// Scales a vector by a constant (X := alpha*X). // // ARGUMENTS // X float or complex matrix // 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)-offset-1)/inc or 0 // if len(x) > offset+1. // inc positive integer, default = 1 // offset nonnegative integer, default = 0 // func Scal(X matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) { ind := linalg.GetIndexOpts(opts...) err = check_level1_func(ind, fscal, X, nil) if err != nil { return } if ind.Nx == 0 { return } switch X.(type) { case *matrix.ComplexMatrix: Xa := X.ComplexArray() cval := alpha.Complex() zscal(ind.Nx, cval, Xa[ind.OffsetX:], ind.IncX) case *matrix.FloatMatrix: Xa := X.FloatArray() rval := alpha.Float() if math.IsNaN(rval) { return errors.New("alpha not float value") } dscal(ind.Nx, rval, Xa[ind.OffsetX:], ind.IncX) 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 }
// 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 }
/* 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 }
/* 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 }
/* 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 }
// Returns ||Re x||_1 + ||Im x||_1. // // ARGUMENTS // X float or complex matrix // // OPTIONS // n integer. If n<0, the default value of n is used. // The default value is equal to n = 1+(len(x)-offset-1)/inc or 0 if // len(x) > offset+1 // inc positive integer // offset nonnegative integer // func Asum(X matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar) { v = matrix.FScalar(math.NaN()) ind := linalg.GetIndexOpts(opts...) err := check_level1_func(ind, fasum, X, nil) if err != nil { return } if ind.Nx == 0 { return } switch X.(type) { case *matrix.ComplexMatrix: Xa := X.ComplexArray() v = matrix.FScalar(dzasum(ind.Nx, Xa[ind.OffsetX:], ind.IncX)) case *matrix.FloatMatrix: Xa := X.FloatArray() v = matrix.FScalar(dasum(ind.Nx, Xa[ind.OffsetX:], ind.IncX)) //default: // err = errors.New("not implemented for parameter types", ) } 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 }
/* 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 }
/* 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 }