The thing I am still not too certain about is what happens with the root process in MPI Scatter / Scatterv.
If I divide an array as I try in my code, do I need to include the root process in the number of receivers (hence making the sendcounts of size nproc) or is it excluded?
In my example code for Matrix Multiplication, I still get an error by one of the processes running into aberrant behaviour, terminating the program prematurely:
void readMatrix();
double StartTime;
int rank, nproc, proc;
//double matrix_A[N_ROWS][N_COLS];
double **matrix_A;
//double matrix_B[N_ROWS][N_COLS];
double **matrix_B;
//double matrix_C[N_ROWS][N_COLS];
double **matrix_C;
int low_bound = 0; //low bound of the number of rows of each process
int upper_bound = 0; //upper bound of the number of rows of [A] of each process
int portion = 0; //portion of the number of rows of [A] of each process
int main (int argc, char *argv[]) {
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &nproc);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
matrix_A = (double **)malloc(N_ROWS * sizeof(double*));
for(int i = 0; i < N_ROWS; i++) matrix_A[i] = (double *)malloc(N_COLS * sizeof(double));
matrix_B = (double **)malloc(N_ROWS * sizeof(double*));
for(int i = 0; i < N_ROWS; i++) matrix_B[i] = (double *)malloc(N_COLS * sizeof(double));
matrix_C = (double **)malloc(N_ROWS * sizeof(double*));
for(int i = 0; i < N_ROWS; i++) matrix_C[i] = (double *)malloc(N_COLS * sizeof(double));
int *counts = new int[nproc](); // array to hold number of items to be sent to each process
// -------------------> If we have more than one process, we can distribute the work through scatterv
if (nproc > 1) {
// -------------------> Process 0 initalizes matrices and scatters the portions of the [A] Matrix
if (rank==0) {
readMatrix();
}
StartTime = MPI_Wtime();
int counter = 0;
for (int proc = 0; proc < nproc; proc++) {
counts[proc] = N_ROWS / nproc ;
counter += N_ROWS / nproc ;
}
counter = N_ROWS - counter;
counts[nproc-1] = counter;
//set bounds for each process
low_bound = rank*(N_ROWS/nproc);
portion = counts[rank];
upper_bound = low_bound + portion;
printf("I am process %i and my lower bound is %i and my portion is %i and my upper bound is %i \n",rank,low_bound, portion,upper_bound);
//scatter the work among the processes
int *displs = new int[nproc]();
displs[0] = 0;
for (int proc = 1; proc < nproc; proc++) displs[proc] = displs[proc-1] + (N_ROWS/nproc);
MPI_Scatterv(matrix_A, counts, displs, MPI_DOUBLE, &matrix_A[low_bound][0], portion, MPI_DOUBLE, 0, MPI_COMM_WORLD);
//broadcast [B] to all the slaves
MPI_Bcast(&matrix_B, N_ROWS*N_COLS, MPI_DOUBLE, 0, MPI_COMM_WORLD);
// -------------------> Everybody does their work
for (int i = low_bound; i < upper_bound; i++) {//iterate through a given set of rows of [A]
for (int j = 0; j < N_COLS; j++) {//iterate through columns of [B]
for (int k = 0; k < N_ROWS; k++) {//iterate through rows of [B]
matrix_C[i][j] += (matrix_A[i][k] * matrix_B[k][j]);
}
}
}
// -------------------> Process 0 gathers the work
MPI_Gatherv(&matrix_C[low_bound][0],portion,MPI_DOUBLE,matrix_C,counts,displs,MPI_DOUBLE,0,MPI_COMM_WORLD);
}
...
The root process also takes place in the receiver side. If you are not interested in that, just set sendcounts[root] = 0.
See MPI_Scatterv for specific information on which values you have to pass exactly.
However, take care of what you are doing. I strongly suggest that you change the way you allocate your matrix as a one-dimensional array, using a single malloc like this:
double* matrix = (double*) malloc( N_ROWS * N_COLS * sizeof(double) );
If you still want to use a two-dimensional array, then you may need to define your types as a MPI derived datatype.
The datatype you are passing is not valid if you want to send more than a row in a single MPI transfer.
With MPI_DOUBLE you are telling MPI that the buffer contains a contiguous array of count MPI_DOUBLE values.
