func calike(a, b complex128) bool {
switch {
case cmplx.IsInf(a) && cmplx.IsInf(b):
return true
case cmplx.IsNaN(a) && cmplx.IsNaN(b):
return true
}
return a == b
}
/*
General matrix-matrix product. (L3)
PURPOSE
Computes
C := alpha*A*B + beta*C if transA = PNoTrans and transB = PNoTrans.
C := alpha*A^T*B + beta*C if transA = PTrans and transB = PNoTrans.
C := alpha*A^H*B + beta*C if transA = PConjTrans and transB = PNoTrans.
C := alpha*A*B^T + beta*C if transA = PNoTrans and transB = PTrans.
C := alpha*A^T*B^T + beta*C if transA = PTrans and transB = PTrans.
C := alpha*A^H*B^T + beta*C if transA = PConjTrans and transB = PTrans.
C := alpha*A*B^H + beta*C if transA = PNoTrans and transB = PConjTrans.
C := alpha*A^T*B^H + beta*C if transA = PTrans and transB = PConjTrans.
C := alpha*A^H*B^H + beta*C if transA = PConjTrans and transB = PConjTrans.
The number of rows of the matrix product is m. The number of columns is n.
The inner dimension is k. If k=0, this reduces to C := beta*C.
ARGUMENTS
A float or complex matrix, m*k
B float or complex matrix, k*n
C float or complex matrix, m*n
alpha number (float or complex singleton matrix)
beta number (float or complex singleton matrix)
OPTIONS
transA PNoTrans, PTrans or PConjTrans
transB PNoTrans, PTrans or PConjTrans
m integer. If negative, the default value is used. The default value is
m = A.Rows of if transA != PNoTrans m = A.Cols.
n integer. If negative, the default value is used. The default value is
n = (transB == PNoTrans) ? B.Cols : B.Rows.
k integer. If negative, the default value is used. The default value is
k=A.Cols or if transA != PNoTrans) k = A.Rows, transA=PNoTrans.
If the default value is used it should also be equal to
(transB == PNoTrans) ? B.Rows : B.Cols.
ldA nonnegative integer. ldA >= max(1,m) of if transA != NoTrans max(1,k).
If zero, the default value is used.
ldB nonnegative integer. ldB >= max(1,k) or if transB != NoTrans max(1,n).
If zero, the default value is used.
ldC nonnegative integer. ldC >= max(1,m).
If zero, the default value is used.
offsetA nonnegative integer
offsetB nonnegative integer
offsetC nonnegative integer;
*/
func Gemm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fgemm, A, B, C, params)
if err != nil {
return
}
if ind.M == 0 || ind.N == 0 {
return
}
if !matrix.EqualTypes(A, B, C) {
return errors.New("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return errors.New("alpha or beta not a number")
}
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
dgemm(transA, transB, ind.M, ind.N, ind.K, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, bval,
Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
Aa := A.ComplexArray()
Ba := B.ComplexArray()
Ca := C.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not a number")
}
bval := beta.Complex()
if cmplx.IsNaN(bval) {
return errors.New("beta not a number")
}
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
zgemm(transA, transB, ind.M, ind.N, ind.K, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, bval,
Ca[ind.OffsetC:], ind.LDc)
default:
return errors.New("Unknown type, not implemented")
}
return
}
func FlexEqual(x, y interface{}) bool {
var isfloat, iscomplex bool
var xf, yf float64
var xc, yc complex128
switch x := x.(type) {
case float32:
if _, ok := y.(float32); !ok {
return false
}
xf, yf = float64(x), float64(y.(float32))
isfloat = true
case float64:
if _, ok := y.(float64); !ok {
return false
}
xf, yf = float64(x), y.(float64)
isfloat = true
case complex64:
if _, ok := y.(complex64); !ok {
return false
}
xc, yc = complex128(x), complex128(y.(complex64))
iscomplex = true
case complex128:
if _, ok := y.(complex128); !ok {
return false
}
xc, yc = complex128(x), y.(complex128)
iscomplex = true
}
if isfloat {
switch {
case math.IsNaN(xf) && math.IsNaN(yf):
return true
case math.IsInf(xf, 1) && math.IsInf(yf, 1):
return true
case math.IsInf(xf, -1) && math.IsInf(yf, -1):
return true
}
}
if iscomplex {
switch {
case cmplx.IsNaN(xc) && cmplx.IsNaN(yc):
return true
case cmplx.IsInf(xc) && cmplx.IsInf(yc):
return true
}
}
return reflect.DeepEqual(x, y)
}
/*
Matrix-matrix product where one matrix is symmetric. (L3)
Computes
C := alpha*A*B + beta*C, if side is PLeft
C := alpha*B*A + beta*C, if side is PRight
C is m by n and A is real symmetric.
