/*
Symmetric rank-2 update.
syr2(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 matrix of order n.
ARGUMENTS
x float matrix
y float matrix
A float matrix
alpha real number (int or float)
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 Syr2(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:
return errors.New("Not implemented yet for complx.Matrix")
default:
return errors.New("Unknown type, not implemented")
}
return
}
// Returns Y = X^H*Y for real or complex X, Y.
//
// ARGUMENTS
// X float or complex matrix
// Y float or complex matrix. Must have the same type as X.
//
// OPTIONS
// n integer. If n<0, the default value of n is used.
// The default value is equal to nx = 1+(len(x)-offsetx-1)/incx or 0 if
// len(x) > offsetx+1. If the default value is used, it must be equal to
// ny = 1+(len(y)-offsetx-1)/|incy| or 0 if len(y) > offsety+1
// incx nonzero integer [default=1]
// incy nonzero integer [default=1]
// offsetx nonnegative integer [default=0]
// offsety nonnegative integer [default=0]
//
func Dot(X, Y matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar) {
v = matrix.FScalar(math.NaN())
//cv = cmplx.NaN()
ind := linalg.GetIndexOpts(opts...)
err := check_level1_func(ind, fdot, X, Y)
if err != nil {
return
}
if ind.Nx == 0 {
return matrix.FScalar(0.0)
}
sameType := matrix.EqualTypes(X, Y)
if ! sameType {
err = errors.New("arrays not of same type")
return
}
switch X.(type) {
case *matrix.ComplexMatrix:
Xa := X.ComplexArray()
Ya := Y.ComplexArray()
v = matrix.CScalar(zdotc(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY))
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Ya := Y.FloatArray()
v = matrix.FScalar(ddot(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY))
//default:
// err = errors.New("not implemented for parameter types", )
}
return
}
// Copies a vector X to a vector Y (Y := X).
//
// ARGUMENTS
// X float or complex matrix
// Y float or complex matrix. Must have the same type as X.
//
// OPTIONS
// n integer. If n<0, the default value of n is used.
// The default value is given by 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 Copy(X, Y matrix.Matrix, opts ...linalg.Option) (err error) {
ind := linalg.GetIndexOpts(opts...)
err = check_level1_func(ind, fcopy, 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()
zcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Ya := Y.FloatArray()
dcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
default:
err = errors.New("not implemented for parameter types", )
}
return
}
/*
Solution of a triangular and banded set of equations.
Tbsv(A, X, uplo=PLower, trans=PNoTrans, diag=PNonDiag, n=A.Cols,
k=max(0,A.Rows-1), ldA=A.size[0], incx=1, offsetA=0, offsetx=0)
PURPOSE
X := A^{-1}*X, if trans is PNoTrans
X := A^{-T}*X, if trans is PTrans
X := A^{-H}*X, if trans is PConjTrans
A is banded triangular of order n and with bandwidth k.
ARGUMENTS
A float or complex m*k matrix.
X float or complex k*1 matrix. Must have the same type as A.
OPTIONS
uplo PLower or PUpper
trans PNoTrans, PTrans or PConjTrans
diag PNoNUnit or PUnit
n nonnegative integer. If negative, the default value is used.
k nonnegative integer. If negative, the default value is used.
ldA nonnegative integer. ldA >= 1+k.
If zero the default value is used.
incx nonzero integer
offsetA nonnegative integer
offsetx nonnegative integer;
*/
func Tbsv(A, X matrix.Matrix, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
if !matrix.EqualTypes(A, X) {
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, ftbsv, X, nil, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
switch X.(type) {
case *matrix.FloatMatrix:
Xa := X.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
diag := linalg.ParamString(params.Diag)
dtbsv(uplo, trans, diag, ind.N, ind.K,
Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX)
case *matrix.ComplexMatrix:
return errors.New("Not implemented yet for complx.Matrix")
default:
return errors.New("Unknown type, not implemented")
}
return
}
/*
Solves a real symmetric or complex Hermitian positive definite set
of linear equations, given the Cholesky factorization computed by
potrf() or posv().
Potrs(A, B, uplo=PLower, n=A.Rows, nrhs=B.Cols,
ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
PURPOSE
Solves
A*X = B
where A is n by n, real symmetric or complex Hermitian and positive definite,
and B is n by nrhs. On entry, A contains the Cholesky factor, as
returned by Posv() or Potrf(). On exit B is replaced by the solution X.
