// See function Gemm.
func GemmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, 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
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
//diag := linalg.ParamString(params.Diag)
dgemm(transA, transB, ind.M, ind.N, ind.K, alpha,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, beta,
Ca[ind.OffsetC:], ind.LDc)
return
}
func GesvdFloat(A, S, U, Vt *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkGesvd(ind, pars, A, S, U, Vt)
if err != nil {
return err
}
if ind.M == 0 || ind.N == 0 {
return nil
}
Aa := A.FloatArray()
Sa := S.FloatArray()
var Ua, Va []float64
Ua = nil
Va = nil
if U != nil {
Ua = U.FloatArray()[ind.OffsetU:]
}
if Vt != nil {
Va = Vt.FloatArray()[ind.OffsetVt:]
}
info := dgesvd(linalg.ParamString(pars.Jobu), linalg.ParamString(pars.Jobvt),
ind.M, ind.N, Aa[ind.OffsetA:], ind.LDa, Sa[ind.OffsetS:], Ua, ind.LDu, Va, ind.LDvt)
if info != 0 {
return errors.New("GesvdFloat not implemented yet")
}
return nil
}
/*
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
}
// See function Symm.
func SymmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, 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
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
uplo := linalg.ParamString(params.Uplo)
side := linalg.ParamString(params.Side)
dsymm(side, uplo, ind.M, ind.N, alpha, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, beta, Ca[ind.OffsetC:], ind.LDc)
return
}
// See function Syrk2.
func Syr2kFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, 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, fsyr2k, A, B, C, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
//diag := linalg.ParamString(params.Diag)
dsyr2k(uplo, trans, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, beta, Ca[ind.OffsetC:], ind.LDc)
return
}
// See function Trsm.
func TrsmFloat(A, B *matrix.FloatMatrix, alpha float64, 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 ind.N == 0 || ind.M == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
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, alpha,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
return
}
/*
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
}
/*
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
}
/*
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
}
/*
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
}
func GbtrsFloat(A, B *matrix.FloatMatrix, ipiv []int32, KL int, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
ind.Kl = KL
err = checkGbtrs(ind, A, B, ipiv)
if err != nil {
return err
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
Aa := A.FloatArray()
Ba := B.FloatArray()
trans := linalg.ParamString(pars.Trans)
info := dgbtrs(trans, ind.N, ind.Kl, ind.Ku, ind.Nrhs,
Aa[ind.OffsetA:], ind.LDa, ipiv, Ba[ind.OffsetB:], ind.LDb)
if info != 0 {
return errors.New(fmt.Sprintf("Gbtrs: call error: %d", info))
}
return nil
}
// See function Gbmv.
func GbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, 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
}
Xa := X.FloatArray()
Ya := Y.FloatArray()
Aa := A.FloatArray()
if params.Trans == linalg.PNoTrans && ind.N == 0 {
dscal(ind.M, beta, Ya[ind.OffsetY:], ind.IncY)
} else if params.Trans == linalg.PTrans && ind.M == 0 {
dscal(ind.N, beta, Ya[ind.OffsetY:], ind.IncY)
} else {
trans := linalg.ParamString(params.Trans)
dgbmv(trans, ind.M, ind.N, ind.Kl, ind.Ku,
alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX,
beta, Ya[ind.OffsetY:], ind.IncY)
}
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
}
func SyevdFloat(A, W *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkSyevd(ind, A, W)
if err != nil {
return err
}
if ind.N == 0 {
return nil
}
jobz := linalg.ParamString(pars.Jobz)
uplo := linalg.ParamString(pars.Uplo)
Aa := A.FloatArray()
Wa := W.FloatArray()
info := dsyevd(jobz, uplo, ind.N, Aa[ind.OffsetA:], ind.LDa, Wa[ind.OffsetW:])
if info != 0 {
return errors.New(fmt.Sprintf("Syevd: call error %d", info))
}
return nil
}
/*
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
}
// See function Tbsv.
func TbsvFloat(A, X *matrix.FloatMatrix, 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, ftbsv, X, nil, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
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)
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
}
func PotrfFloat(A *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkPotrf(ind, A)
if ind.N == 0 {
return nil
}
Aa := A.FloatArray()
uplo := linalg.ParamString(pars.Uplo)
info := dpotrf(uplo, ind.N, Aa[ind.OffsetA:], ind.LDa)
if info != 0 {
return errors.New(fmt.Sprintf("Potrf: call error %d", info))
}
return nil
}
// See function Syr.
func SyrFloat(X, A *matrix.FloatMatrix, alpha float64, 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, fsyr, X, nil, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Xa := X.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
dsyr(uplo, ind.N, alpha, Xa[ind.OffsetX:], ind.IncX, Aa[ind.OffsetA:], ind.LDa)
return
}
// See function Sbmv.
func SbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, 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
}
Xa := X.FloatArray()
Ya := Y.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
dsbmv(uplo, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:],
ind.IncX, beta, Ya[ind.OffsetY:], ind.IncY)
return
}
func SyevrFloat(A, W, Z matrix.Matrix, abstol float64, vlimit []float64, ilimit []int, opts ...linalg.Option) error {
var vl, vu float64
var il, iu int
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
if ind.N < 0 {
ind.N = A.Rows()
if ind.N != A.Cols() {
return errors.New("Syevr: A not square")
}
}
// Check indexes
if ind.N == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.Rows())
}
if ind.LDa < max(1, A.Rows()) {
return errors.New("Syevr: lda")
}
if pars.Range == linalg.PRangeValue {
if vlimit == nil {
return errors.New("Syevr: vlimit is nil")
}
vl = vlimit[0]
vu = vlimit[1]
if vl >= vu {
return errors.New("Syevr: must be: vl < vu")
}
} else if pars.Range == linalg.PRangeInt {
if ilimit == nil {
return errors.New("Syevr: ilimit is nil")
}
il = ilimit[0]
iu = ilimit[1]
if il < 1 || il > iu || iu > ind.N {
return errors.New("Syevr: must be:1 <= il <= iu <= N")
}
}
if pars.Jobz == linalg.PJobValue {
if Z == nil {
return errors.New("Syevr: Z is nil")
}
if ind.LDz == 0 {
ind.LDz = max(1, Z.Rows())
}
if ind.LDz < max(1, ind.N) {
return errors.New("Syevr: ldz")
}
} else {
if ind.LDz == 0 {
ind.LDz = 1
}
if ind.LDz < 1 {
return errors.New("Syevr: ldz")
}
}
if ind.OffsetA < 0 {
return errors.New("Syevr: OffsetA")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*ind.LDa+ind.N {
return errors.New("Syevr: sizeA")
}
if ind.OffsetW < 0 {
return errors.New("Syevr: OffsetW")
}
sizeW := W.NumElements()
if sizeW < ind.OffsetW+ind.N {
return errors.New("Syevr: sizeW")
}
if pars.Jobz == linalg.PJobValue {
if ind.OffsetZ < 0 {
return errors.New("Syevr: OffsetW")
}
minZ := ind.OffsetZ + (ind.N-1)*ind.LDz + ind.N
if pars.Range == linalg.PRangeInt {
minZ = ind.OffsetZ + (iu-il)*ind.LDz + ind.N
}
if Z.NumElements() < minZ {
return errors.New("Syevr: sizeZ")
}
}
Aa := A.FloatArray()
Wa := W.FloatArray()
var Za []float64
if pars.Jobz == linalg.PJobValue {
Za = Z.FloatArray()
} else {
Za = nil
}
jobz := linalg.ParamString(pars.Jobz)
rnge := linalg.ParamString(pars.Range)
uplo := linalg.ParamString(pars.Uplo)
info := dsyevr(jobz, rnge, uplo, ind.N, Aa[ind.OffsetA:], ind.LDa,
vl, vu, il, iu, ind.M, Wa[ind.OffsetW:], Za, ind.LDz)
if info != 0 {
return errors.New(fmt.Sprintf("Syevr: call failed %d", info))
}
return nil
}
/*
Solution of a triangular set of equations with multiple righthand
sides.
Trtrs(A, B, uplo=PLower, trans=PNoTrans, diag=PNonUnit, n=A.Rows,
nrhs=B.Cols, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
PURPOSE
Solves set of equations
A*X = B, if trans is PNoTrans
A^T*X = B, if trans is PTrans
A^H*X = B, if trans is PConjTrans
B is n by nrhs and A is triangular of order n.
ARGUMENTS
A float or complex matrix
B float or complex matrix. Must have the same type as A.
