--- /dev/null
+// Copyright ©2015 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package cblas128
+
+import (
+ "gonum.org/v1/gonum/blas"
+ "gonum.org/v1/gonum/blas/gonum"
+)
+
+var cblas128 blas.Complex128 = gonum.Implementation{}
+
+// Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls.
+// The default implementation is cgo.Implementation.
+func Use(b blas.Complex128) {
+ cblas128 = b
+}
+
+// Implementation returns the current BLAS complex128 implementation.
+//
+// Implementation allows direct calls to the current the BLAS complex128 implementation
+// giving finer control of parameters.
+func Implementation() blas.Complex128 {
+ return cblas128
+}
+
+// Vector represents a vector with an associated element increment.
+type Vector struct {
+ Inc int
+ Data []complex128
+}
+
+// General represents a matrix using the conventional storage scheme.
+type General struct {
+ Rows, Cols int
+ Stride int
+ Data []complex128
+}
+
+// Band represents a band matrix using the band storage scheme.
+type Band struct {
+ Rows, Cols int
+ KL, KU int
+ Stride int
+ Data []complex128
+}
+
+// Triangular represents a triangular matrix using the conventional storage scheme.
+type Triangular struct {
+ N int
+ Stride int
+ Data []complex128
+ Uplo blas.Uplo
+ Diag blas.Diag
+}
+
+// TriangularBand represents a triangular matrix using the band storage scheme.
+type TriangularBand struct {
+ N, K int
+ Stride int
+ Data []complex128
+ Uplo blas.Uplo
+ Diag blas.Diag
+}
+
+// TriangularPacked represents a triangular matrix using the packed storage scheme.
+type TriangularPacked struct {
+ N int
+ Data []complex128
+ Uplo blas.Uplo
+ Diag blas.Diag
+}
+
+// Symmetric represents a symmetric matrix using the conventional storage scheme.
+type Symmetric struct {
+ N int
+ Stride int
+ Data []complex128
+ Uplo blas.Uplo
+}
+
+// SymmetricBand represents a symmetric matrix using the band storage scheme.
+type SymmetricBand struct {
+ N, K int
+ Stride int
+ Data []complex128
+ Uplo blas.Uplo
+}
+
+// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
+type SymmetricPacked struct {
+ N int
+ Data []complex128
+ Uplo blas.Uplo
+}
+
+// Hermitian represents an Hermitian matrix using the conventional storage scheme.
+type Hermitian Symmetric
+
+// HermitianBand represents an Hermitian matrix using the band storage scheme.
+type HermitianBand SymmetricBand
+
+// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
+type HermitianPacked SymmetricPacked
+
+// Level 1
+
+const negInc = "cblas128: negative vector increment"
+
+// Dotu computes the dot product of the two vectors without
+// complex conjugation:
+// x^T * y.
+func Dotu(n int, x, y Vector) complex128 {
+ return cblas128.Zdotu(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Dotc computes the dot product of the two vectors with
+// complex conjugation:
+// x^H * y.
+func Dotc(n int, x, y Vector) complex128 {
+ return cblas128.Zdotc(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Nrm2 computes the Euclidean norm of the vector x:
+// sqrt(\sum_i x[i] * x[i]).
+//
+// Nrm2 will panic if the vector increment is negative.
+func Nrm2(n int, x Vector) float64 {
+ if x.Inc < 0 {
+ panic(negInc)
+ }
+ return cblas128.Dznrm2(n, x.Data, x.Inc)
+}
+
+// Asum computes the sum of magnitudes of the real and imaginary parts of
+// elements of the vector x:
+// \sum_i (|Re x[i]| + |Im x[i]|).
+//
+// Asum will panic if the vector increment is negative.
+func Asum(n int, x Vector) float64 {
+ if x.Inc < 0 {
+ panic(negInc)
+ }
+ return cblas128.Dzasum(n, x.Data, x.Inc)
+}
+
+// Iamax returns the index of an element of x with the largest sum of
+// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
+// If there are multiple such indices, the earliest is returned.
+//
+// Iamax returns -1 if n == 0.
+//
+// Iamax will panic if the vector increment is negative.
+func Iamax(n int, x Vector) int {
+ if x.Inc < 0 {
+ panic(negInc)
+ }
+ return cblas128.Izamax(n, x.Data, x.Inc)
+}
+
+// Swap exchanges the elements of two vectors:
+// x[i], y[i] = y[i], x[i] for all i.
+func Swap(n int, x, y Vector) {
+ cblas128.Zswap(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Copy copies the elements of x into the elements of y:
+// y[i] = x[i] for all i.
+func Copy(n int, x, y Vector) {
+ cblas128.Zcopy(n, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Axpy computes
+// y = alpha * x + y,
+// where x and y are vectors, and alpha is a scalar.
+func Axpy(n int, alpha complex128, x, y Vector) {
+ cblas128.Zaxpy(n, alpha, x.Data, x.Inc, y.Data, y.Inc)
+}
+
+// Scal computes
+// x = alpha * x,
+// where x is a vector, and alpha is a scalar.