ARGUMENTS
A float or complex matrix
B float or complex matrix. Must have the same type as A.
OPTIONS
uplo PLower or PUpper
n nonnegative integer. If negative, the default value is used.
nrhs nonnegative integer. If negative, the default value is used.
ldA positive integer. ldA >= max(1,n). If zero, the default
value is used.
ldB positive integer. ldB >= max(1,n). If zero, the default
value is used.
offsetA nonnegative integer
offsetB nonnegative integer;
*/
func Potrs(A, B matrix.Matrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
if ind.N < 0 {
ind.N = A.Rows()
}
if ind.Nrhs < 0 {
ind.Nrhs = B.Cols()
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.Rows())
}
if ind.LDa < max(1, ind.N) {
return errors.New("lda")
}
if ind.LDb == 0 {
ind.LDb = max(1, B.Rows())
}
if ind.LDb < max(1, ind.N) {
return errors.New("ldb")
}
if ind.OffsetA < 0 {
return errors.New("offsetA")
}
if A.NumElements() < ind.OffsetA+(ind.N-1)*ind.LDa+ind.N {
return errors.New("sizeA")
}
if ind.OffsetB < 0 {
return errors.New("offsetB")
}
if B.NumElements() < ind.OffsetB+(ind.Nrhs-1)*ind.LDb+ind.N {
return errors.New("sizeB")
}
if !matrix.EqualTypes(A, B) {
return errors.New("types")
}
info := -1
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ba := B.FloatArray()
uplo := linalg.ParamString(pars.Uplo)
info = dpotrs(uplo, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
return errors.New("ComplexMatrx: not implemented yet")
}
if info != 0 {
return errors.New("Potrs failed")
}
return nil
}
/*
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
}
/*
Computes selected eigenvalues and eigenvectors of a real symmetric
matrix (RRR driver).
m = Syevr(A, W, jobz=PJobNo, range=PRangeAll, uplo=PLower,
vlimit=[]float{0.0, 0.0}, ilimit=[]int{1, 1}, Z=-1, n=A.Rows,
ldA=max(1,A.Rows), ldZ=-1, abstol=0.0, offsetA=0, offsetW=0, offsetZ=0)
PURPOSE
Computes selected eigenvalues/vectors of a real symmetric n by n
matrix A.
If range is PRangeAll, all eigenvalues are computed.
If range is PRangeV all eigenvalues in the interval (vlimit[0],vlimit[1]] are
computed.
If range is PRangeI, all eigenvalues ilimit[0] through ilimit[1] are computed
(sorted in ascending order with 1 <= ilimit[0] <= ilimit[1] <= n).
If jobz is PJobNo, only the eigenvalues are returned in W.
If jobz is PJobV, the eigenvectors are also returned in Z.
On exit, the content of A is destroyed.
Syevr is usually the fastest of the four eigenvalue routines.
ARGUMENTS
A float matrix
W float matrix of length at least n. On exit, contains
the computed eigenvalues in ascending order.
Z float matrix or nil. Only required when jobz = PJobV.
If range is PRangeAll or PRangeV, Z must have at least n columns.
If range is PRangeI, Z must have at least iu-il+1 columns.
On exit the first m columns of Z contain the computed
(normalized) eigenvectors.
abstol double. Absolute error tolerance for eigenvalues.
If nonpositive, the LAPACK default value is used.
vlmit []float or nil. Only required when range is PRangeV.
ilimit []int or nil. Only required when range is PRangeI.
OPTIONS
jobz PJobNo or PJobV
range PRangeAll, PRangeV or PRangeI
uplo PLower or PUpper
n integer. If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,n).
If zero, the default value is used.
ldZ nonnegative integer. ldZ >= 1 if jobz is 'N' and
ldZ >= max(1,n) if jobz is PJobV. The default value
is 1 if jobz is PJobNo and max(1,Z.Rows) if jobz =PJboV.
If zero, the default value is used.
offsetA nonnegative integer
offsetW nonnegative integer
offsetZ nonnegative integer
m the number of eigenvalues computed
*/
func Syevr(A, W, Z matrix.Matrix, abstol float64, vlimit []float64, ilimit []int, opts ...linalg.Option) error {
if !matrix.EqualTypes(A, W, Z) {
return errors.New("Syevr: not same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Am := A.(*matrix.FloatMatrix)
Wm := W.(*matrix.FloatMatrix)
Zm := Z.(*matrix.FloatMatrix)
return SyevrFloat(Am, Wm, Zm, abstol, vlimit, ilimit, opts...)