ARGUMENTS
A float or complex matrix
B float or complex matrix.
C float m*n matrix.
alpha number (float).
beta number (float).
OPTIONS
side PLeft or PRight'
uplo PLower or PUpper
m integer. If negative, the default value is used.
If the default value is used and side = PLeft, then m
must be equal to A.Rows and A.Cols.
n integer. If negative, the default value is used.
If the default value is used and side = PRight, then
must be equal to A.Rows and A.Cols.
ldA nonnegative integer.
ldA >= max(1, m) or if side == PRight ldA >= max(1, n).
If zero, the default value is used.
ldB nonnegative integer.
ldB >= max(1,n) or if side == PRight ldB >= max(1, m).
If zero, the default value is used.
ldC nonnegative integer. ldC >= max(1,m). If zero, the default value is used.
offsetA nonnegative integer
offsetB nonnegative integer
offsetC nonnegative integer
*/
func Symm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fsymm, A, B, C, params)
if err != nil {
return
}
if ind.M == 0 || ind.N == 0 {
return
}
if !matrix.EqualTypes(A, B, C) {
return onError("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
Ca := C.(*matrix.FloatMatrix).FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return onError("alpha or beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
side := linalg.ParamString(params.Side)
dsymm(side, uplo, ind.M, ind.N, aval, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, bval, Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
Aa := A.(*matrix.ComplexMatrix).ComplexArray()
Ba := B.(*matrix.ComplexMatrix).ComplexArray()
Ca := C.(*matrix.ComplexMatrix).ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return onError("alpha not a number")
}
bval := beta.Complex()
if cmplx.IsNaN(bval) {
return onError("beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
side := linalg.ParamString(params.Side)
zhemm(side, uplo, ind.M, ind.N, aval, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, bval, Ca[ind.OffsetC:], ind.LDc)
default:
return onError("Unknown type, not implemented")
}
return
}
/*
Rank-k update of symmetric matrix. (L3)
Syrk(A, C, alpha=1.0, beta=0.0, uplo=PLower, trans=PNoTrans, n=-1,
k=-1, ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0)
PURPOSE
C := alpha*A*A^T + beta*C, if trans is PNoTrans
C := alpha*A^T*A + beta*C, if trans is PTrans
C := alpha*A^H*A + beta*C, if trans is PConjTrans
C is symmetric (real or complex) of order n.
The inner dimension of the matrix product is k. If k=0 this is
interpreted as C := beta*C.
ARGUMENTS
A float or complex n*k matrix
C float or complex n*n matrix. Must have the same type as A.
alpha number (float or complex singleton matrix). Complex alpha is only
allowed if A is complex.
beta number (float or complex singleton matrix). Complex beta is only
allowed if A is complex.
OPTIONS
uplo PLower or PUpper
trans PNoTrans, PTrans or PConjTrans
n integer. If negative, the default value is used.
The default value is n = A.Rows of if trans != PNoTrans) n = A.Cols.
k integer. If negative, the default value is used.
The default value is k = A.Cols or if trans != PNoTrans k = A.Rows.
ldA nonnegative integer. ldA >= max(1, n) or if trans != PNoTrans max(1, k).
If zero, the default value [max(1, A.Rows)] is used.
ldC nonnegative integer. ldC >= max(1,n). If zero, the default value is used.