Since you are allocating a two-dimensional array using multiple malloc calls, then your data is not contiguous.
I have a function (shown below) that I need some advice on. The function returns the slope of a line which is fit (via the least squares method) to n data points. To give you a context, my project is a barometric pressure based altimeter which uses this function to determine velocity based on the n most recent altitude-time pairs. These altitude-time pairs are stored in 2 global arrays(times[] and alts[]).
My problem is not that this method doesn't work. It usually does. But sometimes I will run the altimeter and this function will return the value 'inf' interspersed with a bunch of other wrong values (I have also seen 'NaN' but that is more rare). There are a few areas of suspicion I have at this point but I would like a fresh perspective. Here is some further contextual information that may or may not be of use:
I am using interrupts for a quadrature encoder
The times[] array is of type unsigned long
The alts[] array is of type float
n is a const int, in this case n = 9
On the ATMEGA328 a double is the same as a float.. Arduino-double
float velF() { // uses the last n data points, fits a line to them,
// and uses the slope of that line as the velocity at that moment
float sumTY = 0, sumT = 0, sumY = 0, sumT2 = 0;
for (int i = 0; i < n; i++) {
sumTY += (float)times[i] * alts[i] / 1000;
sumT += (float)times[i] / 1000;
sumY += alts[i];
sumT2 += (float)times[i] * times[i] / 1000000;
}
return (n*sumTY - sumT*sumY) / (n*sumT2 - sumT*sumT);
}
Any help or advice would be greatly appreciated!
Code is certainly performing division by zero.
For a variety of reasons, n*sumT2 - sumT*sumT will be zero. #John Bollinger In most of these cases, the top (dividend) of the division will also be zero and a return value of zero would be acceptable.
float velF(void) {
float sumTY = 0, sumT = 0, sumY = 0, sumT2 = 0;
for (size_t i = 0; i < n; i++) {
// insure values are reasoable
assert(alts[i] >= ALT_MIN && alts[i] <= ALT_MAX);
assert(times[i] >= TIME_MIN && times[i] <= TIME_MAX);
sumTY += (float)times[i] * alts[i] / 1000;
sumT += (float)times[i] / 1000;
sumY += alts[i];
sumT2 += (float)times[i] * times[i] / 1000000;
}
float d = n*sumT2 - sumT*sumT;
if (d == 0) return 0;
return (n*sumTY - sumT*sumY) / d;
}
Side note: could factor out the division for improved accuracy and speed. Suggest performing the last calculation as double.
float velF(void) {
float sumTY = 0, sumT = 0, sumY = 0, sumT2 = 0;
for (size_t i = 0; i < n; i++) {
float tf = (float) times[i];
sumTY += tf * alts[i];
sumT += tf;
sumY += alts[i];
sumT2 += tf * tf;
}
double nd = n;
double sumTd = sumT;
double d = nd*sumT2 - sumTd*sumTd;
if (d == 0) return 0;
return (nd*sumTY - sumTd*sumY)*1000 / d;
}
I would like to make real time audio processing with Qt and display the spectrum using FFTW3.
What I've done in steps:
I capture any sound from computer device and fill it into the buffer.
I assign sound samples to double array
I compute the fundamental frequency.
