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verify.pyx
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verify.pyx
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cimport tokyo
import tokyo
import numpy as np
cimport numpy as np
import time
import sys
tokyo.verbose = True
speed_base = 200000 # increase to get slower but more precise speed test results
test_sizes = [4, 15, 30]
print
print "Tokyo BLAS wrapper verification against scipy/numpy"
print "---------------------------------------------------"
print
print
print "VERIFY CORRECTNESS BLAS Level 1"
print
sswap_verify()
sscal_verify()
scopy_verify()
saxpy_verify()
sdot_verify()
snrm2_verify()
sasum_verify()
isamax_verify()
srotg_verify()
#srot_verify()
print
dswap_verify()
dscal_verify()
dcopy_verify()
daxpy_verify()
ddot_verify()
dnrm2_verify()
dasum_verify()
idamax_verify()
drotg_verify()
print
print "VERIFY CORRECTNESS BLAS Level 2"
print
sgemv_verify(); print
sger_verify(); print
dgemv_verify(); print
dger_verify(); print
print
print "VERIFY CORRECTNESS BLAS 3"
print
sgemm_verify(); print
dgemm_verify(); print
print
print "VERIFY CORRECTNESS EXTRAS"
print
smsetzero_verify();
svsetzero_verify();
smaxpy_verify();
print
dmsetzero_verify();
dvsetzero_verify();
dmaxpy_verify();
###############################################################################
# A function for checking that different matrices from different
# computations are in some sense "equal" in the verification tests.
cpdef approx_eq(X, Y): return abs(np.sum(X - Y)) < 1e-5
#####################################
# BLAS LEVEL 1 (vector operations)
#####################################
# vector swap: x <-> y
cdef sswap_verify():
x = np.array(np.random.random((4)), dtype=np.float32)
y = np.array(np.random.random((4)), dtype=np.float32)
temp1 = x.copy()
temp2 = y.copy()
tokyo.sswap(x,y)
print "sswap: ", (approx_eq(temp1, y) and approx_eq(temp2, x))
cdef dswap_verify():
x = np.array(np.random.random((4)), dtype=np.float64)
y = np.array(np.random.random((4)), dtype=np.float64)
temp1 = x.copy()
temp2 = y.copy()
tokyo.dswap(x,y)
print "dswap: ", (approx_eq(temp1, y) and approx_eq(temp2, x))
# scalar vector multiply: x *= alpha
cdef sscal_verify():
x = np.array(np.random.random((4)), dtype=np.float32)
temp = 1.2 * x
tokyo.sscal(1.2, x)
print "sscal: ", approx_eq(temp, x)
cdef dscal_verify():
x = np.array(np.random.random((4)), dtype=np.float64)
temp = 1.2 * x
tokyo.dscal(1.2, x)
print "dscal: ", approx_eq(temp, x)
# vector copy: y <- x
cdef scopy_verify():
x = np.array(np.random.random((4)), dtype=np.float32)
y = np.array(np.random.random((4)), dtype=np.float32)
tokyo.scopy(x,y)
print "scopy: ", approx_eq(x, y)
cdef dcopy_verify():
x = np.array(np.random.random((4)), dtype=np.float64)
y = np.array(np.random.random((4)), dtype=np.float64)
tokyo.dcopy(x,y)
print "dcopy: ", approx_eq(x, y)
# vector addition: y += alpha * x
cdef saxpy_verify():
x = np.array(np.random.random((5)), dtype=np.float32)
y = np.array(np.random.random((5)), dtype=np.float32)
temp = 1.2 * x + y
tokyo.saxpy(1.2, x, y)
print "saxpy: ", approx_eq(temp, y)
cdef daxpy_verify():
x = np.array(np.random.random((5)), dtype=np.float64)
y = np.array(np.random.random((5)), dtype=np.float64)
temp = 1.2 * x + y
tokyo.daxpy(1.2, x, y)
print "daxpy: ", approx_eq(temp, y)
# vector dot product: x.T y
cdef sdot_verify():
x = np.array(np.random.random((5)), dtype=np.float32)
y = np.array(np.random.random((5)), dtype=np.float32)