+//
+// Scal will panic if the vector increment is negative.
+func Scal(n int, alpha complex128, x Vector) {
+ if x.Inc < 0 {
+ panic(negInc)
+ }
+ cblas128.Zscal(n, alpha, x.Data, x.Inc)
+}
+
+// Dscal computes
+// x = alpha * x,
+// where x is a vector, and alpha is a real scalar.
+//
+// Dscal will panic if the vector increment is negative.
+func Dscal(n int, alpha float64, x Vector) {
+ if x.Inc < 0 {
+ panic(negInc)
+ }
+ cblas128.Zdscal(n, alpha, x.Data, x.Inc)
+}
+
+// Level 2
+
+// Gemv computes
+// y = alpha * A * x + beta * y, if t == blas.NoTrans,
+// y = alpha * A^T * x + beta * y, if t == blas.Trans,
+// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gemv(t blas.Transpose, alpha complex128, a General, x Vector, beta complex128, y Vector) {
+ cblas128.Zgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Gbmv computes
+// y = alpha * A * x + beta * y, if t == blas.NoTrans,
+// y = alpha * A^T * x + beta * y, if t == blas.Trans,
+// y = alpha * A^H * x + beta * y, if t == blas.ConjTrans,
+// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
+// scalars.
+func Gbmv(t blas.Transpose, alpha complex128, a Band, x Vector, beta complex128, y Vector) {
+ cblas128.Zgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Trmv computes
+// x = A * x, if t == blas.NoTrans,
+// x = A^T * x, if t == blas.Trans,
+// x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix, and x is a vector.
+func Trmv(t blas.Transpose, a Triangular, x Vector) {
+ cblas128.Ztrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbmv computes
+// x = A * x, if t == blas.NoTrans,
+// x = A^T * x, if t == blas.Trans,
+// x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
+ cblas128.Ztbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpmv computes
+// x = A * x, if t == blas.NoTrans,
+// x = A^T * x, if t == blas.Trans,
+// x = A^H * x, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format, and x is a vector.
+func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
+ cblas128.Ztpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Trsv solves
+// A * x = b, if t == blas.NoTrans,
+// A^T * x = b, if t == blas.Trans,
+// A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Trsv(t blas.Transpose, a Triangular, x Vector) {
+ cblas128.Ztrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tbsv solves
+// A * x = b, if t == blas.NoTrans,
+// A^T * x = b, if t == blas.Trans,
+// A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular band matrix, and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
+ cblas128.Ztbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
+}
+
+// Tpsv solves
+// A * x = b, if t == blas.NoTrans,
+// A^T * x = b, if t == blas.Trans,
+// A^H * x = b, if t == blas.ConjTrans,
+// where A is an n×n triangular matrix in packed format and x is a vector.
+//
+// At entry to the function, x contains the values of b, and the result is
+// stored in-place into x.
+//
+// No test for singularity or near-singularity is included in this
+// routine. Such tests must be performed before calling this routine.
+func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
+ cblas128.Ztpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
+}
+
+// Hemv computes
+// y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
+// beta are scalars.
+func Hemv(alpha complex128, a Hermitian, x Vector, beta complex128, y Vector) {
+ cblas128.Zhemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hbmv performs
+// y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
+// and beta are scalars.
+func Hbmv(alpha complex128, a HermitianBand, x Vector, beta complex128, y Vector) {
+ cblas128.Zhbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Hpmv performs
+// y = alpha * A * x + beta * y,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha and beta are scalars.
+func Hpmv(alpha complex128, a HermitianPacked, x Vector, beta complex128, y Vector) {
+ cblas128.Zhpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
+}
+
+// Geru performs a rank-1 update
+// A += alpha * x * y^T,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Geru(alpha complex128, x, y Vector, a General) {
+ cblas128.Zgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Gerc performs a rank-1 update
+// A += alpha * x * y^H,
+// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
+func Gerc(alpha complex128, x, y Vector, a General) {
+ cblas128.Zgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Her performs a rank-1 update
+// A += alpha * x * y^T,
+// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her(alpha float64, x Vector, a Hermitian) {
+ cblas128.Zher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
+}
+
+// Hpr performs a rank-1 update
+// A += alpha * x * x^H,
+// where A is an n×n Hermitian matrix in packed format, x is a vector, and
+// alpha is a scalar.
+func Hpr(alpha float64, x Vector, a HermitianPacked) {
+ cblas128.Zhpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
+}
+
+// Her2 performs a rank-2 update
+// A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
+func Her2(alpha complex128, x, y Vector, a Hermitian) {
+ cblas128.Zher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
+}
+
+// Hpr2 performs a rank-2 update
+// A += alpha * x * y^H + conj(alpha) * y * x^H,
+// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
+// and alpha is a scalar.
+func Hpr2(alpha complex128, x, y Vector, a HermitianPacked) {
+ cblas128.Zhpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
+}
+
+// Level 3
+
+// Gemm computes
+// C = alpha * A * B + beta * C,
+// where A, B, and C are dense matrices, and alpha and beta are scalars.