when I'm display the fundamental frequency and Magnetitude when the microphone is on but no signal(silence) , the fundamental frequency is not what I expected , the code don't always return zero , sometimes the code returns 1500Hz,2000hz as frequency
and when the microphone is off (mute) the code don't return zero as fundamamental frequency but returns a number between 0 and 9000Hz. Any help woulbd be appreciated
here is my code
QByteArray *buffer;
QAudioInput *audioInput;
audioInput = new QAudioInput(format, this);
//Check the number of samples in input buffer
qint64 len = audioInput->bytesReady();
//Limit sample size
if(len > 4096)
len = 4096;
//Read sound samples from input device to buffer
qint64 l = input->read(buffer.data(), len);
int input_size= BufferSize;
int output_size = input_size; //input_size/2+1;
fftw_plan p3;
double in[output_size];
fftw_complex out[output_size];
short *outdata = (short*)m_buffer.data();// assign sample into short array
int data_size = size_t(outdata);
int data_size1 = sizeof(outdata);
int count = 0;
double w = 0;
for(int i(chanelNumber); i < output_size/2; i= i + 2) //fill array in
{
w= 0.5 * (1 - cos(2*M_PI*i/output_size)); // Hann Windows
double x = 0;
if(i < data_size){
x = outdata[i];
}
if(count < output_size){
in[count] = x;// fill Array In with sample from buffer
count++;
}
}
for(int i=count; i<output_size; i++){
in[i] = 0;
}
p3 = fftw_plan_dft_r2c_1d(output_size, in, out, FFTW_ESTIMATE);// create Plan
fftw_execute(p3);// FFT
for (int i = 0; i < (output_size/2); i++) {
long peak=0;
double Amplitudemax=0;
double r1 = out[i][0] * out[i][0];
double im1 = out[i][3] * out[i][4];
double t1 = r1 + im1;
//double t = 20*log(sqrt(t1));
double t = sqrt(t1)/(double)(output_size/2);
double f = (double)i*8000 / ((double)output_size/2);
if(Magnitude > AmplitudeMax)
{
AmplitudeMax = Magnitude;
Peak =2* i;
}
}
fftw_destroy_plan(p3);
return Peak*(static_cast<double>(8000)/output_Size);
What you think is silence might contain some small amount of noise. The FFT of random noise will also appear random, and thus have a random magnitude peak. But it is possible that noise might come from equipment or electronics in the environment (fans, flyback transformers, etc.), or the power supply to your ADC or mic, thus showing some frequency biases.
If the noise level is low enough, normally one checks the level of the magnitude peak, compares it against a threshold, and cuts off frequency estimation reporting below this threshold.
Background
I've implemented this algorithm from Microsoft Research for a radix-2 FFT (Stockham auto sort) using OpenCL.
I use floating point textures (256 cols X N rows) for input and output in the kernel, because I will need to sample at non-integral points and I thought it better to delegate that to the texture sampling hardware. Note that my FFTs are always of 256-point sequences (every row in my texture). At this point, my N is 16384 or 32768 depending on the GPU i'm using and the max 2D texture size allowed.
I also need to perform the FFT of 4 real-valued sequences at once, so the kernel performs the FFT(a, b, c, d) as FFT(a + ib, c + id) from which I can extract the 4 complex sequences out later using an O(n) algorithm. I can elaborate on this if someone wishes - but I don't believe it falls in the scope of this question.
Kernel Source
const sampler_t fftSampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP_TO_EDGE | CLK_FILTER_NEAREST;
__kernel void FFT_Stockham(read_only image2d_t input, write_only image2d_t output, int fftSize, int size)
{
int x = get_global_id(0);
int y = get_global_id(1);
int b = floor(x / convert_float(fftSize)) * (fftSize / 2);
int offset = x % (fftSize / 2);
int x0 = b + offset;
int x1 = x0 + (size / 2);
float4 val0 = read_imagef(input, fftSampler, (int2)(x0, y));
float4 val1 = read_imagef(input, fftSampler, (int2)(x1, y));
float angle = -6.283185f * (convert_float(x) / convert_float(fftSize));
// TODO: Convert the two calculations below into lookups from a __constant buffer
float tA = native_cos(angle);
float tB = native_sin(angle);
float4 coeffs1 = (float4)(tA, tB, tA, tB);
float4 coeffs2 = (float4)(-tB, tA, -tB, tA);
float4 result = val0 + coeffs1 * val1.xxzz + coeffs2 * val1.yyww;
write_imagef(output, (int2)(x, y), result);
}
The host code simply invokes this kernel log2(256) times, ping-ponging the input and output textures.
Note: I tried removing the native_cos and native_sin to see if that impacted timing, but it doesn't seem to change things by very much. Not the factor I'm looking for, in any case.
Access pattern
Knowing that I am probably memory-bandwidth bound, here is the memory access pattern (per-row) for my radix-2 FFT.
X0 - element 1 to combine (read)
X1 - element 2 to combine (read)
X - element to write to (write)
Question
So my question is - can someone help me with/point me toward a higher-radix formulation for this algorithm? I ask because most FFTs are optimized for large cases and single real/complex valued sequences. Their kernel generators are also very case dependent and break down quickly when I try to muck with their internals.