print "sdot: ", approx_eq(np.dot(x,y), tokyo.sdot(x,y))
cdef ddot_verify():
x = np.array(np.random.random((5)), dtype=np.float64)
y = np.array(np.random.random((5)), dtype=np.float64)
print "ddot: ", approx_eq(np.dot(x,y), tokyo.ddot(x,y))
# Euclidean norm: ||x||_2
cdef snrm2_verify():
x = np.array(np.random.random((5)), dtype=np.float32)
print "snrm2: ", approx_eq(np.sqrt(np.sum(np.dot(x,x))), tokyo.snrm2(x))
cdef dnrm2_verify():
x = np.array(np.random.random((5)), dtype=np.float64)
print "dnrm2: ", approx_eq(np.sqrt(np.sum(np.dot(x,x))), tokyo.dnrm2(x))
# sum of absolute values: ||x||_1
cdef sasum_verify():
x = np.array(np.random.random((5)), dtype=np.float32)
print "sasum: ", approx_eq(np.sum(np.abs(x)), tokyo.sasum(x))
cdef dasum_verify():
x = np.array(np.random.random((5)), dtype=np.float64)
print "dasum: ", approx_eq(np.sum(np.abs(x)), tokyo.dasum(x))
# index of maximum absolute value element
cdef isamax_verify():
x = np.array([0.06, -0.1, -0.05, -0.001, 0.07], dtype=np.float32)
print "isamax: ", ( 1 == tokyo.isamax(x))
cdef idamax_verify():
x = np.array([0.06, -0.1, -0.05, -0.001, 0.07], dtype=np.float64)
print "idamax: ", ( 1 == tokyo.idamax(x))
cpdef check_negligible(scomp, strue, ssize, sfac):
"""
Return `True` if difference between `scomp` and `strue` is
negligible elementwise.
"""
sd = scomp - strue
abssize = np.abs(ssize)
return not np.any((abssize + np.abs(sfac*sd)) - abssize)
cdef srotg_verify():
da1 = np.array([0.3, 0.4, -0.3, -0.4, -0.3, 0.0, 0.0, 1.0], np.float32)
db1 = np.array([0.4, 0.3, 0.4, 0.3, -0.4, 0.0, 1.0, 0.0], np.float32)
dc1 = np.array([0.6, 0.8, -0.6, 0.8, 0.6, 1.0, 0.0, 1.0], np.float32)
ds1 = np.array([0.8, 0.6, 0.8, -0.6, 0.8, 0.0, 1.0, 0.0], np.float32)
datrue = np.array([0.5, 0.5, 0.5, -0.5, -0.5, 0.0, 1.0, 1.0], np.float32)
dbtrue = np.array([1.0/0.6, 0.6, -1.0/0.6, -0.6, 1.0/0.6, 0.0, 1.0, 0.0],
np.float32)
a = np.empty(8, np.float32)
b = np.empty(8, np.float32)
c = np.empty(8, np.float32)
s = np.empty(8, np.float32)
for k in range(len(da1)):
(a[k],b[k],c[k],s[k]) = tokyo.srotg(da1[k], db1[k])
a_ok = check_negligible(a, datrue, datrue, 9.765625e-4)
b_ok = check_negligible(b, dbtrue, dbtrue, 9.765625e-4)
c_ok = check_negligible(c, dc1, dc1, 9.765625e-4)
s_ok = check_negligible(s, ds1, ds1, 9.765625e-4)
if not (a_ok and b_ok and c_ok and s_ok):
print 'srotg: '
print 'Got ', (a,b,c,s)
print 'Expected ', (datrue, dbtrue, dc1, ds1)
else:
print 'srotg: All ok'
cdef drotg_verify():
da1 = np.array([0.3, 0.4, -0.3, -0.4, -0.3, 0.0, 0.0, 1.0], np.float64)
db1 = np.array([0.4, 0.3, 0.4, 0.3, -0.4, 0.0, 1.0, 0.0], np.float64)
dc1 = np.array([0.6, 0.8, -0.6, 0.8, 0.6, 1.0, 0.0, 1.0], np.float64)
ds1 = np.array([0.8, 0.6, 0.8, -0.6, 0.8, 0.0, 1.0, 0.0], np.float64)
datrue = np.array([0.5, 0.5, 0.5, -0.5, -0.5, 0.0, 1.0, 1.0], np.float64)
dbtrue = np.array([1.0/0.6, 0.6, -1.0/0.6, -0.6, 1.0/0.6, 0.0, 1.0, 0.0],
np.float64)
a = np.empty(8, np.float64)
b = np.empty(8, np.float64)
c = np.empty(8, np.float64)
s = np.empty(8, np.float64)
for k in range(len(da1)):
(a[k],b[k],c[k],s[k]) = tokyo.drotg(da1[k], db1[k])
a_ok = check_negligible(a, datrue, datrue, 9.765625e-4)
b_ok = check_negligible(b, dbtrue, dbtrue, 9.765625e-4)
c_ok = check_negligible(c, dc1, dc1, 9.765625e-4)
s_ok = check_negligible(s, ds1, ds1, 9.765625e-4)
if not (a_ok and b_ok and c_ok and s_ok):
print 'drotg: '
print 'Got ', (a,b,c,s)
print 'Expected ', (datrue, dbtrue, dc1, ds1)
else:
print 'drotg: All ok'
#cdef srot_verify():