offsetA nonnegative integer
offsetC nonnegative integer;
*/
func Syrk(A, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fsyrk, A, nil, C, params)
if e != nil || err != nil {
return
}
if !matrix.EqualTypes(A, C) {
return errors.New("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ca := C.FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return errors.New("alpha or beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
dsyrk(uplo, trans, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa, bval,
Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
Aa := A.ComplexArray()
Ca := C.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not a number")
}
bval := beta.Complex()
if cmplx.IsNaN(bval) {
return errors.New("beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
zsyrk(uplo, trans, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa, bval,
Ca[ind.OffsetC:], ind.LDc)
default:
return errors.New("Unknown type, not implemented")
}
return
}
func formatSolutions(x1, x2 complex128) string {
exactlyOneSolution := false
if cmplx.IsNaN(x1) && cmplx.IsNaN(x2) {
return noSolution
}
if cmplx.IsNaN(x1) {
exactlyOneSolution = true
x1 = x2
} else if cmplx.IsNaN(x2) || numbers.EqualComplex(x1, x2) {
exactlyOneSolution = true
}
if exactlyOneSolution {
return fmt.Sprintf(oneSolution, formatComplex(x1))
}
return fmt.Sprintf(twoSolutions, formatComplex(x1), formatComplex(x2))
}
func mandelbrot(c complex128) uint16 {
var z complex128
for i := 0; i < Iterations; i++ {
z = z*z + c
if cmplx.IsNaN(z) {
return uint16(i)
}
}
return Iterations
}
/*
Solution of a triangular system of equations with multiple righthand sides. (L3)
Trsm(A, B, alpha, side=PLeft, uplo=PLower, transA=PNoTrans, diag=PNonUnit,
m=-1, n=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
Computes
B := alpha*A^{-1}*B if transA is PNoTrans and side = PLeft
B := alpha*B*A^{-1} if transA is PNoTrans and side = PRight
B := alpha*A^{-T}*B if transA is PTrans and side = PLeft
B := alpha*B*A^{-T} if transA is PTrans and side = PRight
B := alpha*A^{-H}*B if transA is PConjTrans and side = PLeft
B := alpha*B*A^{-H} if transA is PConjTrans and side = PRight
B is m by n and A is triangular. The code does not verify whether A is nonsingular.
ARGUMENTS
A float or complex matrix.
B float or complex matrix. Must have the same type as A.
alpha number (float or complex). Complex alpha is only
allowed if A is complex.
OPTIONS
side PLeft or PRight
uplo PLower or PUpper
transA PNoTrans or PTrans
diag PNonUnit or PUnit
m integer. If negative, the default value is used.
The default value is m = A.Rows or if side == PRight m = B.Rows
If the default value is used and side is PLeft, m must be equal to A.Cols.
n integer. If negative, the default value is used.
The default value is n = B.Cols or if side )= PRight n = A.Rows.
If the default value is used and side is PRight, n must be equal to A.Cols.
ldA nonnegative integer.
ldA >= max(1,m) of if side == PRight lda >= max(1,n).
If zero, the default value is used.
ldB nonnegative integer. ldB >= max(1,m).
If zero, the default value is used.
offsetA nonnegative integer
offsetB nonnegative integer
*/
func Trsm(A, B matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, ftrsm, A, B, nil, params)
if err != nil {
return
}
if !matrix.EqualTypes(A, B) {
return errors.New("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ba := B.FloatArray()
aval := alpha.Float()
if math.IsNaN(aval) {
return errors.New("alpha or beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
transA := linalg.ParamString(params.TransA)
side := linalg.ParamString(params.Side)
diag := linalg.ParamString(params.Diag)
dtrsm(side, uplo, transA, diag, ind.M, ind.N, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
Aa := A.ComplexArray()
Ba := B.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not a number")
}
uplo := linalg.ParamString(params.Uplo)
transA := linalg.ParamString(params.TransA)
side := linalg.ParamString(params.Side)
diag := linalg.ParamString(params.Diag)
ztrsm(side, uplo, transA, diag, ind.M, ind.N, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
default:
return errors.New("Unknown type, not implemented")
}
return
}
/*
General rank-1 update. (L2)
Ger(X, Y, A, alpha=1.0, m=A.Rows, n=A.Cols, incx=1,
incy=1, ldA=max(1,A.Rows), offsetx=0, offsety=0, offsetA=0)
COMPUTES
A := A + alpha*X*Y^H with A m*n, real or complex.
ARGUMENTS
X float or complex matrix.
Y float or complex matrix. Must have the same type as X.
A float or complex matrix. Must have the same type as X.
alpha number (float or complex singleton matrix).
OPTIONS
m integer. If negative, the default value is used.
n integer. If negative, the default value is used.
incx nonzero integer
incy nonzero integer
ldA nonnegative integer. ldA >= max(1,m).