}
return errors.New("Syevr: unknown types")
}
/*
Eigenvalue decomposition of a real symmetric matrix
(divide-and-conquer driver).
Syevd(A, W, jobz=PJboNo, uplo=PLower, n=A.Rows,
ldA = max(1,A.Rows), offsetA=0, offsetW=0)
PURPOSE
Returns eigenvalues/vectors of a real symmetric nxn matrix A.
On exit, W contains the eigenvalues in ascending order.
If jobz is PJobV, the (normalized) eigenvectors are also computed
and returned in A. If jobz is PJobNo, only the eigenvalues are
computed, and the content of A is destroyed.
ARGUMENTS
A float matrix
W float matrix of length at least n. On exit, contains
the computed eigenvalues in ascending order.
OPTIONS
jobz PJobNo or PJobV
uplo PLower or PUpper
n integer. If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,n). If zero, the
default value is used.
offsetA nonnegative integer
offsetB nonnegative integer;
*/
func Syevd(A, W matrix.Matrix, opts ...linalg.Option) error {
if !matrix.EqualTypes(A, W) {
return errors.New("Syevd: arguments not same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Am := A.(*matrix.FloatMatrix)
Wm := W.(*matrix.FloatMatrix)
return SyevdFloat(Am, Wm, opts...)
case *matrix.ComplexMatrix:
return errors.New("Not a complex function")
}
return errors.New("Syevd: unknown types")
}
/*
Rank-k update of symmetric matrix. (L3)
Herk(A, C, alpha, beta, uplo=PLower, trans=PNoTrans, n=-1,
k=-1, ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0)
Computes
C := alpha*A*A^T + beta*C, if trans is PNoTrans
C := alpha*A^T*A + beta*C, if trans is PTrans
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 matrix.
C float or complex 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 or PTrans
n integer. If negative, the default value is used.
The default value is n = A.Rows or 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 ldA >= max(1,k).
If zero, the default value is used.
ldC nonnegative integer. ldC >= max(1,n).
If zero, the default value is used.
offsetA nonnegative integer
offsetC nonnegative integer;
*/
func Herk(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 real or complex number")
}
bval := beta.Float()
if math.IsNaN(bval) {
return errors.New("beta not a real number")
}
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
zherk(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
}
/*
Matrix-vector product with a real symmetric or complex hermitian band matrix.
Computes with A real symmetric and banded of order n and with bandwidth k.
Y := alpha*A*X + beta*Y
ARGUMENTS
A float or complex n*n matrix
X float or complex n*1 matrix
Y float or complex n*1 matrix
alpha number (float or complex singleton matrix)
beta number (float or complex singleton matrix)
OPTIONS
uplo PLower or PUpper
n integer. If negative, the default value is used.
k integer. If negative, the default value is used.
The default value is k = max(0,A.Rows()-1).
ldA nonnegative integer. ldA >= k+1.
If zero, the default vaule is used.
incx nonzero integer
incy nonzero integer
offsetA nonnegative integer
offsetx nonnegative integer
offsety nonnegative integer
*/
func Hbmv(A, X, Y matrix.Matrix, alpha, beta 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, fsbmv, X, Y, A, params)
if err != nil {
return
}
if ind.N == 0 {
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 := Y.FloatArray()
Aa := A.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)
dsbmv(uplo, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa,
Xa[ind.OffsetX:], ind.IncX, bval, Ya[ind.OffsetY:], ind.IncY)
case *matrix.ComplexMatrix:
Xa := X.ComplexArray()
Ya := Y.ComplexArray()
Aa := A.ComplexArray()
aval := alpha.Complex()
bval := beta.Complex()
uplo := linalg.ParamString(params.Uplo)
zhbmv(uplo, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa,
Xa[ind.OffsetX:], ind.IncX, bval, Ya[ind.OffsetY:], ind.IncY)
//zhbmv(uplo, ind.N, aval, Aa[ind.OffsetA:], ind.LDa,
// Xa[ind.OffsetX:], ind.IncX,
// bval, Ya[ind.OffsetY:], ind.IncY)
default:
return errors.New("Unknown type, not implemented")
}
return
}
/*
Solves a real or complex set of linear equations with a banded
coefficient matrix.