# incxs = np.array([1, 2, -2, -1], np.int)
# incys = np.array([1, -2, 1, -2], np.int)
# lens = np.array([[1, 1], [2, 4], [1, 1], [3, 7]], np.int)
# ns = np.array([0, 1, 2, 4], np.int)
#
# dx1 = np.array([0.6, 0.1, -0.5, 0.8, 0.9, -0.3, -0.4], np.float32)
# dy1 = np.array([0.5, -0.9, 0.3, 0.7, -0.6, 0.2, 0.8], np.float32)
# sc = np.array([0.8], np.float32)
# ss = np.array([0.6], np.float32)
#
# sx = dx1.copy() ; stx = np.zeros_like(dx1)
# sy = dy1.copy() ; sty = np.zeros_like(dy1)
#
# # Data to be recovered as 7x4x4 arrays.
# dt9x = np.array([[[ 0.6, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.78],
# [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.78, -0.46]],
# [[ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.78, -0.46, -0.22],
# [ 1.06, 0.0, 0.0, 0.0 ], [ 0.6, 0.0, 0.0, 0.0 ]],
# [[ 0.0, 0.0, 0.0, 0.78], [ 1.0, 0.0, 0.0, 0.0 ],
# [ 0.0, 0.0, 0.66, 0.1 ], [-0.1, 0.0, 0.0, 0.0 ]],
# [[ 0.0, 0.96, 0.1, -0.76], [ 0.8, 0.90, -0.3, -0.02],
# [ 0.6, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.78]],
# [[ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, -0.06, 0.1 ],
# [-0.1, 0.0, 0.0, 0.0 ], [ 0.0, 0.90, 0.1, -0.22]],
# [[ 0.8, 0.18, -0.3, -0.02], [ 0.6, 0.0, 0.0, 0.0 ],
# [ 0.0, 0.0, 0.0, 0.78], [ 0.0, 0.0, 0.0, 0.0 ]],
# [[ 0.0, 0.0, 0.78, 0.26], [ 0.0, 0.0, 0.0, 0.0 ],
# [ 0.0, 0.78, 0.26, -0.76], [ 1.12, 0.0, 0.0, 0.0]]],
# np.float32)
#
# dt9y = np.array([[[0.5, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.04],
# [0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.04, -0.78]],
# [[0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.04, -0.78, 0.54],
# [0.08, 0.0, 0.0, 0.0 ], [ 0.5, 0.0, 0.0, 0.0 ]],
# [[0.0, 0.0, 0.0, 0.04], [ 0.0, 0.0, 0.0, 0.0 ],
# [0.0, 0.0, 0.7, -0.9 ], [-0.12, 0.0, 0.0, 0.0 ]],
# [[0.0, 0.64, -0.9, -0.30], [ 0.7, -0.18, 0.2, 0.28],
# [0.5, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.04]],
# [[0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.7, -1.08],
# [0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.64, -1.26, 0.54]],
# [[0.20, 0.0, 0.0, 0.0 ], [ 0.5, 0.0, 0.0, 0.0 ],
# [0.0, 0.0, 0.0, 0.04], [ 0.0, 0.0, 0.0, 0.0 ]],
# [[0.0, 0.0, 0.04, -0.9 ], [ 0.18, 0.0, 0.0, 0.0 ],
# [0.0, 0.04, -0.9, 0.18], [ 0.7, -0.18, 0.2, 0.16]]],
# np.float32)
#
# ssize2 = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
# 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
# 0.0, 1.17, 1.17, 1.17, 1.17, 1.17,
# 1.17, 1.17, 1.17, 1.17, 1.17, 1.17,
# 1.17, 1.17, 1.17], np.float32)
#
# for j in range(len(incxs)):
# incx = incxs[j]
# incy = incys[j]
# mx = abs(incx)
# my = abs(incy)
#
# for k in range(len(ns)):
# n = ns[k] ; ksize = min(1,k-1)
# lenx = lens[k,mx-1]
# leny = lens[k,my-1]
#
# for i in range(len(dx1)):
# stx[i] = dt9x[i,k,j]
# sty[i] = dt9y[i,k,j]
#
# tokyo.srot(sx, sy, sc[0], ss[0], dx=incx, dy=incy)
# x_ok = check_negligible(sx, stx, ssize2[ksize], 9.765625e-4)
# y_ok = check_negligible(sy, sty, ssize2[ksize], 9.765625e-4)
#
# if not (x_ok and y_ok):
# print 'srot: '
# print 'Got:' ; print 'sx = ', sx ; print 'sy = ', sy
# print 'Expected:' ; print 'sx = ', stx ; print 'sy = ', sty
# else:
# print 'srot: All ok'
###########################################