Are there other options better than simply going to a radix-8 or 16 kernel?
Some of my constraints are - I have to use OpenCL (no cuFFT). I also cannot use clAmdFft from ACML for this purpose. It would be nice to also talk about CPU optimizations (this kernel SUCKS big time on the CPU) - but getting it to run in fewer iterations on the GPU is my main use-case.
Thanks in advance for reading through all this and trying to help!
I tried several versions, but the one with the best performance on CPU and GPU was a radix-16 kernel for my specific case.
Here is the kernel for reference. It was taken from Eric Bainville's (most excellent) website and used with full attribution.
// #define M_PI 3.14159265358979f
//Global size is x.Length/2, Scale = 1 for direct, 1/N to inverse (iFFT)
__kernel void ConjugateAndScale(__global float4* x, const float Scale)
{
int i = get_global_id(0);
float temp = Scale;
float4 t = (float4)(temp, -temp, temp, -temp);
x[i] *= t;
}
// Return a*EXP(-I*PI*1/2) = a*(-I)
float2 mul_p1q2(float2 a) { return (float2)(a.y,-a.x); }
// Return a^2
float2 sqr_1(float2 a)
{ return (float2)(a.x*a.x-a.y*a.y,2.0f*a.x*a.y); }
// Return the 2x DFT2 of the four complex numbers in A
// If A=(a,b,c,d) then return (a',b',c',d') where (a',c')=DFT2(a,c)
// and (b',d')=DFT2(b,d).
float8 dft2_4(float8 a) { return (float8)(a.lo+a.hi,a.lo-a.hi); }
// Return the DFT of 4 complex numbers in A
float8 dft4_4(float8 a)
{
// 2x DFT2
float8 x = dft2_4(a);
// Shuffle, twiddle, and 2x DFT2
return dft2_4((float8)(x.lo.lo,x.hi.lo,x.lo.hi,mul_p1q2(x.hi.hi)));
}
// Complex product, multiply vectors of complex numbers
#define MUL_RE(a,b) (a.even*b.even - a.odd*b.odd)
#define MUL_IM(a,b) (a.even*b.odd + a.odd*b.even)
float2 mul_1(float2 a, float2 b)
{ float2 x; x.even = MUL_RE(a,b); x.odd = MUL_IM(a,b); return x; }
float4 mul_1_F4(float4 a, float4 b)
{ float4 x; x.even = MUL_RE(a,b); x.odd = MUL_IM(a,b); return x; }
float4 mul_2(float4 a, float4 b)
{ float4 x; x.even = MUL_RE(a,b); x.odd = MUL_IM(a,b); return x; }
// Return the DFT2 of the two complex numbers in vector A
float4 dft2_2(float4 a) { return (float4)(a.lo+a.hi,a.lo-a.hi); }
// Return cos(alpha)+I*sin(alpha) (3 variants)
float2 exp_alpha_1(float alpha)
{
float cs,sn;
// sn = sincos(alpha,&cs); // sincos
//cs = native_cos(alpha); sn = native_sin(alpha); // native sin+cos
cs = cos(alpha); sn = sin(alpha); // sin+cos
return (float2)(cs,sn);
}
// Return cos(alpha)+I*sin(alpha) (3 variants)
float4 exp_alpha_1_F4(float alpha)
{
float cs,sn;
// sn = sincos(alpha,&cs); // sincos
// cs = native_cos(alpha); sn = native_sin(alpha); // native sin+cos
cs = cos(alpha); sn = sin(alpha); // sin+cos
return (float4)(cs,sn,cs,sn);
}
// mul_p*q*(a) returns a*EXP(-I*PI*P/Q)
#define mul_p0q1(a) (a)
#define mul_p0q2 mul_p0q1
//float2 mul_p1q2(float2 a) { return (float2)(a.y,-a.x); }
__constant float SQRT_1_2 = 0.707106781186548; // cos(Pi/4)
#define mul_p0q4 mul_p0q2
float2 mul_p1q4(float2 a) { return (float2)(SQRT_1_2)*(float2)(a.x+a.y,-a.x+a.y); }
#define mul_p2q4 mul_p1q2
float2 mul_p3q4(float2 a) { return (float2)(SQRT_1_2)*(float2)(-a.x+a.y,-a.x-a.y); }
__constant float COS_8 = 0.923879532511287; // cos(Pi/8)
__constant float SIN_8 = 0.382683432365089; // sin(Pi/8)
#define mul_p0q8 mul_p0q4
float2 mul_p1q8(float2 a) { return mul_1((float2)(COS_8,-SIN_8),a); }
#define mul_p2q8 mul_p1q4
float2 mul_p3q8(float2 a) { return mul_1((float2)(SIN_8,-COS_8),a); }
#define mul_p4q8 mul_p2q4
float2 mul_p5q8(float2 a) { return mul_1((float2)(-SIN_8,-COS_8),a); }
#define mul_p6q8 mul_p3q4
float2 mul_p7q8(float2 a) { return mul_1((float2)(-COS_8,-SIN_8),a); }
// Compute in-place DFT2 and twiddle
#define DFT2_TWIDDLE(a,b,t) { float2 tmp = t(a-b); a += b; b = tmp; }
// T = N/16 = number of threads.