+// tA and tB specify whether A or B are transposed or conjugated.
+func Gemm(tA, tB blas.Transpose, alpha complex128, a, b General, beta complex128, c General) {
+ var m, n, k int
+ if tA == blas.NoTrans {
+ m, k = a.Rows, a.Cols
+ } else {
+ m, k = a.Cols, a.Rows
+ }
+ if tB == blas.NoTrans {
+ n = b.Cols
+ } else {
+ n = b.Rows
+ }
+ cblas128.Zgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Symm performs
+// C = alpha * A * B + beta * C, if s == blas.Left,
+// C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Symm(s blas.Side, alpha complex128, a Symmetric, b General, beta complex128, c General) {
+ var m, n int
+ if s == blas.Left {
+ m, n = a.N, b.Cols
+ } else {
+ m, n = b.Rows, a.N
+ }
+ cblas128.Zsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Syrk performs a symmetric rank-k update
+// C = alpha * A * A^T + beta * C, if t == blas.NoTrans,
+// C = alpha * A^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Syrk(t blas.Transpose, alpha complex128, a General, beta complex128, c Symmetric) {
+ var n, k int
+ if t == blas.NoTrans {
+ n, k = a.Rows, a.Cols
+ } else {
+ n, k = a.Cols, a.Rows
+ }
+ cblas128.Zsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Syr2k performs a symmetric rank-2k update
+// C = alpha * A * B^T + alpha * B * A^T + beta * C, if t == blas.NoTrans,
+// C = alpha * A^T * B + alpha * B^T * A + beta * C, if t == blas.Trans,
+// where C is an n×n symmetric matrix, A and B are n×k matrices if
+// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
+func Syr2k(t blas.Transpose, alpha complex128, a, b General, beta complex128, c Symmetric) {
+ var n, k int
+ if t == blas.NoTrans {
+ n, k = a.Rows, a.Cols
+ } else {
+ n, k = a.Cols, a.Rows
+ }
+ cblas128.Zsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Trmm performs
+// B = alpha * A * B, if tA == blas.NoTrans and s == blas.Left,
+// B = alpha * A^T * B, if tA == blas.Trans and s == blas.Left,
+// B = alpha * A^H * B, if tA == blas.ConjTrans and s == blas.Left,
+// B = alpha * B * A, if tA == blas.NoTrans and s == blas.Right,
+// B = alpha * B * A^T, if tA == blas.Trans and s == blas.Right,
+// B = alpha * B * A^H, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
+// a scalar.
+func Trmm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
+ cblas128.Ztrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Trsm solves
+// A * X = alpha * B, if tA == blas.NoTrans and s == blas.Left,
+// A^T * X = alpha * B, if tA == blas.Trans and s == blas.Left,
+// A^H * X = alpha * B, if tA == blas.ConjTrans and s == blas.Left,
+// X * A = alpha * B, if tA == blas.NoTrans and s == blas.Right,
+// X * A^T = alpha * B, if tA == blas.Trans and s == blas.Right,
+// X * A^H = alpha * B, if tA == blas.ConjTrans and s == blas.Right,
+// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
+// alpha is a scalar.
+//
+// At entry to the function, b contains the values of B, and the result is
+// stored in-place into b.
+//
+// No check is made that A is invertible.
+func Trsm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
+ cblas128.Ztrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
+}
+
+// Hemm performs
+// C = alpha * A * B + beta * C, if s == blas.Left,
+// C = alpha * B * A + beta * C, if s == blas.Right,
+// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
+// alpha and beta are scalars.
+func Hemm(s blas.Side, alpha complex128, a Hermitian, b General, beta complex128, c General) {
+ var m, n int
+ if s == blas.Left {
+ m, n = a.N, b.Cols
+ } else {
+ m, n = b.Rows, a.N
+ }
+ cblas128.Zhemm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
+
+// Herk performs the Hermitian rank-k update
+// C = alpha * A * A^H + beta*C, if t == blas.NoTrans,
+// C = alpha * A^H * A + beta*C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
+// and a k×n matrix otherwise, and alpha and beta are scalars.
+func Herk(t blas.Transpose, alpha float64, a General, beta float64, c Hermitian) {
+ var n, k int
+ if t == blas.NoTrans {
+ n, k = a.Rows, a.Cols
+ } else {
+ n, k = a.Cols, a.Rows
+ }
+ cblas128.Zherk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
+}
+
+// Her2k performs the Hermitian rank-2k update
+// C = alpha * A * B^H + conj(alpha) * B * A^H + beta * C, if t == blas.NoTrans,
+// C = alpha * A^H * B + conj(alpha) * B^H * A + beta * C, if t == blas.ConjTrans,
+// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
+// and k×n matrices otherwise, and alpha and beta are scalars.
+func Her2k(t blas.Transpose, alpha complex128, a, b General, beta float64, c Hermitian) {
+ var n, k int
+ if t == blas.NoTrans {
+ n, k = a.Rows, a.Cols
+ } else {
+ n, k = a.Cols, a.Rows
+ }
+ cblas128.Zher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
+}
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