float i2 = image2->kernel[y][x]; + double i1 = image1->kernel[y][x]; + double i2 = image2->kernel[y][x]; double i1i1 = i1 * i1; @@ -352,13 +491,25 @@ double i1i2 = i1 * i2; -#ifdef USE_WEIGHT - float wtVal = weight->kernel[y][x]; - i1 *= wtVal; - i1i1 *= wtVal; - one *= wtVal; - i2 *= wtVal; - i1i2 *= wtVal; -#endif - + if (PS_SQR(x) + PS_SQR(y) <= PS_SQR(normWindow)) { + normI1 += i1; + normI2 += i2; + } + + if (weight) { + float wtVal = weight->kernel[y][x]; + i1 *= wtVal; + i1i1 *= wtVal; + one *= wtVal; + i2 *= wtVal; + i1i2 *= wtVal; + } + if (window) { + float wtVal = window->kernel[y][x]; + i1 *= wtVal; + i1i1 *= wtVal; + one *= wtVal; + i2 *= wtVal; + i1i2 *= wtVal; + } sumI1 += i1; sumI1I1 += i1i1; @@ -368,80 +519,43 @@ } } - matrix1->data.F64[bgIndex][normIndex] = sumI1; - matrix1->data.F64[normIndex][bgIndex] = sumI1; - matrix1->data.F64[normIndex][normIndex] = sumI1I1; - matrix1->data.F64[bgIndex][bgIndex] = sum1; - vector1->data.F64[bgIndex] = sumI2; - vector1->data.F64[normIndex] = sumI1I2; + + *norm = normI2 / normI1; + + if (mode & PM_SUBTRACTION_EQUATION_NORM) { + matrix->data.F64[normIndex][normIndex] = sumI1I1; + vector->data.F64[normIndex] = sumI1I2; + } + if (mode & PM_SUBTRACTION_EQUATION_BG) { + matrix->data.F64[bgIndex][bgIndex] = sum1; + vector->data.F64[bgIndex] = sumI2; + } + if ((mode & PM_SUBTRACTION_EQUATION_NORM) && (mode & PM_SUBTRACTION_EQUATION_BG)) { + matrix->data.F64[bgIndex][normIndex] = sumI1; + matrix->data.F64[normIndex][bgIndex] = sumI1; + } + + // check for any NAN values in the result, skip if found: + for (int iy = 0; iy < matrix->numRows; iy++) { + for (int ix = 0; ix < matrix->numCols; ix++) { + if (!isfinite(matrix->data.F64[iy][ix])) { + fprintf (stderr, "WARNING: NAN in matrix\n"); + return false; + } + } + } + for (int ix = 0; ix < vector->n; ix++) { + if (!isfinite(vector->data.F64[ix])) { + fprintf (stderr, "WARNING: NAN in vector\n"); + return false; + } + } + return true; } -// Merge dual matrices and vectors into single matrix equation -// Have: Aa = Ct.b + d -// Have: Ca = Bb + e -// Set: F = ( A -Ct ; C -B ) -// Set: g = ( a ; b ) -// Set: h = ( d ; e ) -// So that we combine the above two equations: Fg = h -static bool calculateEquationDual(psImage **outMatrix, - psVector **outVector, - const psImage *sumMatrix1, - const psImage *sumMatrix2, - const psImage *sumMatrixX, - const psVector *sumVector1, - const psVector *sumVector2 - ) -{ - psAssert(sumMatrix1 && sumMatrix2 && sumMatrixX, "Require input matrices"); - psAssert(sumVector1 && sumVector2, "Require input vectors"); - int num1 = sumVector1->n; // Number of parameters in first set - int num2 = sumVector2->n; // Number of parameters in second set - int num = num1 + num2; // Number of parameters in new set - - psAssert(sumMatrix1->type.type == PS_TYPE_F64 && - sumMatrix2->type.type == PS_TYPE_F64 && - sumMatrixX->type.type == PS_TYPE_F64 && - sumVector1->type.type == PS_TYPE_F64 && - sumVector2->type.type == PS_TYPE_F64, - "Require input type is F64"); - - psAssert(outMatrix, "Require output matrix"); - psAssert(outVector, "Require output vector"); - if (!*outMatrix) { - *outMatrix = psImageAlloc(num, num, PS_TYPE_F64); - } - if (!*outVector) { - *outVector = psVectorAlloc(num, PS_TYPE_F64); - } - psImage *matrix = *outMatrix; - psVector *vector = *outVector; - - psAssert(sumMatrix1->numCols == num1 && sumMatrix1->numRows == num1, "Require size NxN"); - psAssert(sumMatrix2->numCols == num2 && sumMatrix2->numRows == num2, "Require size MxM"); - psAssert(sumMatrixX->numCols == num1 && sumMatrixX->numRows == num2, "Require size MxN"); - - memcpy(vector->data.F64, sumVector1->data.F64, num1 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); - memcpy(&vector->data.F64[num1], sumVector2->data.F64, num2 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); - - for (int i = 0; i < num1; i++) { - memcpy(matrix->data.F64[i], sumMatrix1->data.F64[i], num1 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); - for (int j = 0, k = num1; j < num2; j++, k++) { - matrix->data.F64[i][k] = - sumMatrixX->data.F64[j][i]; - } - } - for (int i1 = 0, i2 = num1; i1 < num2; i1++, i2++) { - memcpy(matrix->data.F64[i2], sumMatrixX->data.F64[i1], num1 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); - for (int j = 0, k = num1; j < num2; j++, k++) { - matrix->data.F64[i2][k] = - sumMatrix2->data.F64[i1][j]; - } - } - - return true; -} - - +#if 1 // Add in penalty term to least-squares vector -static bool calculatePenalty(psImage *matrix, // Matrix to which to add in penalty term +bool calculatePenalty(psImage *matrix, // Matrix to which to add in penalty term psVector *vector, // Vector to which to add in penalty term const pmSubtractionKernels *kernels, // Kernel parameters @@ -456,9 +570,29 @@ int spatialOrder = kernels->spatialOrder; // Order of spatial variations int numKernels = kernels->num; // Number of kernel components + int numSpatial = PM_SUBTRACTION_POLYTERMS(spatialOrder); // Number of spatial variations + int numParams = numKernels * numSpatial; // Number of kernel parameters + + // order is : + // [p_0,x_0,y_0 p_1,x_0,y_0, p_2,x_0,y_0] + // [p_0,x_1,y_0 p_1,x_1,y_0, p_2,x_1,y_0] + // [p_0,x_0,y_1 p_1,x_0,y_1, p_2,x_0,y_1] + // [norm] + // [bg] + // [q_0,x_0,y_0 q_1,x_0,y_0, q_2,x_0,y_0] + // [q_0,x_1,y_0 q_1,x_1,y_0, q_2,x_1,y_0] + // [q_0,x_0,y_1 q_1,x_0,y_1, q_2,x_0,y_1] + for (int i = 0; i < numKernels; i++) { for (int yOrder = 0, index = i; yOrder <= spatialOrder; yOrder++) { for (int xOrder = 0; xOrder <= spatialOrder - yOrder; xOrder++, index += numKernels) { // Contribution to chi^2: a_i^2 P_i - matrix->data.F64[index][index] -= norm * penalties->data.F32[i]; + psAssert(isfinite(penalties->data.F32[i]), "Invalid penalty"); + matrix->data.F64[index][index] += norm * penalties->data.F32[i]; + if (kernels->mode == PM_SUBTRACTION_MODE_DUAL) { + matrix->data.F64[index + numParams + 2][index + numParams + 2] += norm * penalties->data.F32[i]; + // matrix[i][i] is ~ (k_i * I_1)(k_i * I_1) + // penalties scale with second moments + // + } } } @@ -467,4 +601,5 @@ return true; } +# endif ////////////////////////////////////////////////////////////////////////////////////////////////////////////// @@ -476,9 +611,9 @@ // Calculate the value of a polynomial, specified by coefficients and polynomial values double p_pmSubtractionCalculatePolynomial(const psVector *coeff, // Coefficients - const psImage *polyValues, // Polynomial values - int order, // Order of polynomials - int index, // Index at which to begin - int step // Step between subsequent indices - ) + const psImage *polyValues, // Polynomial values + int order, // Order of polynomials + int index, // Index at which to begin + int step // Step between subsequent indices + ) { double sum = 0.0; // Value of the polynomial sum @@ -495,5 +630,5 @@ double p_pmSubtractionSolutionCoeff(const pmSubtractionKernels *kernels, const psImage *polyValues, - int index, bool wantDual) + int index, bool wantDual) { #if 0 @@ -548,10 +683,11 @@ const pmSubtractionKernels *kernels = job->args->data[1]; // Kernels int index = PS_SCALAR_VALUE(job->args->data[2], S32); // Stamp index - - return pmSubtractionCalculateEquationStamp(stamps, kernels, index); + pmSubtractionEquationCalculationMode mode = PS_SCALAR_VALUE(job->args->data[3], S32); // calculation model + + return pmSubtractionCalculateEquationStamp(stamps, kernels, index, mode); } bool pmSubtractionCalculateEquationStamp(pmSubtractionStampList *stamps, const pmSubtractionKernels *kernels, - int index) + int index, const pmSubtractionEquationCalculationMode mode) { PM_ASSERT_SUBTRACTION_STAMP_LIST_NON_NULL(stamps, false); @@ -566,12 +702,19 @@ int numBackground = PM_SUBTRACTION_POLYTERMS(kernels->bgOrder); // Number of background terms + // numKernels is the number of unique kernel images (one for each Gaussian modified by a specific