# BLAS LEVEL 2 (matrix-vector operations)
###########################################
# single precision matrix times vector: y = alpha * A x + beta * y
# or y = alpha * A.T x + beta * y
cdef sgemv_verify():
A = np.array(np.random.random((4,5)), dtype=np.float32)
x = np.array(np.random.random((5)), dtype=np.float32)
y = np.array(np.random.random((4)), dtype=np.float32)
cdef np.ndarray[float, ndim=2, mode='c'] A_
cdef np.ndarray[float, ndim=1, mode='c'] x_, y_
A_ = A; x_ = x; y_ = y
temp = np.dot(A,x)
temp2 = tokyo.sgemv(A, x)
print "sgemv: ", approx_eq(temp, temp2)
temp = np.dot(A,x)
tokyo.sgemv3(A, x, y)
print "sgemv3: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.sgemv5(1.2, A, x, 2.1, y)
print "sgemv5: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.sgemv6(tokyo.CblasNoTrans, 1.2, A, x, 2.1, y)
print "sgemv6: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.sgemv_(tokyo.CblasRowMajor, tokyo.CblasNoTrans, 4, 5,
1.2, <float*>A_.data, 5, <float*>x_.data, 1,
2.1, <float*>y_.data, 1)
print "sgemv_: ", approx_eq(temp, y)
# double precision matrix times vector: y = alpha * A x + beta * y
# or y = alpha * A.T x + beta * y
cdef dgemv_verify():
A = np.array(np.random.random((4,5)), dtype=np.float64)
x = np.array(np.random.random((5)), dtype=np.float64)
y = np.array(np.random.random((4)), dtype=np.float64)
cdef np.ndarray[double, ndim=2, mode='c'] A_
cdef np.ndarray[double, ndim=1, mode='c'] x_, y_
A_ = A; x_ = x; y_ = y
temp = np.dot(A,x)
temp2 = tokyo.dgemv(A, x)
print "dgemv: ", approx_eq(temp, temp2)
temp = np.dot(A,x)
tokyo.dgemv3(A, x, y)
print "dgemv3: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.dgemv5(1.2, A, x, 2.1, y)
print "dgemv5: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.dgemv6(tokyo.CblasNoTrans, 1.2, A, x, 2.1, y)
print "dgemv6: ", approx_eq(temp, y)
temp = 1.2*np.dot(A,x) + 2.1*y
tokyo.dgemv_(tokyo.CblasRowMajor, tokyo.CblasNoTrans, 4, 5,
1.2, <double*>A_.data, 5, <double*>x_.data, 1,
2.1, <double*>y_.data, 1)
print "dgemv_: ", approx_eq(temp, y)
# single precision vector outer-product: A = alpha * outer_product(x, y.T)
cdef sger_verify():
x = np.array(np.random.random((4)), dtype=np.float32)
y = np.array(np.random.random((5)), dtype=np.float32)
A = np.array(np.random.random((4,5)), dtype=np.float32)
result = np.outer(x, y)
print "sger: ", approx_eq(result, tokyo.sger(x, y))
result = A + np.outer(x, y)
tokyo.sger3(x, y, A)
print "sger3: ", approx_eq(result, A)
result = A + 1.2*np.outer(x, y)
tokyo.sger4(1.2, x, y, A)
print "sger4: ", approx_eq(result, A)
# double precision vector outer-product: A = alpha * outer_product(x, y.T)
cdef dger_verify():
x = np.array(np.random.random((4)), dtype=np.float64)
y = np.array(np.random.random((5)), dtype=np.float64)
A = np.array(np.random.random((4,5)), dtype=np.float64)
result = np.outer(x, y)
print "dger: ", approx_eq(result, tokyo.dger(x, y))
result = A + np.outer(x, y)
tokyo.dger3(x, y, A)
print "dger3: ", approx_eq(result, A)
result = A + 1.2*np.outer(x, y)
tokyo.dger4(1.2, x, y, A)
print "dger4: ", approx_eq(result, A)
###########################################
#
# BLAS LEVEL 3 (matrix-matrix operations)
#
###########################################