Gbsv(A, B, ipiv, kl, ku=-1, n=A.Cols, nrhs=B.Cols,
ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
PURPOSE
Solves A*X = B
A an n by n real or complex band matrix with kl subdiagonals and
ku superdiagonals.
If ipiv is provided, then on entry the kl+ku+1 diagonals of the
matrix are stored in rows kl+1 to 2*kl+ku+1 of A, in the BLAS
format for general band matrices. On exit, A and ipiv contain the
details of the factorization. If ipiv is not provided, then on
entry the diagonals of the matrix are stored in rows 1 to kl+ku+1
of A, and Gbsv() does not return the factorization and does not
modify A. On exit B is replaced with solution X.
ARGUMENTS.
A float or complex banded matrix
B float or complex matrix. Must have the same type as A.
kl nonnegative integer
ipiv int array of length at least n
OPTIONS
ku nonnegative integer. If negative, the default value is
used. The default value is A.Rows-kl-1 if ipiv is
not provided, and A.Rows-2*kl-1 otherwise.
n nonnegative integer. If negative, the default value is used.
nrhs nonnegative integer. If negative, the default value is used.
ldA positive integer. ldA >= kl+ku+1 if ipiv is not provided
and ldA >= 2*kl+ku+1 if ipiv is provided. If zero, the
default value is used.
ldB positive integer. ldB >= max(1,n). If zero, the default
default value is used.
offsetA nonnegative integer
offsetB nonnegative integer;
*/
func Gbsv(A, B matrix.Matrix, ipiv []int32, kl int, opts ...linalg.Option) error {
if !matrix.EqualTypes(A, B) {
return errors.New("Gbsv: not same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Am := A.(*matrix.FloatMatrix)
Bm := B.(*matrix.FloatMatrix)
return GbsvFloat(Am, Bm, ipiv, kl, opts...)
case *matrix.ComplexMatrix:
Am := A.(*matrix.ComplexMatrix)
Bm := B.(*matrix.ComplexMatrix)
return GbsvComplex(Am, Bm, ipiv, kl, opts...)
}
return errors.New("Gbsv: unknown types types!")
}
/*
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
}
/*
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
}
/*
Matrix-vector product with a general banded matrix. (L2)
Computes
Y := alpha*A*X + beta*Y, if trans = PNoTrans
Y := alpha*A^T*X + beta*Y, if trans = PTrans
Y := beta*y, if n=0, m>0, and trans = PNoTrans
Y := beta*y, if n>0, m=0, and trans = PTrans
The matrix A is m by n with upper bandwidth ku and lower bandwidth kl.
Returns immediately if n=0 and trans is 'Trans', or if m=0 and trans is 'N'.
ARGUMENTS
X float n*1 matrix.
Y float m*1 matrix
A float m*n matrix.
alpha number (float).
beta number (float).
OPTIONS
trans NoTrans or Trans
m nonnegative integer, default A.Rows()
kl nonnegative integer
n nonnegative integer. If negative, the default value is used.
ku nonnegative integer. If negative, the default value is used.
ldA positive integer. ldA >= kl+ku+1. If zero, the default value is used.
incx nonzero integer, default =1
incy nonzero integer, default =1
offsetA nonnegative integer, default =0
offsetx nonnegative integer, default =0
offsety nonnegative integer, default =0
*/
func Gbmv(A, X, Y matrix.Matrix, alpha, beta 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, fgbmv, X, Y, A, params)
if err != nil {
return
}
if ind.M == 0 && ind.N == 0 {
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 := Y.FloatArray()
Aa := A.FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return errors.New("alpha or beta not a number")
}
if params.Trans == linalg.PNoTrans && ind.N == 0 {
dscal(ind.M, bval, Ya[ind.OffsetY:], ind.IncY)
} else if params.Trans == linalg.PTrans && ind.M == 0 {
dscal(ind.N, bval, Ya[ind.OffsetY:], ind.IncY)
} else {
trans := linalg.ParamString(params.Trans)
dgbmv(trans, ind.M, ind.N, ind.Kl, ind.Ku,
aval, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX,
bval, Ya[ind.OffsetY:], ind.IncY)
}
case *matrix.ComplexMatrix:
return errors.New("Not implemented yet for complx.Matrix")
default:
return errors.New("Unknown type, not implemented")
}
return
}
/*
QR factorization.