polynomial). + // = \sum_i^N_Gaussians [(order + 1) * (order + 2) / 2], eg for 1 Gauss and 1st order, numKernels = 3 + // Total number of parameters to solve for: coefficient of each kernel basis function, multipled by the // number of coefficients for the spatial polynomial, normalisation and a constant background offset. int numParams = numKernels * numSpatial + 1 + numBackground; + if (kernels->mode == PM_SUBTRACTION_MODE_DUAL) { + // An additional image is convolved + numParams += numKernels * numSpatial; + } pmSubtractionStamp *stamp = stamps->stamps->data[index]; // Stamp of interest psAssert(stamp->status == PM_SUBTRACTION_STAMP_CALCULATE, "We only operate on stamps with this state."); - // Generate convolutions + // Generate convolutions: these are generated once and saved if (!pmSubtractionConvolveStamp(stamp, kernels, footprint)) { psError(PS_ERR_UNKNOWN, false, "Unable to convolve stamp %d.", index); @@ -603,44 +746,47 @@ #endif + // XXX visualize the set of convolved stamps + psImage *polyValues = p_pmSubtractionPolynomial(NULL, spatialOrder, stamp->xNorm, stamp->yNorm); // Polynomial terms - bool new = stamp->vector1 ? false : true; // Is this a new run? + bool new = stamp->vector ? false : true; // Is this a new run? if (new) { - stamp->matrix1 = psImageAlloc(numParams, numParams, PS_TYPE_F64); - stamp->vector1 = psVectorAlloc(numParams, PS_TYPE_F64); + stamp->matrix = psImageAlloc(numParams, numParams, PS_TYPE_F64); + stamp->vector = psVectorAlloc(numParams, PS_TYPE_F64); } #ifdef TESTING - psImageInit(stamp->matrix1, NAN); - psVectorInit(stamp->vector1, NAN); + psImageInit(stamp->matrix, NAN); + psVectorInit(stamp->vector, NAN); #endif bool status; // Status of least-squares matrix/vector calculation + + psKernel *weight = NULL; + psKernel *window = NULL; + +#ifdef USE_WEIGHT + weight = stamp->weight; +#endif +#ifdef USE_WINDOW + window = stamps->window; +#endif + switch (kernels->mode) { case PM_SUBTRACTION_MODE_1: - status = calculateMatrixVector(stamp->matrix1, stamp->vector1, stamp->image2, stamp->image1, - stamp->weight, stamp->convolutions1, kernels, polyValues, - footprint); + status = calculateMatrixVector(stamp->matrix, stamp->vector, &stamp->norm, stamp->image2, stamp->image1, + weight, window, stamp->convolutions1, kernels, + polyValues, footprint, stamps->normWindow, mode); break; case PM_SUBTRACTION_MODE_2: - status = calculateMatrixVector(stamp->matrix1, stamp->vector1, stamp->image1, stamp->image2, - stamp->weight, stamp->convolutions2, kernels, polyValues, - footprint); + status = calculateMatrixVector(stamp->matrix, stamp->vector, &stamp->norm, stamp->image1, stamp->image2, + weight, window, stamp->convolutions2, kernels, + polyValues, footprint, stamps->normWindow, mode); break; case PM_SUBTRACTION_MODE_DUAL: - if (new) { - stamp->matrix2 = psImageAlloc(numKernels * numSpatial, numKernels * numSpatial, PS_TYPE_F64); - stamp->matrixX = psImageAlloc(numParams, numKernels * numSpatial, PS_TYPE_F64); - stamp->vector2 = psVectorAlloc(numKernels * numSpatial, PS_TYPE_F64); - } -#ifdef TESTING - psImageInit(stamp->matrix2, NAN); - psImageInit(stamp->matrixX, NAN); - psVectorInit(stamp->vector2, NAN); -#endif - status = calculateDualMatrixVector(stamp->matrix1, stamp->vector1, stamp->matrix2, stamp->vector2, - stamp->matrixX, stamp->image1, stamp->image2, stamp->weight, - stamp->convolutions1, stamp->convolutions2, kernels, polyValues, - footprint); + status = calculateDualMatrixVector(stamp->matrix, stamp->vector, &stamp->norm, + stamp->image1, stamp->image2, + weight, window, stamp->convolutions1, stamp->convolutions2, + kernels, polyValues, footprint, stamps->normWindow, mode); break; default: @@ -651,5 +797,5 @@ stamp->status = PM_SUBTRACTION_STAMP_REJECTED; psWarning("Rejecting stamp %d (%d,%d) because of bad equation", - index, (int)(stamp->x + 0.5), (int)(stamp->y + 0.5)); + index, (int)(stamp->x - 0.5), (int)(stamp->y - 0.5)); } else { stamp->status = PM_SUBTRACTION_STAMP_USED; @@ -659,15 +805,15 @@ { psString matrixName = NULL; - psStringAppend(&matrixName, "matrix1_%d.fits", index); + psStringAppend(&matrixName, "matrix_%d.fits", index); psFits *matrixFile = psFitsOpen(matrixName, "w"); psFree(matrixName); - psFitsWriteImage(matrixFile, NULL, stamp->matrix1, 0, NULL); + psFitsWriteImage(matrixFile, NULL, stamp->matrix, 0, NULL); psFitsClose(matrixFile); matrixName = NULL; - psStringAppend(&matrixName, "vector1_%d.fits", index); - psImage *dummy = psImageAlloc(stamp->vector1->n, 1, PS_TYPE_F64); - memcpy(dummy->data.F64[0], stamp->vector1->data.F64, - PSELEMTYPE_SIZEOF(PS_TYPE_F64) * stamp->vector1->n); + psStringAppend(&matrixName, "vector_%d.fits", index); + psImage *dummy = psImageAlloc(stamp->vector->n, 1, PS_TYPE_F64); + memcpy(dummy->data.F64[0], stamp->vector->data.F64, + PSELEMTYPE_SIZEOF(PS_TYPE_F64) * stamp->vector->n); matrixFile = psFitsOpen(matrixName, "w"); psFree(matrixName); @@ -675,33 +821,4 @@ psFree(dummy); psFitsClose(matrixFile); - - if (stamp->vector2) { - matrixName = NULL; - psStringAppend(&matrixName, "vector2_%d.fits", index); - dummy = psImageAlloc(stamp->vector2->n, 1, PS_TYPE_F64); - memcpy(dummy->data.F64[0], stamp->vector2->data.F64, - PSELEMTYPE_SIZEOF(PS_TYPE_F64) * stamp->vector2->n); - matrixFile = psFitsOpen(matrixName, "w"); - psFree(matrixName); - psFitsWriteImage(matrixFile, NULL, dummy, 0, NULL); - psFree(dummy); - psFitsClose(matrixFile); - } - - if (kernels->mode == PM_SUBTRACTION_MODE_DUAL) { - matrixName = NULL; - psStringAppend(&matrixName, "matrix2_%d.fits", index); - matrixFile = psFitsOpen(matrixName, "w"); - psFree(matrixName); - psFitsWriteImage(matrixFile, NULL, stamp->matrix2, 0, NULL); - psFitsClose(matrixFile); - - matrixName = NULL; - psStringAppend(&matrixName, "matrixX_%d.fits", index); - matrixFile = psFitsOpen(matrixName, "w"); - psFree(matrixName); - psFitsWriteImage(matrixFile, NULL, stamp->matrixX, 0, NULL); - psFitsClose(matrixFile); - } } #endif @@ -712,5 +829,6 @@ } -bool pmSubtractionCalculateEquation(pmSubtractionStampList *stamps, const pmSubtractionKernels *kernels) +bool pmSubtractionCalculateEquation(pmSubtractionStampList *stamps, const pmSubtractionKernels *kernels, + const pmSubtractionEquationCalculationMode mode) { PM_ASSERT_SUBTRACTION_STAMP_LIST_NON_NULL(stamps, false); @@ -727,4 +845,11 @@ } + if ((stamp->x <= 0.0) && (stamp->y <= 0.0)) { + psAbort ("bad stamp"); + } + if (!isfinite(stamp->x) && !isfinite(stamp->y)) { + psAbort ("bad stamp"); + } + if (pmSubtractionThreaded()) { psThreadJob *job = psThreadJobAlloc("PSMODULES_SUBTRACTION_CALCULATE_EQUATION"); @@ -732,4 +857,5 @@ psArrayAdd(job->args, 1, (pmSubtractionKernels*)kernels); // Casting away const to put on array PS_ARRAY_ADD_SCALAR(job->args, i, PS_TYPE_S32); + PS_ARRAY_ADD_SCALAR(job->args, mode, PS_TYPE_S32); if (!psThreadJobAddPending(job)) { psFree(job); @@ -738,5 +864,5 @@ psFree(job); } else { - pmSubtractionCalculateEquationStamp(stamps, kernels, i); + pmSubtractionCalculateEquationStamp(stamps, kernels, i, mode); } } @@ -748,4 +874,6 @@ pmSubtractionVisualPlotLeastSquares(stamps); + pmSubtractionVisualShowKernels((pmSubtractionKernels *)kernels); + pmSubtractionVisualShowBasis(stamps); psLogMsg("psModules.imcombine", PS_LOG_INFO, "Calculate equation: %f sec", @@ -756,5 +884,28 @@ } -bool pmSubtractionSolveEquation(pmSubtractionKernels *kernels, const pmSubtractionStampList *stamps) +// private functions used on pmSubtractionSolveEquation +bool psVectorWriteFile (char *filename, const psVector *vector); +bool psFitsWriteImageSimple (char *filename, psImage *image, psMetadata *header); + +psImage *p_pmSubSolve_wUt (psVector *w, psImage *U); +psImage *p_pmSubSolve_VwUt (psImage *V, psImage *wUt); + +bool p_pmSubSolve_SetWeights (psVector *wApply, psVector *w, psVector *wMask); + +bool p_pmSubSolve_UtB (psVector **UtB, psImage *U, psVector *B); +bool p_pmSubSolve_wUtB (psVector **wUtB, psVector *w, psVector *UtB); +bool p_pmSubSolve_VwUtB (psVector **VwUtB, psImage *V, psVector *wUtB); + +bool p_pmSubSolve_Ax (psVector **B, psImage *A, psVector *x); +bool p_pmSubSolve_VdV (double *value, psVector *x, psVector *y); +bool p_pmSubSolve_y2 (double *y2, pmSubtractionKernels *kernels, const pmSubtractionStampList *stamps); + +psImage *p_pmSubSolve_Xvar (psImage *V, psVector *w); + +double p_pmSubSolve_ChiSquare (pmSubtractionKernels *kernels, const pmSubtractionStampList *stamps); + +bool pmSubtractionSolveEquation(pmSubtractionKernels *kernels, + const pmSubtractionStampList *stamps, + const pmSubtractionEquationCalculationMode mode) { PM_ASSERT_SUBTRACTION_KERNELS_NON_NULL(kernels, false); @@ -762,6 +913,15 @@ // Check inputs - int numParams = -1; // Number of parameters - int numParams2 = 0; // Number of parameters for part solution (DUAL mode) + int numKernels = kernels->num; // Number of kernel basis functions + int numSpatial = PM_SUBTRACTION_POLYTERMS(kernels->spatialOrder); // Number of spatial variations + int numBackground = PM_SUBTRACTION_POLYTERMS(kernels->bgOrder); // Number of background terms + int numParams = numKernels * numSpatial + 1 + numBackground; // Number of parameters being solved for + int numSolution1 = numParams, numSolution2 = 0; // Number of parameters for each solution + if (kernels->mode == PM_SUBTRACTION_MODE_DUAL) { + // An additional image is convolved + numSolution2 = numKernels * numSpatial; + numParams += numSolution2; + } + for (int i = 0; i < stamps->num; i++) { pmSubtractionStamp *stamp = stamps->stamps->data[i]; // Stamp of interest @@ -771,32 +931,10 @@ } - PS_ASSERT_VECTOR_NON_NULL(stamp->vector1, false); - if (numParams == -1) { - numParams = stamp->vector1->n; - } - PS_ASSERT_VECTOR_SIZE(stamp->vector1, (long)numParams, false); - PS_ASSERT_VECTOR_TYPE(stamp->vector1, PS_TYPE_F64, false); - PS_ASSERT_IMAGE_NON_NULL(stamp->matrix1, false); - PS_ASSERT_IMAGE_SIZE(stamp->matrix1, numParams, numParams, false); - PS_ASSERT_IMAGE_TYPE(stamp->matrix1, PS_TYPE_F64, false); - - if (kernels->mode == PM_SUBTRACTION_MODE_DUAL) { - PS_ASSERT_IMAGE_NON_NULL(stamp->matrix2, false); - PS_ASSERT_IMAGE_NON_NULL(stamp->matrixX, false); - if (numParams2 == 0) { - numParams2 = stamp->matrix2->numCols; - } - PS_ASSERT_IMAGE_SIZE(stamp->matrix2, numParams2, numParams2, false); - PS_ASSERT_IMAGE_SIZE(stamp->matrixX, numParams, numParams2, false); - PS_ASSERT_IMAGE_TYPE(stamp->matrix2, PS_TYPE_F64, false); - PS_ASSERT_IMAGE_TYPE(stamp->matrixX, PS_TYPE_F64, false); - PS_ASSERT_VECTOR_NON_NULL(stamp->vector2, false); - PS_ASSERT_VECTOR_SIZE(stamp->vector2, (long)numParams2, false); - PS_ASSERT_VECTOR_TYPE(stamp->vector2, PS_TYPE_F64, false); - } - } - if (numParams == -1) { - psError(PS_ERR_BAD_PARAMETER_VALUE, true, "No suitable stamps found."); - return NULL; + PS_ASSERT_VECTOR_NON_NULL(stamp->vector, false); + PS_ASSERT_VECTOR_SIZE(stamp->vector, (long)numParams, false); + PS_ASSERT_VECTOR_TYPE(stamp->vector, PS_TYPE_F64, false); + PS_ASSERT_IMAGE_NON_NULL(stamp->matrix, false); + PS_ASSERT_IMAGE_SIZE(stamp->matrix, numParams, numParams, false); + PS_ASSERT_IMAGE_TYPE(stamp->matrix, PS_TYPE_F64, false); } @@ -814,28 +952,14 @@ psVectorInit(sumVector, 0.0); psImageInit(sumMatrix, 0.0); + + psVector *norms = psVectorAllocEmpty(stamps->num, PS_TYPE_F64); // Normalisations + int numStamps = 0; // Number of good stamps for (int i = 0; i < stamps->num; i++) { pmSubtractionStamp *stamp = stamps->stamps->data[i]; // Stamp of interest - if (stamp->status == PM_SUBTRACTION_STAMP_USED) { - -#ifdef TESTING - // XXX double-check for NAN in data: - for (int iy = 0; iy < stamp->matrix1->numRows; iy++) { - for (int ix = 0; ix < stamp->matrix1->numCols; ix++) { - if (!isfinite(stamp->matrix1->data.F64[iy][ix])) { - fprintf (stderr, "WARNING: NAN in matrix1\n"); - } - } - } - for (int ix = 0; ix < stamp->vector1->n; ix++) { - if (!isfinite(stamp->vector1->data.F64[ix])) { - fprintf (stderr, "WARNING: NAN in vector1\n"); - } - } -#endif - - (void)psBinaryOp(sumMatrix, sumMatrix, "+", stamp->matrix1); - (void)psBinaryOp(sumVector, sumVector, "+", stamp->vector1); + (void)psBinaryOp(sumMatrix, sumMatrix, "+", stamp->matrix); + (void)psBinaryOp(sumVector, sumVector, "+", stamp->vector); + psVectorAppend(norms, stamp->norm); pmSubtractionStampPrint(ds9, stamp->x, stamp->y, stamps->footprint, "green"); numStamps++; @@ -845,12 +969,4 @@ } -#ifdef TESTING - for (int ix = 0; ix < sumVector->n; ix++) { - if (!isfinite(sumVector->data.F64[ix])) { - fprintf (stderr, "WARNING: NAN in vector1\n"); - } - } -#endif - #if 0 int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index for background @@ -858,41 +974,80 @@ #endif -#ifdef TESTING - for (int ix = 0; ix < sumVector->n; ix++) { - if (!isfinite(sumVector->data.F64[ix])) { - fprintf (stderr, "WARNING: NAN in vector1\n"); - } - } + psVector *solution = NULL; // Solution to equation! + solution = psVectorAlloc(numParams, PS_TYPE_F64); + psVectorInit(solution, 0); + +#if 0 + // Regular, straight-forward solution + solution = psMatrixSolveSVD(solution, sumMatrix, sumVector, NAN); +#else { - psImage *inverse = psMatrixInvert(NULL, sumMatrix, NULL); - psFits *fits = psFitsOpen("matrixInv.fits", "w"); - psFitsWriteImage(fits, NULL, inverse, 0, NULL); - psFitsClose(fits); - psFree(inverse); - } - { - psImage *X = psMatrixInvert(NULL, sumMatrix, NULL); - psImage *Xt = psMatrixTranspose(NULL, X); - psImage *XtX = psMatrixMultiply(NULL, Xt, X); - psFits *fits = psFitsOpen("matrixErr.fits", "w"); - psFitsWriteImage(fits, NULL, XtX, 0, NULL); - psFitsClose(fits); - psFree(X); - psFree(Xt); - psFree(XtX); - } -#endif - - psVector *permutation = NULL; // Permutation vector, required for LU decomposition - psImage *luMatrix = psMatrixLUDecomposition(NULL, &permutation, sumMatrix); + // Solve normalisation and background separately + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index for background + + psStats *stats = psStatsAlloc(PS_STAT_ROBUST_MEDIAN); // Statistics for norm + if (!psVectorStats(stats, norms, NULL, NULL, 0)) { + psError(PS_ERR_UNKNOWN, false, "Unable to determine median normalisation"); + psFree(stats); + psFree(sumMatrix); + psFree(sumVector); + psFree(norms); + return false; + } + + double normValue = stats->robustMedian; + // double bgValue = 0.0; + + psFree(stats); + + fprintf(stderr, "Norm: %lf\n", normValue); + + // Solve kernel components + for (int i = 0; i < numSolution1; i++) { + sumVector->data.F64[i] -= normValue * sumMatrix->data.F64[normIndex][i]; + + sumMatrix->data.F64[i][normIndex] = 0.0; + sumMatrix->data.F64[normIndex][i] = 0.0; + } + sumVector->data.F64[bgIndex] -= normValue * sumMatrix->data.F64[normIndex][bgIndex]; + sumMatrix->data.F64[bgIndex][normIndex] = 0.0; + sumMatrix->data.F64[normIndex][bgIndex] = 0.0; + + sumMatrix->data.F64[normIndex][normIndex] = 1.0; + sumVector->data.F64[normIndex] = 0.0; + + solution = psMatrixSolveSVD(solution, sumMatrix, sumVector, NAN); + + solution->data.F64[normIndex] = normValue; + } +# endif + + if (!kernels->solution1) { + kernels->solution1 = psVectorAlloc(sumVector->n, PS_TYPE_F64); + psVectorInit(kernels->solution1, 0.0); + } + + // only update the solutions that we chose to calculate: + if (mode & PM_SUBTRACTION_EQUATION_NORM) { + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + kernels->solution1->data.F64[normIndex] = solution->data.F64[normIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_BG) { + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index in matrix for background + kernels->solution1->data.F64[bgIndex] = solution->data.F64[bgIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + int numKernels = kernels->num; + int spatialOrder = kernels->spatialOrder; // Order of spatial variation + int numPoly = PM_SUBTRACTION_POLYTERMS(spatialOrder); // Number of polynomial terms + for (int i = 0; i < numKernels * numPoly; i++) { + kernels->solution1->data.F64[i] = solution->data.F64[i]; + } + } + + psFree(solution); + psFree(sumVector); psFree(sumMatrix); - if (!luMatrix) { - psError(PS_ERR_UNKNOWN, true, "LU Decomposition of least-squares matrix failed.