// P is the length of input sub-sequences, 1,16,256,...,N/16.
__kernel void FFT_Radix16(__global const float4 * x, __global float4 * y, int pp)
{
int p = pp;
int t = get_global_size(0); // number of threads
int i = get_global_id(0); // current thread
////// y[i] = 2*x[i];
////// return;
int k = i & (p-1); // index in input sequence, in 0..P-1
// Inputs indices are I+{0,..,15}*T
x += i;
// Output indices are J+{0,..,15}*P, where
// J is I with four 0 bits inserted at bit log2(P)
y += ((i-k)<<4) + k;
// Load
float4 u[16];
for (int m=0;m<16;m++) u[m] = x[m*t];
// Twiddle, twiddling factors are exp(_I*PI*{0,..,15}*K/4P)
float alpha = -M_PI*(float)k/(float)(8*p);
for (int m=1;m<16;m++) u[m] = mul_1_F4(exp_alpha_1_F4(m * alpha), u[m]);
// 8x in-place DFT2 and twiddle (1)
DFT2_TWIDDLE(u[0].lo,u[8].lo,mul_p0q8);
DFT2_TWIDDLE(u[0].hi,u[8].hi,mul_p0q8);
DFT2_TWIDDLE(u[1].lo,u[9].lo,mul_p1q8);
DFT2_TWIDDLE(u[1].hi,u[9].hi,mul_p1q8);
DFT2_TWIDDLE(u[2].lo,u[10].lo,mul_p2q8);
DFT2_TWIDDLE(u[2].hi,u[10].hi,mul_p2q8);
DFT2_TWIDDLE(u[3].lo,u[11].lo,mul_p3q8);
DFT2_TWIDDLE(u[3].hi,u[11].hi,mul_p3q8);
DFT2_TWIDDLE(u[4].lo,u[12].lo,mul_p4q8);
DFT2_TWIDDLE(u[4].hi,u[12].hi,mul_p4q8);
DFT2_TWIDDLE(u[5].lo,u[13].lo,mul_p5q8);
DFT2_TWIDDLE(u[5].hi,u[13].hi,mul_p5q8);
DFT2_TWIDDLE(u[6].lo,u[14].lo,mul_p6q8);
DFT2_TWIDDLE(u[6].hi,u[14].hi,mul_p6q8);
DFT2_TWIDDLE(u[7].lo,u[15].lo,mul_p7q8);
DFT2_TWIDDLE(u[7].hi,u[15].hi,mul_p7q8);
// 8x in-place DFT2 and twiddle (2)
DFT2_TWIDDLE(u[0].lo,u[4].lo,mul_p0q4);
DFT2_TWIDDLE(u[0].hi,u[4].hi,mul_p0q4);
DFT2_TWIDDLE(u[1].lo,u[5].lo,mul_p1q4);
DFT2_TWIDDLE(u[1].hi,u[5].hi,mul_p1q4);
DFT2_TWIDDLE(u[2].lo,u[6].lo,mul_p2q4);
DFT2_TWIDDLE(u[2].hi,u[6].hi,mul_p2q4);
DFT2_TWIDDLE(u[3].lo,u[7].lo,mul_p3q4);
DFT2_TWIDDLE(u[3].hi,u[7].hi,mul_p3q4);
DFT2_TWIDDLE(u[8].lo,u[12].lo,mul_p0q4);
DFT2_TWIDDLE(u[8].hi,u[12].hi,mul_p0q4);
DFT2_TWIDDLE(u[9].lo,u[13].lo,mul_p1q4);
DFT2_TWIDDLE(u[9].hi,u[13].hi,mul_p1q4);
DFT2_TWIDDLE(u[10].lo,u[14].lo,mul_p2q4);
DFT2_TWIDDLE(u[10].hi,u[14].hi,mul_p2q4);
DFT2_TWIDDLE(u[11].lo,u[15].lo,mul_p3q4);
DFT2_TWIDDLE(u[11].hi,u[15].hi,mul_p3q4);