Geqrf(A, tau, m=A.Rows, n=A.Cols, ldA=max(1,A.Rows), offsetA=0)
PURPOSE
QR factorization of an m by n real or complex matrix A:
A = Q*R = [Q1 Q2] * [R1; 0] if m >= n
A = Q*R = Q * [R1 R2] if m <= n,
where Q is m by m and orthogonal/unitary and R is m by n with R1
upper triangular. On exit, R is stored in the upper triangular
part of A. Q is stored as a product of k=min(m,n) elementary
reflectors. The parameters of the reflectors are stored in the
first k entries of tau and in the lower triangular part of the
first k columns of A.
ARGUMENTS
A float or complex matrix
tau float or complex matrix of length at least min(m,n). Must
have the same type as A.
m integer. If negative, the default value is used.
n integer. If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,m). If zero, the
default value is used.
offsetA nonnegative integer
*/
func Geqrf(A, tau matrix.Matrix, opts ...linalg.Option) error {
ind := linalg.GetIndexOpts(opts...)
if ind.N < 0 {
ind.N = A.Rows()
}
if ind.M < 0 {
ind.M = A.Cols()
}
if ind.N == 0 || ind.M == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.Rows())
}
if ind.LDa < max(1, ind.M) {
return errors.New("lda")
}
if ind.OffsetA < 0 {
return errors.New("offsetA")
}
if A.NumElements() < ind.OffsetA+ind.K*ind.LDa {
return errors.New("sizeA")
}
if tau.NumElements() < min(ind.M, ind.N) {
return errors.New("sizeTau")
}
if !matrix.EqualTypes(A, tau) {
return errors.New("not same type")
}
info := -1
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
taua := tau.FloatArray()
info = dgeqrf(ind.M, ind.N, Aa[ind.OffsetA:], ind.LDa, taua)
case *matrix.ComplexMatrix:
return errors.New("ComplexMatrx: not implemented yet")
}
if info != 0 {
return errors.New("Geqrf failed")
}
return nil
}
/*
Singular value decomposition of a real or complex matrix.
Gesvd(A, S, jobu=PJobNo, jobvt=PJobNo, U=nil, Vt=nil, m=A.Rows,
n=A.Cols, ldA=max(1,A.Rows), ldU=-1, ldVt=-1,
offsetA=0, offsetS=0, offsetU=0, offsetVt=0)
PURPOSE
Computes singular values and, optionally, singular vectors of a
real or complex m by n matrix A.
The argument jobu controls how many left singular vectors are
computed:
PJobNo : no left singular vectors are computed.
PJobAll: all left singular vectors are computed and returned as
columns of U.
PJobS : the first min(m,n) left singular vectors are computed and
returned as columns of U.
PJobO : the first min(m,n) left singular vectors are computed and
returned as columns of A.
The argument jobvt controls how many right singular vectors are
computed:
PJobNo : no right singular vectors are computed.
PJobAll: all right singular vectors are computed and returned as
rows of Vt.
PJobS : the first min(m,n) right singular vectors are computed and
returned as rows of Vt.
PJobO : the first min(m,n) right singular vectors are computed and
returned as rows of A.
Note that the (conjugate) transposes of the right singular
vectors are returned in Vt or A.
On exit (in all cases), the contents of A are destroyed.
ARGUMENTS
A float or complex matrix
S float matrix of length at least min(m,n). On exit,
contains the computed singular values in descending order.
jobu PJobNo, PJobAll, PJobS or PJobO
jobvt PJobNo, PJobAll, PJobS or PJobO
U float or complex matrix. Must have the same type as A.
Not referenced if jobu is PJobNo or PJobO. If jobu is PJobAll,
a matrix with at least m columns. If jobu is PJobS, a
matrix with at least min(m,n) columns.
On exit (with jobu PJobAll or PJobS), the columns of U
contain the computed left singular vectors.
Vt float or complex matrix. Must have the same type as A.
Not referenced if jobvt is PJobNo or PJobO. If jobvt is
PJobAll or PJobS, a matrix with at least n columns.
On exit (with jobvt PJobAll or PJobS), the rows of Vt
contain the computed right singular vectors, or, in
the complex case, their complex conjugates.
m integer. If negative, the default value is used.
n integer. If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,m).
If zero, the default value is used.
ldU nonnegative integer.
ldU >= 1 if jobu is PJobNo or PJobO
ldU >= max(1,m) if jobu is PJobAll or PJobS.