If zero, the default value is used.
offsetx nonnegative integer
offsety nonnegative integer
offsetA nonnegative integer;
*/
func Ger(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
if !matrix.EqualTypes(A, X, Y) {
err = errors.New("Parameters not of same type")
return
}
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, fger, X, Y, A, params)
if err != nil {
return
}
if ind.N == 0 || ind.M == 0 {
return
}
switch X.(type) {
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Ya := Y.FloatArray()
Aa := A.FloatArray()
aval := alpha.Float()
if math.IsNaN(aval) {
return errors.New("alpha not a number")
}
dger(ind.M, ind.N, aval, Xa[ind.OffsetX:], ind.IncX,
Ya[ind.OffsetY:], ind.IncY, Aa[ind.OffsetA:], ind.LDa)
case *matrix.ComplexMatrix:
Xa := X.ComplexArray()
Ya := Y.ComplexArray()
Aa := A.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not a number")
}
zgerc(ind.M, ind.N, aval, Xa[ind.OffsetX:], ind.IncX,
Ya[ind.OffsetY:], ind.IncY, Aa[ind.OffsetA:], ind.LDa)
default:
return errors.New("Unknown type, not implemented")
}
return
}
/*
Symmetric rank-2 update.
her2(x, y, A, uplo='L', alpha=1.0, n=A.size[0], incx=1, incy=1,
ldA=max(1,A.size[0]), offsetx=0, offsety=0, offsetA=0)
PURPOSE
Computes A := A + alpha*(x*y^T + y*x^T) with A real symmetric or complex hermitian
matix of order n.
ARGUMENTS
x float or complex matrix
y float or complex matrix
A float or complex matrix
alpha float or complex singleton value
OPTIONS:
uplo 'L' or 'U'
n integer. If negative, the default value is used.
incx nonzero integer
incy nonzero integer
ldA nonnegative integer. ldA >= max(1,n).
If zero the default value is used.
offsetx nonnegative integer
offsety nonnegative integer
offsetA nonnegative integer;
*/
func Her2(X, Y, A matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, fsyr2, X, Y, A, params)
if err != nil {
return
}
if !matrix.EqualTypes(A, X, Y) {
return errors.New("Parameters not of same type")
}
switch X.(type) {
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Ya := X.FloatArray()
Aa := A.FloatArray()
aval := alpha.Float()
if math.IsNaN(aval) {
return errors.New("alpha not a number")
}
uplo := linalg.ParamString(params.Uplo)
dsyr2(uplo, ind.N, aval, Xa[ind.OffsetX:], ind.IncX,
Ya[ind.OffsetY:], ind.IncY,
Aa[ind.OffsetA:], ind.LDa)
case *matrix.ComplexMatrix:
Xa := X.ComplexArray()
Ya := X.ComplexArray()
Aa := A.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not a number")
}
uplo := linalg.ParamString(params.Uplo)
zher2(uplo, ind.N, aval, Xa[ind.OffsetX:], ind.IncX,
Ya[ind.OffsetY:], ind.IncY,
Aa[ind.OffsetA:], ind.LDa)
//zher(uplo, ind.N, aval, Xa[ind.OffsetX:], ind.IncX,
// Aa[ind.OffsetA:], ind.LDa)
default:
return errors.New("Unknown type, not implemented")
}
return
}
// Constant times a vector plus a vector (Y := alpha*X+Y).
//
// ARGUMENTS
// X float or complex matrix
// Y float or complex matrix. Must have the same type as X.
// alpha number (float or complex singleton matrix). Complex alpha is only
// allowed if x is complex.
//
// OPTIONS
// n integer. If n<0, the default value of n is used.
// The default value is equal to 1+(len(x)-offsetx-1)/incx
// or 0 if len(x) >= offsetx+1
// incx nonzero integer
// incy nonzero integer
// offsetx nonnegative integer
// offsety nonnegative integer;
//
func Axpy(X, Y matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
ind := linalg.GetIndexOpts(opts...)
err = check_level1_func(ind, faxpy, X, Y)
if err != nil {
return
}
if ind.Nx == 0 {
return
}
sameType := matrix.EqualTypes(X, Y)
if ! sameType {
err = errors.New("arrays not same type")
return
}
switch X.(type) {
case *matrix.ComplexMatrix:
Xa := X.ComplexArray()
Ya := Y.ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return errors.New("alpha not complex value")
}
zaxpy(ind.Nx, aval, Xa[ind.OffsetX:],
ind.IncX, Ya[ind.OffsetY:], ind.IncY)
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Ya := Y.FloatArray()
aval := alpha.Float()
if math.IsNaN(aval) {
return errors.New("alpha not float value")
}
daxpy(ind.Nx, aval, Xa[ind.OffsetX:],
ind.IncX, Ya[ind.OffsetY:], ind.IncY)
default:
err = errors.New("not implemented for parameter types", )
}
return
}