\n"); - psFree(sumVector); - psFree(luMatrix); - psFree(permutation); - return NULL; - } - kernels->solution1 = psMatrixLUSolution(kernels->solution1, luMatrix, sumVector, permutation); #ifdef TESTING @@ -900,30 +1055,19 @@ for (int ix = 0; ix < kernels->solution1->n; ix++) { if (!isfinite(kernels->solution1->data.F64[ix])) { - fprintf (stderr, "WARNING: NAN in vector1\n"); - } - } -#endif - - psFree(sumVector); - psFree(luMatrix); - psFree(permutation); - if (!kernels->solution1) { - psError(PS_ERR_UNKNOWN, true, "Failed to solve the least-squares system.\n"); - return NULL; - } + fprintf (stderr, "WARNING: NAN in vector\n"); + } + } +#endif + } else { // Dual convolution solution // Accumulation of stamp matrices/vectors - psImage *sumMatrix1 = psImageAlloc(numParams, numParams, PS_TYPE_F64); - psImage *sumMatrix2 = psImageAlloc(numParams2, numParams2, PS_TYPE_F64); - psImage *sumMatrixX = psImageAlloc(numParams, numParams2, PS_TYPE_F64); - psVector *sumVector1 = psVectorAlloc(numParams, PS_TYPE_F64); - psVector *sumVector2 = psVectorAlloc(numParams, PS_TYPE_F64); - psImageInit(sumMatrix1, 0.0); - psImageInit(sumMatrix2, 0.0); - psImageInit(sumMatrixX, 0.0); - psVectorInit(sumVector1, 0.0); - psVectorInit(sumVector2, 0.0); + psImage *sumMatrix = psImageAlloc(numParams, numParams, PS_TYPE_F64); + psVector *sumVector = psVectorAlloc(numParams, PS_TYPE_F64); + psImageInit(sumMatrix, 0.0); + psVectorInit(sumVector, 0.0); + + psVector *norms = psVectorAllocEmpty(stamps->num, PS_TYPE_F64); // Normalisations int numStamps = 0; // Number of good stamps @@ -931,9 +1075,9 @@ pmSubtractionStamp *stamp = stamps->stamps->data[i]; // Stamp of interest if (stamp->status == PM_SUBTRACTION_STAMP_USED) { - (void)psBinaryOp(sumMatrix1, sumMatrix1, "+", stamp->matrix1); - (void)psBinaryOp(sumMatrix2, sumMatrix2, "+", stamp->matrix2); - (void)psBinaryOp(sumMatrixX, sumMatrixX, "+", stamp->matrixX); - (void)psBinaryOp(sumVector1, sumVector1, "+", stamp->vector1); - (void)psBinaryOp(sumVector2, sumVector2, "+", stamp->vector2); + (void)psBinaryOp(sumMatrix, sumMatrix, "+", stamp->matrix); + (void)psBinaryOp(sumVector, sumVector, "+", stamp->vector); + + psVectorAppend(norms, stamp->norm); + pmSubtractionStampPrint(ds9, stamp->x, stamp->y, stamps->footprint, "green"); numStamps++; @@ -941,174 +1085,136 @@ } - int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index for background - calculatePenalty(sumMatrix1, sumVector1, kernels, sumMatrix1->data.F64[bgIndex][bgIndex]); - calculatePenalty(sumMatrix2, sumVector2, kernels, -sumMatrix1->data.F64[bgIndex][bgIndex]); - - psImage *sumMatrix = NULL; // Combined matrix - psVector *sumVector = NULL; // Combined vector - calculateEquationDual(&sumMatrix, &sumVector, sumMatrix1, sumMatrix2, - sumMatrixX, sumVector1, sumVector2); - #ifdef TESTING + psFitsWriteImageSimple ("sumMatrix.fits", sumMatrix, NULL); + psVectorWriteFile("sumVector.dat", sumVector); +#endif + +#if 1 + // int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index for background + // calculatePenalty(sumMatrix, sumVector, kernels, sumMatrix->data.F64[bgIndex][bgIndex]); + + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + calculatePenalty(sumMatrix, sumVector, kernels, sumMatrix->data.F64[normIndex][normIndex] / 1000.0); +#endif + + psVector *solution = NULL; // Solution to equation! + solution = psVectorAlloc(numParams, PS_TYPE_F64); + psVectorInit(solution, 0); + +#if 0 + // Regular, straight-forward solution + solution = psMatrixSolveSVD(solution, sumMatrix, sumVector, NAN); +#else { - psFits *fits = psFitsOpen("sumMatrix.fits", "w"); - psFitsWriteImage(fits, NULL, sumMatrix, 0, NULL); - psFitsClose(fits); - } - { - psImage *image = psImageAlloc(1, numParams + numParams2, PS_TYPE_F64); - psFits *fits = psFitsOpen("sumVector.fits", "w"); - for (int i = 0; i < numParams + numParams2; i++) { - image->data.F64[0][i] = sumVector->data.F64[i]; - } - psFitsWriteImage(fits, NULL, image, 0, NULL); - psFree(image); - psFitsClose(fits); - } -#endif - - psVector *solution = NULL; // Solution to equation! - { - solution = psMatrixSolveSVD(solution, sumMatrix, sumVector); - if (!solution) { - psError(PS_ERR_UNKNOWN, false, "SVD solution of least-squares equation failed.\n"); + // Solve normalisation and background separately + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index for background + +#if 0 + psImage *normMatrix = psImageAlloc(2, 2, PS_TYPE_F64); + psVector *normVector = psVectorAlloc(2, PS_TYPE_F64); + + normMatrix->data.F64[0][0] = sumMatrix->data.F64[normIndex][normIndex]; + normMatrix->data.F64[1][1] = sumMatrix->data.F64[bgIndex][bgIndex]; + normMatrix->data.F64[0][1] = normMatrix->data.F64[1][0] = sumMatrix->data.F64[normIndex][bgIndex]; + + normVector->data.F64[0] = sumVector->data.F64[normIndex]; + normVector->data.F64[1] = sumVector->data.F64[bgIndex]; + + psVector *normSolution = psMatrixSolveSVD(NULL, normMatrix, normVector, NAN); + + double normValue = normSolution->data.F64[0]; + double bgValue = normSolution->data.F64[1]; + + psFree(normMatrix); + psFree(normVector); + psFree(normSolution); +#endif + + psStats *stats = psStatsAlloc(PS_STAT_ROBUST_MEDIAN); // Statistics for norm + if (!psVectorStats(stats, norms, NULL, NULL, 0)) { + psError(PS_ERR_UNKNOWN, false, "Unable to determine median normalisation"); + psFree(stats); psFree(sumMatrix); psFree(sumVector); - return NULL; - } - - int numSpatial = PM_SUBTRACTION_POLYTERMS(kernels->spatialOrder); // Number of spatial variations - int numKernels = kernels->num; // Number of kernel basis functions - - // Remove a kernel basis for image 1 from the equation -#define MASK_BASIS_1(INDEX) \ - { \ - for (int j = 0, index = INDEX; j < numSpatial; j++, index += numKernels) { \ - for (int k = 0; k < numParams2; k++) { \ - sumMatrix1->data.F64[k][index] = 0.0; \ - sumMatrix1->data.F64[index][k] = 0.0; \ - sumMatrixX->data.F64[k][index] = 0.0; \ - } \ - sumMatrix1->data.F64[bgIndex][index] = 0.0; \ - sumMatrix1->data.F64[index][bgIndex] = 0.0; \ - sumMatrix1->data.F64[normIndex][index] = 0.0; \ - sumMatrix1->data.F64[index][normIndex] = 0.0; \ - sumMatrix1->data.F64[index][index] = 1.0; \ - sumVector1->data.F64[index] = 0.0; \ - } \ - } - - // Remove a kernel basis for image 2 from the equation -#define MASK_BASIS_2(INDEX) \ - { \ - for (int j = 0, index = INDEX; j < numSpatial; j++, index += numKernels) { \ - for (int k = 0; k < numParams2; k++) { \ - sumMatrix2->data.F64[k][index] = 0.0; \ - sumMatrix2->data.F64[index][k] = 0.0; \ - sumMatrixX->data.F64[index][k] = 0.0; \ - } \ - sumMatrix2->data.F64[index][index] = 1.0; \ - sumMatrixX->data.F64[index][normIndex] = 0.0; \ - sumMatrixX->data.F64[index][bgIndex] = 0.0; \ - sumVector2->data.F64[index] = 0.0; \ - } \ - } - - #define TOL 1.0e-5 - int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation - double norm = fabs(solution->data.F64[normIndex]); // Normalisation - double thresh = norm * TOL; // Threshold for low parameters - for (int i = 0; i < numKernels; i++) { - // Getting 0th order parameter value. In the presence of spatial variation, the actual value - // of the parameter will vary over the image. We are in effect getting the value in the - // centre of the image. If we use different polynomial functions (e.g., Chebyshev), we may - // have to change this to properly determine the value of the parameter at the centre. - double param1 = solution->data.F64[i], - param2 = solution->data.F64[numParams + i]; // Parameters of interest - bool mask1 = false, mask2 = false; // Masked the parameter? - if (fabs(param1) < thresh) { - psTrace("psModules.imcombine", 7, "Parameter %d: 1 below threshold\n", i); - MASK_BASIS_1(i); - mask1 = true; - } - if (fabs(param2) < thresh) { - psTrace("psModules.imcombine", 7, "Parameter %d: 2 below threshold\n", i); - MASK_BASIS_2(i); - mask2 = true; - } - - if (!mask1 && !mask2) { - if (fabs(param1) < fabs(param2)) { - psTrace("psModules.imcombine", 7, "Parameter %d: 1 < 2\n", i); - MASK_BASIS_1(i); - } else { - psTrace("psModules.imcombine", 7, "Parameter %d: 2 < 1\n", i); - MASK_BASIS_2(i); - } - } - } - } - - calculateEquationDual(&sumMatrix, &sumVector, sumMatrix1, sumMatrix2, - sumMatrixX, sumVector1, sumVector2); + psFree(norms); + return false; + } + + double normValue = stats->robustMedian; + + psFree(stats); + + fprintf(stderr, "Norm: %lf\n", normValue); + + // Solve kernel components + for (int i = 0; i < numSolution2; i++) { + sumVector->data.F64[i] -= normValue * sumMatrix->data.F64[normIndex][i]; + sumVector->data.F64[i + numSolution1] -= normValue * sumMatrix->data.F64[normIndex][i + numSolution1]; + + sumMatrix->data.F64[i][normIndex] = 0.0; + sumMatrix->data.F64[normIndex][i] = 0.0; + + sumMatrix->data.F64[i + numSolution1][normIndex] = 0.0; + sumMatrix->data.F64[normIndex][i + numSolution1] = 0.0; + } + sumVector->data.F64[bgIndex] -= normValue * sumMatrix->data.F64[normIndex][bgIndex]; + sumMatrix->data.F64[bgIndex][normIndex] = 0.0; + sumMatrix->data.F64[normIndex][bgIndex] = 0.0; + + sumMatrix->data.F64[normIndex][normIndex] = 1.0; + + sumVector->data.F64[normIndex] = 0.0; + + solution = psMatrixSolveSVD(solution, sumMatrix, sumVector, NAN); + + solution->data.F64[normIndex] = normValue; + } +#endif + #ifdef TESTING - { - psFits *fits = psFitsOpen("sumMatrixFix.fits", "w"); - psFitsWriteImage(fits, NULL, sumMatrix, 0, NULL); - psFitsClose(fits); - } - { - psImage *image = psImageAlloc(1, numParams + numParams2, PS_TYPE_F64); - psFits *fits = psFitsOpen("sumVectorFix.fits", "w"); - for (int i = 0; i < numParams + numParams2; i++) { - image->data.F64[0][i] = sumVector->data.F64[i]; - } - psFitsWriteImage(fits, NULL, image, 0, NULL); - psFree(image); - psFitsClose(fits); - } -#endif - - solution = psMatrixSolveSVD(solution, sumMatrix, sumVector); - if (!solution) { - psError(PS_ERR_UNKNOWN, false, "SVD solution of least-squares equation failed.\n"); - psFree(sumMatrix); - psFree(sumVector); - return NULL; - } - - psFree(sumMatrix1); - psFree(sumMatrix2); - psFree(sumMatrixX); - psFree(sumVector1); - psFree(sumVector2); + for (int i = 0; i < solution->n; i++) { + fprintf(stderr, "Dual solution %d: %lf\n", i, solution->data.F64[i]); + } +#endif psFree(sumMatrix); psFree(sumVector); -#ifdef TESTING - { - psImage *image = psImageAlloc(1, numParams + numParams2, PS_TYPE_F64); - psFits *fits = psFitsOpen("solnVector.fits", "w"); - for (int i = 0; i < numParams + numParams2; i++) { - image->data.F64[0][i] = solution->data.F64[i]; - } - psFitsWriteImage(fits, NULL, image, 0, NULL); - psFree(image); - psFitsClose(fits); - } -#endif + psFree(norms); if (!kernels->solution1) { - kernels->solution1 = psVectorAlloc(numParams, PS_TYPE_F64); + kernels->solution1 = psVectorAlloc(numSolution1, PS_TYPE_F64); + psVectorInit (kernels->solution1, 0.0); } if (!kernels->solution2) { - kernels->solution2 = psVectorAlloc(numParams2, PS_TYPE_F64); - } - - memcpy(kernels->solution1->data.F64, solution->data.F64, numParams * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); - memcpy(kernels->solution2->data.F64, &solution->data.F64[numParams], - numParams2 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); + kernels->solution2 = psVectorAlloc(numSolution2, PS_TYPE_F64); + psVectorInit (kernels->solution2, 0.0); + } + + // only update the solutions that we chose to calculate: + if (mode & PM_SUBTRACTION_EQUATION_NORM) { + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + kernels->solution1->data.F64[normIndex] = solution->data.F64[normIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_BG) { + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index in matrix for background + kernels->solution1->data.F64[bgIndex] = solution->data.F64[bgIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + int numKernels = kernels->num; + for (int i = 0; i < numKernels * numSpatial; i++) { + // XXX fprintf (stderr, "keep\n"); + kernels->solution1->data.F64[i] = solution->data.F64[i]; + kernels->solution2->data.F64[i] = solution->data.F64[i + numSolution1]; + } + } + + + memcpy(kernels->solution1->data.F64, solution->data.F64, + numSolution1 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); + memcpy(kernels->solution2->data.F64, &solution->data.F64[numSolution1], + numSolution2 * PSELEMTYPE_SIZEOF(PS_TYPE_F64)); psFree(solution); @@ -1131,10 +1237,55 @@ } - pmSubtractionVisualPlotLeastSquares((pmSubtractionStampList *) stamps); //casting away const + // pmSubtractionVisualPlotLeastSquares((pmSubtractionStampList *) stamps); //casting away const return true; } +bool pmSubtractionResidualStats(psVector *fSigRes, psVector *fMaxRes, psVector *fMinRes, psKernel *target, psKernel *source, psKernel *residual, double norm, int footprint) { + + // XXX measure some useful stats on the residuals + float sum = 0.0; + float peak = 0.0; + for (int y = - footprint; y <= footprint; y++) { + for (int x = - footprint; x <= footprint; x++) { + sum += 0.5*(target->kernel[y][x] + source->kernel[y][x] * norm); + peak = PS_MAX(peak, 0.5*(target->kernel[y][x] + source->kernel[y][x] * norm)); + } + } + + // only count pixels with more than X% of the source flux + // calculate stdev(dflux) + float dflux1 = 0.0; + float dflux2 = 0.0; + int npix = 0; + + float dmax = 0.0; + float dmin = 0.0; + + for (int y = - footprint; y <= footprint; y++) { + for (int x = - footprint; x <= footprint; x++) { + float dflux = 0.5*(target->kernel[y][x] + source->kernel[y][x] * norm); + if (dflux < 0.02*sum) continue; + dflux1 += residual->kernel[y][x]; + dflux2 += PS_SQR(residual->kernel[y][x]); + dmax = PS_MAX(residual->kernel[y][x], dmax); + dmin = PS_MIN(residual->kernel[y][x], dmin); + npix ++; + } + } + float sigma = sqrt(dflux2 / npix - PS_SQR(dflux1/npix)); + if (!isfinite(sum)) return false; + if (!isfinite(dmax)) return false; + if (!isfinite(dmin)) return false; + if (!isfinite(peak)) return false; + + // fprintf (stderr, "sum: %f, peak: %f, sigma: %f, fsigma: %f, fmax: %f, fmin: %f\n", sum, peak, sigma, sigma/sum, dmax/peak, dmin/peak); + psVectorAppend(fSigRes, sigma/sum); + psVectorAppend(fMaxRes, dmax/peak); + psVectorAppend(fMinRes, dmin/peak); + return true; +} + psVector *pmSubtractionCalculateDeviations(pmSubtractionStampList *stamps, - const pmSubtractionKernels *kernels) + pmSubtractionKernels *kernels) { PM_ASSERT_SUBTRACTION_STAMP_LIST_NON_NULL(stamps, NULL); @@ -1151,4 +1302,43 @@ psKernel *residual = psKernelAlloc(-footprint, footprint, -footprint, footprint); // Residual image + // set up holding images for the visualization + pmSubtractionVisualShowFitInit (stamps); + + psVector *fSigRes = psVectorAllocEmpty(stamps->num, PS_TYPE_F32); + psVector *fMinRes = psVectorAllocEmpty(stamps->num, PS_TYPE_F32); + psVector *fMaxRes = psVectorAllocEmpty(stamps->num, PS_TYPE_F32); + + // we want to save the residual images for the 9 brightest stamps. + // identify the 9 brightest stamps + psVector *keepStamps = psVectorAlloc(stamps->num, PS_TYPE_S32); + psVectorInit (keepStamps, 0); + { + psVector *flux = psVectorAlloc(stamps->num, PS_TYPE_F32); + psVectorInit (flux, 0.0); + + for (int i = 0; i < stamps->num; i++) { + pmSubtractionStamp *stamp = stamps->stamps->data[i]; + if (!isfinite(stamp->flux)) continue; + flux->data.F32[i] = stamp->flux; + } + + psVector *index = psVectorSortIndex(NULL, flux); + for (int i = 0; (i < stamps->num) && (i < 9); i++) { + int n = stamps->num - i - 1; + keepStamps->data.S32[index->data.S32[n]] = 1; + fprintf (stderr, "keeping %d (%d of %d)\n", index->data.S32[n], n, 9); + } + psFree (flux); + psFree (index); + + // this function is called multiple times in the iteration, but + // we only know after the interation is done if we will try again. + // therefore we must save the sample each time, and blow away the old one + // if it exists. + psFree (kernels->sampleStamps); + kernels->sampleStamps = psArrayAllocEmpty(9); + } + + psString log = psStringCopy("Deviations:\n"); // Log message with deviations for (int i = 0; i < stamps->num; i++) { pmSubtractionStamp *stamp = stamps->stamps->data[i]; // The stamp of interest @@ -1210,13 +1400,26 @@ for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - residual->kernel[y][x] -= convolution->kernel[y][x] * coefficient; + residual->kernel[y][x] += convolution->kernel[y][x] * coefficient; } } } + + // XXX visualize the target, source, convolution and residual + pmSubtractionVisualShowFitAddStamp (target, source, residual, background, norm, i); + for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - residual->kernel[y][x] += target->kernel[y][x] - background - source->kernel[y][x] * norm; - } - } + residual->kernel[y][x] += background + source->kernel[y][x] * norm - target->kernel[y][x]; + } + } + + if (keepStamps->data.S32[i]) { + psImage *sample = psImageCopy(NULL, residual->image, PS_TYPE_F32); + psArrayAdd (kernels->sampleStamps, 9, sample); + psFree (sample); + } + + pmSubtractionResidualStats(fSigRes, fMaxRes, fMinRes, target, source, residual, norm, footprint); + } else { // Dual convolution @@ -1234,13 +1437,24 @@ for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - residual->kernel[y][x] += conv2->kernel[y][x] * coeff2 - conv1->kernel[y][x] * coeff1; + residual->kernel[y][x] += conv2->kernel[y][x] * coeff2 + conv1->kernel[y][x] * coeff1; } } } + + // XXX visualize the target, source, convolution and residual + pmSubtractionVisualShowFitAddStamp (image2, image1, residual, background, norm, i); + for (int y = - footprint; y <= footprint; y++) { for (int x = - footprint; x <= footprint; x++) { - residual->kernel[y][x] += image2->kernel[y][x] - background - image1->kernel[y][x] * norm; - } - } + residual->kernel[y][x] += background + image1->kernel[y][x] * norm - image2->kernel[y][x]; + } + } + if (keepStamps->data.S32[i]) { + psImage *sample = psImageCopy(NULL, residual->image, PS_TYPE_F32); + psArrayAdd (kernels->sampleStamps, 9, sample); + psFree (sample); + } + + pmSubtractionResidualStats(fSigRes, fMaxRes, fMinRes, image1, image2, residual, norm, footprint); } @@ -1257,10 +1471,12 @@ deviations->data.F32[i] = devNorm * deviation; psTrace("psModules.imcombine", 5, "Deviation for stamp %d (%d,%d): %f\n", - i, (int)(stamp->x + 0.5), (int)(stamp->y + 0.5), deviations->data.F32[i]); + i, (int)(stamp->x - 0.5), (int)(stamp->y - 0.5), deviations->data.F32[i]); + psStringAppend(&log, "Stamp %d (%d,%d): %f\n", + i, (int)(stamp->x - 0.5), (int)(stamp->y - 0.5), deviations->data.F32[i]); if (!isfinite(deviations->data.F32[i])) { stamp->status = PM_SUBTRACTION_STAMP_REJECTED; psTrace("psModules.imcombine", 5, "Rejecting stamp %d (%d,%d) because of non-finite deviation\n", - i, (int)(stamp->x + 0.5), (int)(stamp->y + 0.5)); + i, (int)(stamp->x - 0.5), (int)(stamp->y - 0.5)); continue; } @@ -1302,7 +1518,681 @@ } + + psLogMsg("psModules.imcombine", PS_LOG_DETAIL, "%s", log); + psFree(log); + + // calculate and report the normalization and background for the image center + { + polyValues = p_pmSubtractionPolynomial(polyValues, kernels->spatialOrder, 0.0, 0.0); + double norm = p_pmSubtractionSolutionNorm(kernels); // Normalisation + double background = p_pmSubtractionSolutionBackground(kernels, polyValues);// Difference in background + psLogMsg("psModules.imcombine", PS_LOG_INFO, "normalization: %f, background: %f", norm, background); + + pmSubtractionVisualShowFit(norm); + pmSubtractionVisualPlotFit(kernels); + + psStats *stats = psStatsAlloc(PS_STAT_ROBUST_MEDIAN | PS_STAT_ROBUST_STDEV); + psVectorStats (stats, fSigRes, NULL, NULL, 0); + kernels->fSigResMean = stats->robustMedian; + kernels->fSigResStdev = stats->robustStdev; + + psStatsInit (stats); + psVectorStats (stats, fMaxRes, NULL, NULL, 0); + kernels->fMaxResMean = stats->robustMedian; + kernels->fMaxResStdev = stats->robustStdev; + + psStatsInit (stats); + psVectorStats (stats, fMinRes, NULL, NULL, 0); + kernels->fMinResMean = stats->robustMedian; + kernels->fMinResStdev = stats->robustStdev; + + // XXX save these values somewhere + psLogMsg("psModules.imcombine", PS_LOG_INFO, "fSigma: %f +/- %f, fMaxRes: %f +/- %f, fMinRes: %f +/- %f", + kernels->fSigResMean, kernels->fSigResStdev, + kernels->fMaxResMean, kernels->fMaxResStdev, + kernels->fMinResMean, kernels->fMinResStdev); + + psFree (fSigRes); + psFree (fMaxRes); + psFree (fMinRes); + psFree (stats); + } + psFree(residual); psFree(polyValues); + return deviations; } + +// we are supplied U, not Ut; w represents a diagonal matrix (also, we apply 1/w instead of w) +psImage *p_pmSubSolve_wUt (psVector *w, psImage *U) { + + psAssert (w->n == U->numCols, "w and U dimensions do not match"); + + // wUt has dimensions transposed relative to Ut. + psImage *wUt = psImageAlloc (U->numRows, U->numCols, PS_TYPE_F64); + psImageInit (wUt, 0.0); + + for (int i = 0; i < wUt->numCols; i++) { + for (int j = 0; j < wUt->numRows; j++) { + if (!isfinite(w->data.F64[j])) continue; + if (w->data.F64[j] == 0.0) continue; + wUt->data.F64[j][i] = U->data.F64[i][j] / w->data.F64[j]; + } + } + return wUt; +} + +// XXX this is just standard matrix multiplication: use psMatrixMultiply? +psImage *p_pmSubSolve_VwUt (psImage *V, psImage *wUt) { + + psAssert (V->numCols == wUt->numRows, "matrix dimensions do not match"); + + psImage *Ainv = psImageAlloc (wUt->numCols, V->numRows, PS_TYPE_F64); + + for (int i = 0; i < Ainv->numCols; i++) { + for (int j = 0; j < Ainv->numRows; j++) { + double sum = 0.0; + for (int k = 0; k < V->numCols; k++) { + sum += V->data.F64[j][k] * wUt->data.F64[k][i]; + } + Ainv->data.F64[j][i] = sum; + } + } + return Ainv; +} + +// we are supplied U, not Ut +bool p_pmSubSolve_UtB (psVector **UtB, psImage *U, psVector *B) { + + psAssert (U->numRows == B->n, "U and B dimensions do not match"); + + UtB[0] = psVectorRecycle (UtB[0], U->numCols, PS_TYPE_F64); + + for (int i = 0; i < U->numCols; i++) { + double sum = 0.0; + for (int j = 0; j < U->numRows; j++) { + sum += B->data.F64[j] * U->data.F64[j][i]; + } + UtB[0]->data.F64[i] = sum; + } + return true; +} + +// w is diagonal +bool p_pmSubSolve_wUtB (psVector **wUtB, psVector *w, psVector *UtB) { + + psAssert (w->n == UtB->n, "w and UtB dimensions do not match"); + + // wUt has dimensions transposed relative to Ut. + wUtB[0] = psVectorRecycle (wUtB[0], w->n, PS_TYPE_F64); + psVectorInit (wUtB[0], 0.0); + + for (int i = 0; i < w->n; i++) { + if (!isfinite(w->data.F64[i])) continue; + if (w->data.F64[i] == 0.0) continue; + wUtB[0]->data.F64[i] = UtB->data.F64[i] / w->data.F64[i]; + } + return true; +} + +// this is basically matrix * vector +bool p_pmSubSolve_VwUtB (psVector **VwUtB, psImage *V, psVector *wUtB) { + + psAssert (V->numCols == wUtB->n, "V and wUtB dimensions do not match"); + + VwUtB[0] = psVectorRecycle (*VwUtB, V->numRows, PS_TYPE_F64); + + for (int j = 0; j < V->numRows; j++) { + double sum = 0.0; + for (int i = 0; i < V->numCols; i++) { + sum += V->data.F64[j][i] * wUtB->data.F64[i]; + } + VwUtB[0]->data.F64[j] = sum; + } + return true; +} + +// this is basically matrix * vector +bool p_pmSubSolve_Ax (psVector **B, psImage *A, psVector *x) { + + psAssert (A->numCols == x->n, "A and x dimensions do not match"); + + B[0] = psVectorRecycle (*B, A->numRows, PS_TYPE_F64); + + for (int j = 0; j < A->numRows; j++) { + double sum = 0.0; + for (int i = 0; i < A->numCols; i++) { + sum += A->data.F64[j][i] * x->data.F64[i]; + } + B[0]->data.F64[j] = sum; + } + return true; +} + +// this is basically Vector * vector +bool