// 8x in-place DFT2 and twiddle (3)
DFT2_TWIDDLE(u[0].lo,u[2].lo,mul_p0q2);
DFT2_TWIDDLE(u[0].hi,u[2].hi,mul_p0q2);
DFT2_TWIDDLE(u[1].lo,u[3].lo,mul_p1q2);
DFT2_TWIDDLE(u[1].hi,u[3].hi,mul_p1q2);
DFT2_TWIDDLE(u[4].lo,u[6].lo,mul_p0q2);
DFT2_TWIDDLE(u[4].hi,u[6].hi,mul_p0q2);
DFT2_TWIDDLE(u[5].lo,u[7].lo,mul_p1q2);
DFT2_TWIDDLE(u[5].hi,u[7].hi,mul_p1q2);
DFT2_TWIDDLE(u[8].lo,u[10].lo,mul_p0q2);
DFT2_TWIDDLE(u[8].hi,u[10].hi,mul_p0q2);
DFT2_TWIDDLE(u[9].lo,u[11].lo,mul_p1q2);
DFT2_TWIDDLE(u[9].hi,u[11].hi,mul_p1q2);
DFT2_TWIDDLE(u[12].lo,u[14].lo,mul_p0q2);
DFT2_TWIDDLE(u[12].hi,u[14].hi,mul_p0q2);
DFT2_TWIDDLE(u[13].lo,u[15].lo,mul_p1q2);
DFT2_TWIDDLE(u[13].hi,u[15].hi,mul_p1q2);
// 8x DFT2 and store (reverse binary permutation)
y[0] = u[0] + u[1];
y[p] = u[8] + u[9];
y[2*p] = u[4] + u[5];
y[3*p] = u[12] + u[13];
y[4*p] = u[2] + u[3];
y[5*p] = u[10] + u[11];
y[6*p] = u[6] + u[7];
y[7*p] = u[14] + u[15];
y[8*p] = u[0] - u[1];
y[9*p] = u[8] - u[9];
y[10*p] = u[4] - u[5];
y[11*p] = u[12] - u[13];
y[12*p] = u[2] - u[3];
y[13*p] = u[10] - u[11];
y[14*p] = u[6] - u[7];
y[15*p] = u[14] - u[15];
}
Note that I have modified the kernel to perform the FFT of 2 complex-valued sequences at once instead of one. Also, since I only need the FFT of 256 elements at a time in a much larger sequence, I perform only 2 runs of this kernel, which leaves me with 256-length DFTs in the larger array.
Here's some of the relevant host code as well.
var ev = new[] { new Cl.Event() };
var pEv = new[] { new Cl.Event() };
int fftSize = 1;
int iter = 0;
int n = distributionSize >> 5;
while (fftSize <= n)
{
Cl.SetKernelArg(fftKernel, 0, memA);
Cl.SetKernelArg(fftKernel, 1, memB);
Cl.SetKernelArg(fftKernel, 2, fftSize);
Cl.EnqueueNDRangeKernel(commandQueue, fftKernel, 1, null, globalWorkgroupSize, localWorkgroupSize,
(uint)(iter == 0 ? 0 : 1),
iter == 0 ? null : pEv,
out ev[0]).Check();
if (iter > 0)
pEv[0].Dispose();
Swap(ref ev, ref pEv);
Swap(ref memA, ref memB); // ping-pong
fftSize = fftSize << 4;
iter++;
Cl.Finish(commandQueue);
}
Swap(ref memA, ref memB);
Hope this helps someone!