حسابات المصفوفات وعملياتها

العمليات على مستوى العنصر مقابل عمليات المصفوفات

A <- matrix(c(1,2,3,4), nrow = 2)
B <- matrix(c(5,6,7,8), nrow = 2)
cat('A:
'); print(A)
cat('B:
'); print(B)

# Element-wise multiply
cat('A * B (element-wise):
'); print(A * B)
# Matrix multiply
cat('A %*% B (matrix mult):
'); print(A %*% B)

الجمع والطرح على مستوى العنصر

# Monthly revenue vs target (in thousands)
revenue <- matrix(c(120,135,110,98, 145,160,132,115),
                  nrow = 2, byrow = TRUE)
target  <- matrix(c(130,130,130,130, 150,150,150,150),
                  nrow = 2, byrow = TRUE)

deviation <- revenue - target
cat('Revenue vs Target deviation:
')
print(deviation)
cat('Above target?:
')
print(revenue >= target)

القسمة والضرب على مستوى العنصر

# Scale a matrix by another (element-wise)
prices <- matrix(c(10, 20, 15, 25), nrow = 2)
quantities <- matrix(c(5, 3, 8, 2), nrow = 2)

total_cost <- prices * quantities
cat('Total cost per item:
')
print(total_cost)

# Normalise to row maximum
max_prices <- matrix(rep(apply(prices, 1, max), 2), nrow = 2)
norm_prices <- prices / max_prices
cat('Normalised prices:
')
print(norm_prices)

العمليات العددية على المصفوفات

m <- matrix(c(10, 20, 30, 40, 50, 60), nrow = 2, ncol = 3)
cat('Original:
'); print(m)

cat('m + 5:
');  print(m + 5)
cat('m * 2:
');  print(m * 2)
cat('m / 10:
'); print(m / 10)
cat('m ^ 2:
');  print(m ^ 2)

الضرب الحقيقي للمصفوفات %*%

# 2x3 times 3x2 = 2x2
A <- matrix(c(1,2,3, 4,5,6), nrow = 2, byrow = TRUE)
B <- matrix(c(7,8, 9,10, 11,12), nrow = 3, byrow = TRUE)
cat('A (2x3):
'); print(A)
cat('B (3x2):
'); print(B)
cat('A %*% B (2x2):
'); print(A %*% B)

rowSums() و colSums()

sales <- matrix(
  c(120,135,110,98,  145,160,132,115,  88,95,102,78),
  nrow = 3, byrow = TRUE,
  dimnames = list(c('Q1','Q2','Q3'), c('Jan','Feb','Mar','Apr'))
)
cat('Sales matrix:
'); print(sales)
cat('Quarterly totals:', rowSums(sales), '
')
cat('Monthly totals: ', colSums(sales), '
')

rowMeans() و colMeans()

exam_scores <- matrix(
  c(88,92,75,81, 79,85,90,73, 95,78,82,88),
  nrow = 3, byrow = TRUE,
  dimnames = list(c('Alice','Bob','Carol'), c('Math','Sci','Eng','Hist'))
)
cat('Student averages:
')
print(rowMeans(exam_scores))
cat('Subject averages:
')
print(colMeans(exam_scores))

عمليات المقارنة على المصفوفات

scores <- matrix(c(88,45,92,61,73,55,84,79), nrow = 2)
cat('Scores:
'); print(scores)

# Which elements pass?
passing_mask <- scores >= 60
cat('Passing mask:
'); print(passing_mask)
cat('Number passing:', sum(passing_mask), '
')
cat('Passing scores:', scores[passing_mask], '
')

apply() لعمليات الصفوف أو الأعمدة المخصصة

m <- matrix(c(3,1,4,1,5,9,2,6,5,3,5,8), nrow = 3)
cat('Matrix:
'); print(m)

# Max of each row
cat('Row max:  ', apply(m, 1, max), '
')
# Range of each column
cat('Col range:
')
print(apply(m, 2, range))
# Custom: count values > 4 per row
cat('Values > 4 per row:', apply(m, 1, function(x) sum(x > 4)), '
')

تعميم متجه عبر الصفوف

m <- matrix(c(10,20,30, 40,50,60), nrow = 2)
cat('Matrix:
'); print(m)

# Add a 3-element vector: R recycles column-by-column
v <- c(1, 2, 3)
cat('m + c(1,2,3):
'); print(m + v)

# For row-wise scaling, use sweep()
row_weights <- c(0.5, 2.0)  # scale row 1 by 0.5, row 2 by 2
cat('Row-wise scaled:
'); print(sweep(m, 1, row_weights, '*'))

ملخص العمليات الحسابية

m <- matrix(c(4,9,16,25), nrow = 2)
cat('Original:
'); print(m)
cat('sqrt (element-wise):
'); print(sqrt(m))
cat('rowSums:', rowSums(m), '
')
cat('colMeans:', colMeans(m), '
')

تحقق سريع

مراجعة: العمليات الحسابية على المصفوفات

# Final: compute grade curve (add 5 to all scores, cap at 100)
raw <- matrix(c(88,55,92,73,60,45,78,95), nrow = 2)
curved <- pmin(raw + 5, 100)  # pmin applies min element-wise
cat('Raw:
');    print(raw)
cat('Curved:
'); print(curved)