p_pmSubSolve_VdV (double *value, psVector *x, psVector *y) { + + psAssert (x->n == y->n, "x and y dimensions do not match"); + + double sum = 0.0; + for (int i = 0; i < x->n; i++) { + sum += x->data.F64[i] * y->data.F64[i]; + } + *value = sum; + return true; +} + +bool p_pmSubSolve_y2 (double *y2, pmSubtractionKernels *kernels, const pmSubtractionStampList *stamps) { + + int footprint = stamps->footprint; // Half-size of stamps + + double sum = 0.0; + for (int i = 0; i < stamps->num; i++) { + + pmSubtractionStamp *stamp = stamps->stamps->data[i]; + if (stamp->status != PM_SUBTRACTION_STAMP_USED) continue; + + psKernel *weight = NULL; + psKernel *window = NULL; + psKernel *input = NULL; + +#ifdef USE_WEIGHT + weight = stamp->weight; +#endif +#ifdef USE_WINDOW + window = stamps->window; +#endif + + switch (kernels->mode) { + // MODE_1 : convolve image 1 to match image 2 (and vice versa) + case PM_SUBTRACTION_MODE_1: + input = stamp->image2; + break; + case PM_SUBTRACTION_MODE_2: + input = stamp->image1; + break; + default: + psAbort ("programming error"); + } + + for (int y = - footprint; y <= footprint; y++) { + for (int x = - footprint; x <= footprint; x++) { + double in = input->kernel[y][x]; + double value = in*in; + if (weight) { + float wtVal = weight->kernel[y][x]; + value *= wtVal; + } + if (window) { + float winVal = window->kernel[y][x]; + value *= winVal; + } + sum += value; + } + } + } + *y2 = sum; + return true; +} + +double p_pmSubSolve_ChiSquare (pmSubtractionKernels *kernels, const pmSubtractionStampList *stamps) { + + int footprint = stamps->footprint; // Half-size of stamps + int numKernels = kernels->num; // Number of kernels + + double sum = 0.0; + + psKernel *residual = psKernelAlloc(-footprint, footprint, -footprint, footprint); // Residual image + psImageInit(residual->image, 0.0); + + psImage *polyValues = NULL; // Polynomial values + + for (int i = 0; i < stamps->num; i++) { + + pmSubtractionStamp *stamp = stamps->stamps->data[i]; + if (stamp->status != PM_SUBTRACTION_STAMP_USED) continue; + + psKernel *weight = NULL; + psKernel *window = NULL; + psKernel *target = NULL; + psKernel *source = NULL; + + psArray *convolutions = NULL; + +#ifdef USE_WEIGHT + weight = stamp->weight; +#endif +#ifdef USE_WINDOW + window = stamps->window; +#endif + + switch (kernels->mode) { + // MODE_1 : convolve image 1 to match image 2 (and vice versa) + case PM_SUBTRACTION_MODE_1: + target = stamp->image2; + source = stamp->image1; + convolutions = stamp->convolutions1; + break; + case PM_SUBTRACTION_MODE_2: + target = stamp->image1; + source = stamp->image2; + convolutions = stamp->convolutions2; + break; + default: + psAbort ("programming error"); + } + + // Calculate coefficients of the kernel basis functions + polyValues = p_pmSubtractionPolynomial(polyValues, kernels->spatialOrder, stamp->xNorm, stamp->yNorm); + double norm = p_pmSubtractionSolutionNorm(kernels); // Normalisation + double background = p_pmSubtractionSolutionBackground(kernels, polyValues);// Difference in background + + psImageInit(residual->image, 0.0); + for (int j = 0; j < numKernels; j++) { + psKernel *convolution = convolutions->data[j]; // Convolution + double coefficient = p_pmSubtractionSolutionCoeff(kernels, polyValues, j, false); // Coefficient + for (int y = - footprint; y <= footprint; y++) { + for (int x = - footprint; x <= footprint; x++) { + residual->kernel[y][x] -= convolution->kernel[y][x] * coefficient; + } + } + } + + for (int y = - footprint; y <= footprint; y++) { + for (int x = - footprint; x <= footprint; x++) { + double resid = target->kernel[y][x] - background - source->kernel[y][x] * norm + residual->kernel[y][x]; + double value = PS_SQR(resid); + if (weight) { + float wtVal = weight->kernel[y][x]; + value *= wtVal; + } + if (window) { + float winVal = window->kernel[y][x]; + value *= winVal; + } + sum += value; + } + } + } + psFree (polyValues); + psFree (residual); + + return sum; +} + +bool p_pmSubSolve_SetWeights (psVector *wApply, psVector *w, psVector *wMask) { + + for (int i = 0; i < w->n; i++) { + wApply->data.F64[i] = wMask->data.U8[i] ? 0.0 : w->data.F64[i]; + } + return true; +} + +// we are supplied V and w; w represents a diagonal matrix (also, we apply 1/w instead of w) +psImage *p_pmSubSolve_Xvar (psImage *V, psVector *w) { + + psAssert (w->n == V->numCols, "w and U dimensions do not match"); + + psImage *Vn = psImageAlloc (V->numCols, V->numRows, PS_TYPE_F64); + psImageInit (Vn, 0.0); + + // generate Vn = V * w^{-1} + for (int j = 0; j < Vn->numRows; j++) { + for (int i = 0; i < Vn->numCols; i++) { + if (!isfinite(w->data.F64[i])) continue; + if (w->data.F64[i] == 0.0) continue; + Vn->data.F64[j][i] = V->data.F64[j][i] / w->data.F64[i]; + } + } + + psImage *Xvar = psImageAlloc (V->numCols, V->numRows, PS_TYPE_F64); + psImageInit (Xvar, 0.0); + + // generate Xvar = Vn * Vn^T + for (int j = 0; j < Vn->numRows; j++) { + for (int i = 0; i < Vn->numCols; i++) { + double sum = 0.0; + for (int k = 0; k < Vn->numCols; k++) { + sum += Vn->data.F64[k][i]*Vn->data.F64[k][j]; + } + Xvar->data.F64[j][i] = sum; + } + } + return Xvar; +} + +// I get confused by the index values between the image vs matrix usage: In terms +// of the elements of an image A(x,y) = A->data.F64[y][x] = A_x,y, a matrix +// multiplication is: A_k,j * B_i,k = C_i,j + + +bool psFitsWriteImageSimple (char *filename, psImage *image, psMetadata *header) { + + psFits *fits = psFitsOpen(filename, "w"); + psFitsWriteImage(fits, header, image, 0, NULL); + psFitsClose(fits); + + return true; +} + +bool psVectorWriteFile (char *filename, const psVector *vector) { + + FILE *f = fopen (filename, "w"); + int fd = fileno(f); + p_psVectorPrint (fd, vector, "unnamed"); + fclose (f); + + return true; +} + + +# if 0 + +#ifdef TESTING + psFitsWriteImageSimple("A.fits", sumMatrix, NULL); + psVectorWriteFile ("B.dat", sumVector); +#endif + +# define SVD_ANALYSIS 0 +# define COEFF_SIG 0.0 +# define SVD_TOL 0.0 + + // Use SVD to determine the kernel coeffs (and validate) + if (SVD_ANALYSIS) { + + // We have sumVector and sumMatrix. we are trying to solve the following equation: + // sumMatrix * x = sumVector. + + // we can use any standard matrix inversion to solve this. However, the basis + // functions in general have substantial correlation, so that the solution may be + // somewhat poorly determined or unstable. If not numerically ill-conditioned, the + // system of equations may be statistically ill-conditioned. Noise in the image + // will drive insignificant, but correlated, terms in the solution. To avoid these + // problems, we can use SVD to identify numerically unconstrained values and to + // avoid statistically badly determined value. + + // A = sumMatrix, B = sumVector + // SVD: A = U w V^T -> A^{-1} = V (1/w) U^T + // x = V (1/w) (U^T B) + // \sigma_x = sqrt(diag(A^{-1})) + // solve for x and A^{-1} to get x & dx + // identify the elements of (1/w) that are nan (1/0.0) -> set to 0.0 + // identify the elements of x that are insignificant (x / dx < 1.0? < 0.5?) -> set to 0.0 + + // If I use the SVD trick to re-condition the matrix, I need to break out the + // kernel and normalization terms from the background term. + // XXX is this true? or was this due to an error in the analysis? + + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index in matrix for background + + // now pull out the kernel elements into their own square matrix + psImage *kernelMatrix = psImageAlloc (sumMatrix->numCols - 1, sumMatrix->numRows - 1, PS_TYPE_F64); + psVector *kernelVector = psVectorAlloc (sumMatrix->numCols - 1, PS_TYPE_F64); + + for (int ix = 0, kx = 0; ix < sumMatrix->numCols; ix++) { + if (ix == bgIndex) continue; + for (int iy = 0, ky = 0; iy < sumMatrix->numRows; iy++) { + if (iy == bgIndex) continue; + kernelMatrix->data.F64[ky][kx] = sumMatrix->data.F64[iy][ix]; + ky++; + } + kernelVector->data.F64[kx] = sumVector->data.F64[ix]; + kx++; + } + + psImage *U = NULL; + psImage *V = NULL; + psVector *w = NULL; + if (!psMatrixSVD (&U, &w, &V, kernelMatrix)) { + psError(PS_ERR_UNKNOWN, false, "failed to perform SVD on sumMatrix\n"); + return NULL; + } + + // calculate A_inverse: + // Ainv = V * w * U^T + psImage *wUt = p_pmSubSolve_wUt (w, U); + psImage *Ainv = p_pmSubSolve_VwUt (V, wUt); + psImage *Xvar = NULL; + psFree (wUt); + +# ifdef TESTING + // kernel terms: + for (int i = 0; i < w->n; i++) { + fprintf (stderr, "w: %f\n", w->data.F64[i]); + } +# endif + // loop over w adding in more and more of the values until chisquare is no longer + // dropping significantly. + // XXX this does not seem to work very well: we seem to need all terms even for + // simple cases... + + psVector *Xsvd = NULL; + { + psVector *Ax = NULL; + psVector *UtB = NULL; + psVector *wUtB = NULL; + + psVector *wApply = psVectorAlloc(w->n, PS_TYPE_F64); + psVector *wMask = psVectorAlloc(w->n, PS_TYPE_U8); + psVectorInit (wMask, 1); // start by masking everything + + double chiSquareLast = NAN; + int maxWeight = 0; + + double Axx, Bx, y2; + + // XXX this is an attempt to exclude insignificant modes. + // it was not successful with the ISIS kernel set: removing even + // the least significant mode leaves additional ringing / noise + // because the terms are so coupled. + for (int k = 0; false && (k < w->n); k++) { + + // unmask the k-th weight + wMask->data.U8[k] = 0; + p_pmSubSolve_SetWeights(wApply, w, wMask); + + // solve for x: + // x = V * w * (U^T * B) + p_pmSubSolve_UtB (&UtB, U, kernelVector); + p_pmSubSolve_wUtB (&wUtB, wApply, UtB); + p_pmSubSolve_VwUtB (&Xsvd, V, wUtB); + + // chi-square for this system of equations: + // chi-square = sum over terms of: (Ax - B)*x - b*x - y^2 + // y^2 = \sum_stamps \sum_pixels input->kernel[y][x]^2 + p_pmSubSolve_Ax (&Ax, kernelMatrix, Xsvd); + p_pmSubSolve_VdV (&Axx, Ax, Xsvd); + p_pmSubSolve_VdV (&Bx, kernelVector, Xsvd); + p_pmSubSolve_y2 (&y2, kernels, stamps); + + // apparently, this works (compare with the brute force value below + double chiSquare = Axx - 2.0*Bx + y2; + double deltaChi = (k == 0) ? chiSquare : chiSquareLast - chiSquare; + chiSquareLast = chiSquare; + + // fprintf (stderr, "chi square = %f, delta: %f\n", chiSquare, deltaChi); + if (k && !maxWeight && (deltaChi < 1.0)) { + maxWeight = k; + } + } + + // keep all terms or we get extra ringing + maxWeight = w->n; + psVectorInit (wMask, 1); + for (int k = 0; k < maxWeight; k++) { + wMask->data.U8[k] = 0; + } + p_pmSubSolve_SetWeights(wApply, w, wMask); + + // solve for x: + // x = V * w * (U^T * B) + p_pmSubSolve_UtB (&UtB, U, kernelVector); + p_pmSubSolve_wUtB (&wUtB, wApply, UtB); + p_pmSubSolve_VwUtB (&Xsvd, V, wUtB); + + // chi-square for this system of equations: + // chi-square = sum over terms of: (Ax - B)*x - b*x - y^2 + // y^2 = \sum_stamps \sum_pixels input->kernel[y][x]^2 + p_pmSubSolve_Ax (&Ax, kernelMatrix, Xsvd); + p_pmSubSolve_VdV (&Axx, Ax, Xsvd); + p_pmSubSolve_VdV (&Bx, kernelVector, Xsvd); + p_pmSubSolve_y2 (&y2, kernels, stamps); + + // apparently, this works (compare with the brute force value below + double chiSquare = Axx - 2.0*Bx + y2; + psLogMsg ("psModules.imcombine", PS_LOG_INFO, "model kernel with %d terms; chi square = %f\n", maxWeight, chiSquare); + + // re-calculate A^{-1} to get new variances: + // Ainv = V * w * U^T + // XXX since we keep all terms, this is identical to Ainv + psImage *wUt = p_pmSubSolve_wUt (wApply, U); + Xvar = p_pmSubSolve_VwUt (V, wUt); + psFree (wUt); + + psFree (Ax); + psFree (UtB); + psFree (wUtB); + psFree (wApply); + psFree (wMask); + } + + // copy the kernel solutions to the full solution vector: + solution = psVectorAlloc(sumVector->n, PS_TYPE_F64); + solutionErr = psVectorAlloc(sumVector->n, PS_TYPE_F64); + + for (int ix = 0, kx = 0; ix < sumVector->n; ix++) { + if (ix == bgIndex) { + solution->data.F64[ix] = 0; + solutionErr->data.F64[ix] = 0.001; + continue; + } + solutionErr->data.F64[ix] = sqrt(Ainv->data.F64[kx][kx]); + solution->data.F64[ix] = Xsvd->data.F64[kx]; + kx++; + } + + psFree (kernelMatrix); + psFree (kernelVector); + + psFree (U); + psFree (V); + psFree (w); + + psFree (Ainv); + psFree (Xsvd); + } else { + psVector *permutation = NULL; // Permutation vector, required for LU decomposition + psImage *luMatrix = psMatrixLUDecomposition(NULL, &permutation, sumMatrix); + if (!luMatrix) { + psError(PS_ERR_UNKNOWN, true, "LU Decomposition of least-squares matrix failed.\n"); + psFree(solution); + psFree(sumVector); + psFree(sumMatrix); + psFree(luMatrix); + psFree(permutation); + return NULL; + } + + solution = psMatrixLUSolution(NULL, luMatrix, sumVector, permutation); + psFree(luMatrix); + psFree(permutation); + if (!solution) { + psError(PS_ERR_UNKNOWN, true, "Failed to solve the least-squares system.\n"); + psFree(solution); + psFree(sumVector); + psFree(sumMatrix); + return NULL; + } + + // XXX LUD does not provide A^{-1}? fake the error for now + solutionErr = psVectorAlloc(sumVector->n, PS_TYPE_F64); + for (int ix = 0; ix < sumVector->n; ix++) { + solutionErr->data.F64[ix] = 0.1*solution->data.F64[ix]; + } + } + + if (!kernels->solution1) { + kernels->solution1 = psVectorAlloc (sumVector->n, PS_TYPE_F64); + psVectorInit (kernels->solution1, 0.0); + } + + // only update the solutions that we chose to calculate: + if (mode & PM_SUBTRACTION_EQUATION_NORM) { + int normIndex = PM_SUBTRACTION_INDEX_NORM(kernels); // Index for normalisation + kernels->solution1->data.F64[normIndex] = solution->data.F64[normIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_BG) { + int bgIndex = PM_SUBTRACTION_INDEX_BG(kernels); // Index in matrix for background + kernels->solution1->data.F64[bgIndex] = solution->data.F64[bgIndex]; + } + if (mode & PM_SUBTRACTION_EQUATION_KERNELS) { + int numKernels = kernels->num; + int spatialOrder = kernels->spatialOrder; // Order of spatial variation + int numPoly = PM_SUBTRACTION_POLYTERMS(spatialOrder); // Number of polynomial terms + for (int i = 0; i < numKernels * numPoly; i++) { + // XXX fprintf (stderr, "%f +/- %f (%f) -> ", solution->data.F64[i], solutionErr->data.F64[i], fabs(solution->data.F64[i]/solutionErr->data.F64[i])); + if (fabs(solution->data.F64[i] / solutionErr->data.F64[i]) < COEFF_SIG) { + // XXX fprintf (stderr, "drop\n"); + kernels->solution1->data.F64[i] = 0.0; + } else { + // XXX fprintf (stderr, "keep\n"); + kernels->solution1->data.F64[i] = solution->data.F64[i]; + } + } + } + // double chiSquare = p_pmSubSolve_ChiSquare (kernels, stamps); + // fprintf (stderr, "chi square Brute = %f\n", chiSquare); + + psFree(solution); + psFree(sumVector); + psFree(sumMatrix); +# endif + +#ifdef TESTING + // XXX double-check for NAN in data: + for (int iy = 0; iy < stamp->matrix->numRows; iy++) { + for (int ix = 0; ix < stamp->matrix->numCols; ix++) { + if (!isfinite(stamp->matrix->data.F64[iy][ix])) { + fprintf (stderr, "WARNING: NAN in matrix\n"); + } + } + } + for (int ix = 0; ix < stamp->vector->n; ix++) { + if (!isfinite(stamp->vector->data.F64[ix])) { + fprintf (stderr, "WARNING: NAN in vector\n"); + } + } +#endif + +#ifdef TESTING + for (int ix = 0; ix < sumVector->n; ix++) { + if (!isfinite(sumVector->data.F64[ix])) { + fprintf (stderr, "WARNING: NAN in vector\n"); + } + } +#endif + +#ifdef TESTING + for (int ix = 0; ix < sumVector->n; ix++) { + if (!isfinite(sumVector->data.F64[ix])) { + fprintf (stderr, "WARNING: NAN in vector\n"); + } + } + { + psImage *inverse = psMatrixInvert(NULL, sumMatrix, NULL); + psFitsWriteImageSimple("matrixInv.fits", inverse, NULL); + psFree(inverse); + } + { + psImage *X = psMatrixInvert(NULL, sumMatrix, NULL); + psImage *Xt = psMatrixTranspose(NULL, X); + psImage *XtX = psMatrixMultiply(NULL, Xt, X); + psFitsWriteImageSimple("matrixErr.fits", XtX, NULL); + psFree(X); + psFree(Xt); + psFree(XtX); + } +#endif +