# matrix times matrix: C = alpha * A B + beta * C
# or C = alpha * A.T B + beta * C
# or C = alpha * A B.T + beta * C
# or C = alpha * A.T B.T + beta * C
#
# single precision
cdef sgemm_verify():
X = np.array(np.random.random((3,4)), dtype=np.float32)
Y = np.array(np.random.random((4,5)), dtype=np.float32)
print "sgemm: ", approx_eq(np.dot(X, Y), tokyo.sgemm(X, Y))
Z = np.array(np.random.random((3,5)), dtype=np.float32)
tokyo.sgemm3(X, Y, Z)
print "sgemm3: ", approx_eq(np.dot(X, Y), Z)
Z = np.array(np.random.random((3,5)), dtype=np.float32)
result = 2.3*np.dot(X, Y) + 1.2*Z
tokyo.sgemm5(2.3, X, Y, 1.2, Z)
print "sgemm5: ", approx_eq(result, Z)
Z = np.array(np.random.random((3,5)), dtype=np.float32)
result = 2.3*np.dot(X, Y) + 1.2*Z
tokyo.sgemm7(tokyo.CblasNoTrans, tokyo.CblasNoTrans, 2.3, X, Y, 1.2, Z)
print "sgemm7: ", approx_eq(result, Z)
# matrix times matrix: C = alpha * A B + beta * C
# or C = alpha * A.T B + beta * C
# or C = alpha * A B.T + beta * C
# or C = alpha * A.T B.T + beta * C
#
# double precision
cdef dgemm_verify():
X = np.array(np.random.random((3,4)), dtype=np.float64)
Y = np.array(np.random.random((4,5)), dtype=np.float64)
print "dgemm: ", approx_eq(np.dot(X, Y), tokyo.dgemm(X, Y))
Z = np.array(np.random.random((3,5)), dtype=np.float64)
tokyo.dgemm3(X, Y, Z)
print "dgemm3: ", approx_eq(np.dot(X, Y), Z)
Z = np.array(np.random.random((3,5)), dtype=np.float64)
result = 2.3*np.dot(X, Y) + 1.2*Z
tokyo.dgemm5(2.3, X, Y, 1.2, Z)
print "dgemm5: ", approx_eq(result, Z)
Z = np.array(np.random.random((3,5)), dtype=np.float64)
result = 2.3*np.dot(X, Y) + 1.2*Z
tokyo.dgemm7(tokyo.CblasNoTrans, tokyo.CblasNoTrans, 2.3, X, Y, 1.2, Z)
print "dgemm7: ", approx_eq(result, Z)
####################################################################
#
# Utility function I have put together that aren't in BLAS or LAPACK
#
####################################################################
# set a matrix of floats to all zeros
cdef smsetzero_verify():
A = np.array(np.random.random((4,4)), dtype=np.float32)
B = np.zeros((4,4))
tokyo.smsetzero(A)
print "smsetzero: ", approx_eq(A, B)
# set a matrix of floats to all zeros
cdef dmsetzero_verify():
A = np.array(np.random.random((4,4)), dtype=np.float64)
B = np.zeros((4,4))
tokyo.dmsetzero(A)
print "dmsetzero: ", approx_eq(A, B)
# set a vector of doubles to all zeros
cdef svsetzero_verify():
x = np.array(np.random.random((4)), dtype=np.float32)
y = np.zeros((4))
tokyo.svsetzero(x)
print "svsetzero: ", approx_eq(x, y)
# set a vector of doubles to all zeros
cdef dvsetzero_verify():
x = np.array(np.random.random((4)), dtype=np.float64)
y = np.zeros((4))
tokyo.dvsetzero(x)
print "dvsetzero: ", approx_eq(x, y)
# double precision matrix += scalar * matrix
cdef smaxpy_verify():
X = np.array(np.random.random((4,4)), dtype=np.float32)
Y = np.array(np.random.random((4,4)), dtype=np.float32)
temp = 1.2 * X + Y
tokyo.smaxpy(1.2, X, Y)
print "smaxpy: ", approx_eq(temp, Y)
# double precision matrix += scalar * matrix
cdef dmaxpy_verify():
X = np.array(np.random.random((4,4)), dtype=np.float64)
Y = np.array(np.random.random((4,4)), dtype=np.float64)
temp = 1.2 * X + Y
tokyo.dmaxpy(1.2, X, Y)
print "dmaxpy: ", approx_eq(temp, Y)