OPTIONS
uplo PLower or PUpper
trans PNoTrans, PTrans, PConjTrans
diag PNonUnit, PUnit
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 Trtrs(A, B matrix.Matrix, ipiv []int32, 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.N != A.Cols() {
return errors.New("A not square")
}
}
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")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*ind.LDa+ind.N {
return errors.New("sizeA")
}
if ind.OffsetB < 0 {
return errors.New("offsetB")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*ind.LDb+ind.N {
return errors.New("sizeB")
}
info := -1
uplo := linalg.ParamString(pars.Uplo)
trans := linalg.ParamString(pars.Trans)
diag := linalg.ParamString(pars.Diag)
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ba := B.FloatArray()
info = dtrtrs(uplo, trans, diag, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
}
if info != 0 {
return errors.New("sytrf failed")
}
return nil
}
func Gtrrs(DL, D, DU, DU2, B matrix.Matrix, ipiv []int32, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
if ind.OffsetD < 0 {
return errors.New("offset D")
}
if ind.N < 0 {
ind.N = D.NumElements() - ind.OffsetD
}
if ind.N < 0 {
return errors.New("size D")
}
if ind.N == 0 {
return nil
}
if ind.OffsetDL < 0 {
return errors.New("offset DL")
}
sizeDL := DL.NumElements()
if sizeDL < ind.OffsetDL+ind.N-1 {
return errors.New("sizeDL")
}
if ind.OffsetDU < 0 {
return errors.New("offset DU")
}
sizeDU := DU.NumElements()
if sizeDU < ind.OffsetDU+ind.N-1 {
return errors.New("sizeDU")
}
sizeDU2 := DU2.NumElements()
if sizeDU2 < ind.N-2 {
return errors.New("sizeDU2")
}
if ind.Nrhs < 0 {
ind.Nrhs = B.Cols()
}
if ind.Nrhs == 0 {
return nil
}
if ind.LDb == 0 {
ind.LDb = max(1, B.Rows())
}
if ind.LDb < max(1, ind.N) {
return errors.New("ldB")
}
if ind.OffsetB < 0 {
return errors.New("offset B")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*ind.LDb+ind.N {
return errors.New("sizeB")
}
if len(ipiv) < ind.N {
return errors.New("size ipiv")
}
DLa := DL.FloatArray()
Da := D.FloatArray()
DUa := DU.FloatArray()
DU2a := DU2.FloatArray()
Ba := B.FloatArray()
trans := linalg.ParamString(pars.Trans)
info := dgttrs(trans, ind.N, ind.Nrhs,
DLa[ind.OffsetDL:], Da[ind.OffsetD:], DUa[ind.OffsetDU:], DU2a,
ipiv, Ba[ind.OffsetB:], ind.LDb)
if info != 0 {
return errors.New("dgttrs call error")
}
return nil
}
/*
Solves a real or complex set of linear equations with a banded
coefficient matrix, given the LU factorization computed by gbtrf()
or gbsv().
Gbtrs(A, B, ipiv, kl, trans=PNoTrans, n=A.Cols, ku=A.Rows-2*kl-1,
nrhs=B.Cols, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
PURPOSE
Solves linear equations
A*X = B, if trans is PNoTrans
A^T*X = B, if trans is PTrans
A^H*X = B, if trans is PConjTrans
On entry, A and ipiv contain the LU factorization of an n by n
band matrix A as computed by Getrf() or Gbsv(). 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.
ipiv int vector
kl nonnegative integer
OPTIONS
trans PNoTrans, PTrans or PConjTrans
n nonnegative integer. If negative, the default value is used.
ku nonnegative integer. If negative, the default value is used.
nrhs nonnegative integer. If negative, the default value is used.
ldA positive integer, ldA >= 2*kl+ku+1. 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 Gbtrs(A, B matrix.Matrix, ipiv []int32, KL int, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
//err = lapack_check(ind, fgbtrs, A, B, ipiv, pars)
ind.Kl = KL
if ind.Kl < 0 {
return errors.New("invalid kl")
}
if ind.N < 0 {
ind.N = A.Rows()
}
if ind.Nrhs < 0 {
ind.Nrhs = A.Cols()
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
if ind.Ku < 0 {
ind.Ku = A.Rows() - 2*ind.Kl - 1
}
if ind.Ku < 0 {
return errors.New("invalid ku")
}
if ind.LDa == 0 {
ind.LDa = max(1, A.Rows())
}
if ind.LDa < 2*ind.Kl+ind.Ku+1 {
return errors.New("lda")
}
if ind.OffsetA < 0 {
return errors.New("offsetA")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*ind.LDa+2*ind.Kl+ind.Ku+1 {
return errors.New("sizeA")
}
if ind.LDb == 0 {
ind.LDb = max(1, B.Rows())
}
if ind.OffsetB < 0 {
return errors.New("offsetB")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*ind.LDb+ind.N {
return errors.New("sizeB")
}
if ipiv != nil && len(ipiv) < ind.N {
return errors.New("size ipiv")
}
info := -1
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.FloatArray()
Ba := B.FloatArray()
trans := linalg.ParamString(pars.Trans)
info = dgbtrs(trans, ind.N, ind.Kl, ind.Ku, ind.Nrhs,
Aa[ind.OffsetA:], ind.LDa, ipiv, Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
return errors.New("Gbtrs for complex not yet implemented")
}
if info != 0 {
return errors.New("gbtrs call error")
}
return nil
}
/*
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
}