The default value is max(1,U.Rows) if jobu is PJobAll
or PJobS, and 1 otherwise.
If zero, the default value is used.
ldVt nonnegative integer.
ldVt >= 1 if jobvt is PJobNo or PJobO.
ldVt >= max(1,n) if jobvt is PJobAll.
ldVt >= max(1,min(m,n)) if ldVt is PJobS.
The default value is max(1,Vt.Rows) if jobvt is PJobAll
or PJobS, and 1 otherwise.
If zero, the default value is used.
offsetA nonnegative integer
offsetS nonnegative integer
offsetU nonnegative integer
offsetVt nonnegative integer
*/
func Gesvd(A, S, U, Vt matrix.Matrix, opts ...linalg.Option) error {
if !matrix.EqualTypes(A, S, U, Vt) {
return errors.New("Gesvd: arguments not same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Am := A.(*matrix.FloatMatrix)
Sm := S.(*matrix.FloatMatrix)
Um := U.(*matrix.FloatMatrix)
Vm := Vt.(*matrix.FloatMatrix)
return GesvdFloat(Am, Sm, Um, Vm, opts...)
case *matrix.ComplexMatrix:
Am := A.(*matrix.ComplexMatrix)
Sm := S.(*matrix.ComplexMatrix)
Um := U.(*matrix.ComplexMatrix)
Vm := Vt.(*matrix.ComplexMatrix)
return GesvdComplex(Am, Sm, Um, Vm, opts...)
}
return errors.New("Gesvd: unknown parameter types")
}
// 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
}
/*
Product with a real orthogonal matrix.
Ormqr(A, tau, C, side='L', trans='N', m=C.Rows, n=C.Cols,
k=len(tau), ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetC=0)
PURPOSE
Computes
C := Q*C if side = PLeft and trans = PNoTrans
C := Q^T*C if side = PLeft and trans = PTrans
C := C*Q if side = PRight and trans = PNoTrans
C := C*Q^T if side = PRight and trans = PTrans
C is m by n and Q is a square orthogonal matrix computed by geqrf.
Q is defined as a product of k elementary reflectors, stored as
the first k columns of A and the first k entries of tau.
ARGUMENTS
A float matrix
tau float matrix of length at least k
C float matrix
OPTIONS
side PLeft or PRight
trans PNoTrans or PTrans
m integer. If negative, the default value is used.
n integer. If negative, the default value is used.
k integer. k <= m if side = PRight and k <= n if side = PLeft.
If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,m) if side = PLeft
and ldA >= max(1,n) if side = PRight. 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
*/
func Ormqf(A, tau, C matrix.Matrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
if ind.N < 0 {
ind.N = C.Cols()
}
if ind.M < 0 {
ind.M = C.Rows()
}
if ind.K < 0 {
ind.K = tau.NumElements()
}
if ind.N == 0 || ind.M == 0 || ind.K == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.Rows())
}
if ind.LDc == 0 {
ind.LDc = max(1, C.Rows())
}
switch pars.Side {
case linalg.PLeft:
if ind.K > ind.M {
errors.New("K")
}
if ind.LDa < max(1, ind.M) {
return errors.New("lda")
}
case linalg.PRight:
if ind.K > ind.N {
errors.New("K")
}
if ind.LDa < max(1, ind.N) {
return errors.New("lda")
}
}
if ind.OffsetA < 0 {
return errors.New("offsetA")
}
if A.NumElements() < ind.OffsetA+ind.K*ind.LDa {
return errors.New("sizeA")
}
if ind.OffsetC < 0 {
return errors.New("offsetC")
}
if C.NumElements() < ind.OffsetC+(ind.N-1)*ind.LDa+ind.M {
return errors.New("sizeC")
}
if tau.NumElements() < ind.K {
return errors.New("sizeTau")
}
if !matrix.EqualTypes(A, C, tau) {
return errors.New("not same type")
}
info := -1
side := linalg.ParamString(pars.Side)
trans := linalg.ParamString(pars.Trans)
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ca := C.FloatArray()
taua := tau.FloatArray()
info = dormqr(side, trans, ind.M, ind.N, ind.K, Aa[ind.OffsetA:], ind.LDa,
taua, Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
return errors.New("ComplexMatrx: not implemented yet")
}
if info != 0 {
return errors.New("Ormqr failed")
}
return nil
}