PPPK_mvmult -- Sage

%auto
implicit_multiplication (True)

A = matrix ([[10, 0, 3, 4, 0],
             [0, 40, 0, 6, 0],
             [2, 0, 60, 0, 0],
             [3, 5, 0, 70, 9],
             [0, 0, 0, 8, 90],
             [1, 0, 1, 0, 0]])
A

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

x = vector ([1, 1, 1, 1, 1])
x

(1, 1, 1, 1, 1)

(1, 1, 1, 1, 1)

A x

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

def rmv (A, x) :
    m = A.nrows()
    n = A.ncols()    
    y = zero_vector (m)
    for i in xrange (m) :
        for j in xrange (n) :
            y[i] += A[i,j] * x[j]
    return y

rmv (A, x)

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

Ar = vector ([10, 3, 4, 40, 6, 2, 60, 3, 5, 70, 9, 8, 90, 1, 1])
Jr = vector ([0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 4, 3, 4, 0, 2])
Ir = vector ([0, 3, 5, 7, 11, 13, 15])

def Arij (i, j, Ar, Ir, Jr) : 
    r = Ir[i]
    r1 = Ir[i + 1] 
    a = 0
    for jj in xrange (r1 - r) : 
        if Jr[r + jj] == j :
            a = Ar[r + jj]
            break
    return a

for i in xrange (A.nrows()) :
    for j in xrange (A.ncols()) :
        print Arij (i, j, Ar, Ir, Jr),
    print

A

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

def srmv (Ar, Ir, Jr, x) :
    m = len (Ir) - 1   
    y = zero_vector (m)
    for i in xrange (m) :
        j = Ir[i]
        j1 = Ir[i + 1]
        while j < j1 :
            y[i] += Ar[j] * x[ Jr[j] ]
            j += 1
    return y

srmv (Ar, Ir, Jr, x)

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

A x

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

def rmv (A, x) :
    m = A.nrows()
    n = A.ncols()    
    y = zero_vector (m)
    for i in xrange (m) :
        for j in xrange (n) :
            y[i] += A[i,j] * x[j]
    return y

def cmv (A, x) :
    m = A.nrows()
    n = A.ncols()    
    y = zero_vector (m)
    for j in xrange (n) :
        for i in xrange (m) :
            y[i] += x[j] * A[i,j]
    return y

cmv (A, x)

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

A

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

[10  0  3  4  0]
[ 0 40  0  6  0]
[ 2  0 60  0  0]
[ 3  5  0 70  9]
[ 0  0  0  8 90]
[ 1  0  1  0  0]

Ac = vector ([10, 2, 3, 1, 40, 5, 3, 60, 1, 4, 6, 70, 8, 9, 90])
Ic = vector ([0, 2, 3, 5, 1, 3, 0, 2, 5, 0, 1, 3, 4, 3, 4])
Jc = vector ([0, 4, 6, 9, 13, 15])

def Acij (i, j, Ac, Ic, Jc) : 
    c = Jc[j]
    c1 = Jc[j + 1] 
    a = 0
    for ii in xrange (c1 - c) : 
        if Ic[c + ii] == i :
            a = Ac[c + ii]
            break
    return a

for i in xrange (A.nrows()) :
    for j in xrange (A.ncols()) :
        print Acij (i, j, Ac, Ic, Jc),
    print

def scmv (Ac, Ic, Jc, x, nr) :
    m = nr
    n = len (Jc) - 1   
    y = zero_vector (m)
    for j in xrange (n) :
        i = Jc[j]
        i1 = Jc[j + 1]
        xj = x[j]
        while i < i1 :
            y[ Ic[i] ] += Ac[i] * xj
            i += 1
    return y

scmv (Ac, Ic, Jc, x, 6)

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

A x

(17, 46, 62, 87, 98, 2)

(17, 46, 62, 87, 98, 2)

As = matrix ([[10, 0, 2, 3, 0],
              [0, 40, 0, 5, 0],
              [2, 0, 60, 0, 0],
              [3, 5, 0, 70, 8],
              [0, 0, 0, 8, 90]])
As

[10  0  2  3  0]
[ 0 40  0  5  0]
[ 2  0 60  0  0]
[ 3  5  0 70  8]
[ 0  0  0  8 90]

[10  0  2  3  0]
[ 0 40  0  5  0]
[ 2  0 60  0  0]
[ 3  5  0 70  8]
[ 0  0  0  8 90]

Asur = vector ([10, 2, 3, 40, 5, 60, 70, 8, 90])
Js = vector ([0, 2, 3, 1, 3, 2, 3, 4, 4])
Is = vector ([0, 3, 5, 6, 8, 9])

As

[10  0  2  3  0]
[ 0 40  0  5  0]
[ 2  0 60  0  0]
[ 3  5  0 70  8]
[ 0  0  0  8 90]

[10  0  2  3  0]
[ 0 40  0  5  0]
[ 2  0 60  0  0]
[ 3  5  0 70  8]
[ 0  0  0  8 90]

def Asurij (i, j, Asur, Is, Js) : 
    if i <= j :
        ii = i
        jj = j
    else :
        ii = j
        jj = i
    r = Is[ii]
    r1 = Is[ii + 1] 
    a = 0
    for k in xrange (r1 - r) : 
        if Js[r + k] == jj :
            a = Asur[r + k]
            break
    return a

for i in xrange (As.nrows()) :
    for j in xrange (As.ncols()) :
        print Asurij (i, j, Asur, Is, Js),
    print

def ssurmv (Asr, Ir, Jr, x) :
    m = len (Ir) - 1   
    y = zero_vector (m) 
    for i in xrange (m) :
        j = Ir[i]
        y[i] += Asr[j] * x[ Jr[j] ]     # D x 
        j += 1
        j1 = Ir[i + 1]
        while j < j1 :
            y[i] += Asr[j] * x[ Jr[j] ]    # U x
            y[ Jr[j] ] += Asr[j] * x[i]    # L x  
            j += 1
    return y

ssurmv (Asur, Is, Js, x)

(15, 45, 62, 86, 98)

(15, 45, 62, 86, 98)

As x

(15, 45, 62, 86, 98)

(15, 45, 62, 86, 98)

PPPK_mvmult

170 days ago by fresl