gonum

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 Go to latest Published: Mar 15, 2024 License: BSD-3-Clause Imports: 11 Imported by: 30

Documentation

Overview

Package gonum is a Go implementation of the BLAS API. This implementation panics when the input arguments are invalid as per the standard, for example if a vector increment is zero. Note that the treatment of NaN values is not specified, and differs among the BLAS implementations. gonum.org/v1/gonum/blas/blas64 provides helpful wrapper functions to the BLAS interface. The rest of this text describes the layout of the data for the input types.

Note that in the function documentation, x[i] refers to the i^th element of the vector, which will be different from the i^th element of the slice if incX != 1.

See http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html for more license information.

Vector arguments are effectively strided slices. They have two input arguments, a number of elements, n, and an increment, incX. The increment specifies the distance between elements of the vector. The actual Go slice may be longer than necessary. The increment may be positive or negative, except in functions with only a single vector argument where the increment may only be positive. If the increment is negative, s[0] is the last element in the slice. Note that this is not the same as counting backward from the end of the slice, as len(s) may be longer than necessary. So, for example, if n = 5 and incX = 3, the elements of s are 

[0 * * 1 * * 2 * * 3 * * 4 * * * ...]

where ∗ elements are never accessed. If incX = -3, the same elements are accessed, just in reverse order (4, 3, 2, 1, 0).

Dense matrices are specified by a number of rows, a number of columns, and a stride. The stride specifies the number of entries in the slice between the first element of successive rows. The stride must be at least as large as the number of columns but may be longer. 

[a00 ... a0n a0* ... a1stride-1 a21 ... amn am* ... amstride-1]

Thus, dense[i*ld + j] refers to the {i, j}th element of the matrix.

Symmetric and triangular matrices (non-packed) are stored identically to Dense, except that only elements in one triangle of the matrix are accessed.

Packed symmetric and packed triangular matrices are laid out with the entries condensed such that all of the unreferenced elements are removed. So, the upper triangular matrix 

[
  1  2  3
  0  4  5
  0  0  6
]

and the lower-triangular matrix 

[
  1  0  0
  2  3  0
  4  5  6
]

will both be compacted as [1 2 3 4 5 6]. The (i, j) element of the original dense matrix can be found at element i*n - (i-1)*i/2 + j for upper triangular, and at element i * (i+1) /2 + j for lower triangular.

Banded matrices are laid out in a compact format, constructed by removing the zeros in the rows and aligning the diagonals. For example, the matrix 

[
  1  2  3  0  0  0
  4  5  6  7  0  0
  0  8  9 10 11  0
  0  0 12 13 14 15
  0  0  0 16 17 18
  0  0  0  0 19 20
]

implicitly becomes (∗ entries are never accessed) 

[
   *  1  2  3
   4  5  6  7
   8  9 10 11
  12 13 14 15
  16 17 18  *
  19 20  *  *
]

which is given to the BLAS routine as [∗ 1 2 3 4 ...].

See http://www.crest.iu.edu/research/mtl/reference/html/banded.html for more information

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

This section is empty.

Types

type Implementation 

type Implementation struct{}

func (Implementation) Caxpy 

func (Implementation) Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int)

Caxpy adds alpha times x to y: 

y[i] += alpha * x[i] for all i

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ccopy 

func (Implementation) Ccopy(n int, x []complex64, incX int, y []complex64, incY int)

Ccopy copies the vector x to vector y.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cdotc 

func (Implementation) Cdotc(n int, x []complex64, incX int, y []complex64, incY int) complex64

Cdotc computes the dot product 

xᴴ · y

of two complex vectors x and y.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cdotu 

func (Implementation) Cdotu(n int, x []complex64, incX int, y []complex64, incY int) complex64

Cdotu computes the dot product 

xᵀ · y

of two complex vectors x and y.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cgbmv 

func (Implementation) Cgbmv(trans blas.Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

Cgbmv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if trans = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if trans = blas.Trans
y = alpha * Aᴴ * x + beta * y  if trans = blas.ConjTrans

where alpha and beta are scalars, x and y are vectors, and A is an m×n band matrix with kL sub-diagonals and kU super-diagonals.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cgemm 

func (Implementation) Cgemm(tA, tB blas.Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

Cgemm performs one of the matrix-matrix operations 

C = alpha * op(A) * op(B) + beta * C

where op(X) is one of 

op(X) = X  or  op(X) = Xᵀ  or  op(X) = Xᴴ,

alpha and beta are scalars, and A, B and C are matrices, with op(A) an m×k matrix, op(B) a k×n matrix and C an m×n matrix.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cgemv 

func (Implementation) Cgemv(trans blas.Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

Cgemv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if trans = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if trans = blas.Trans
y = alpha * Aᴴ * x + beta * y  if trans = blas.ConjTrans

where alpha and beta are scalars, x and y are vectors, and A is an m×n dense matrix.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cgerc 

func (Implementation) Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

Cgerc performs the rank-one operation 

A += alpha * x * yᴴ

where A is an m×n dense matrix, alpha is a scalar, x is an m element vector, and y is an n element vector.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cgeru 

func (Implementation) Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

Cgeru performs the rank-one operation 

A += alpha * x * yᵀ

where A is an m×n dense matrix, alpha is a scalar, x is an m element vector, and y is an n element vector.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chbmv 

func (Implementation) Chbmv(uplo blas.Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

Chbmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian band matrix with k super-diagonals. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chemm 

func (Implementation) Chemm(side blas.Side, uplo blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

Chemm performs one of the matrix-matrix operations 

C = alpha*A*B + beta*C  if side == blas.Left
C = alpha*B*A + beta*C  if side == blas.Right

where alpha and beta are scalars, A is an m×m or n×n hermitian matrix and B and C are m×n matrices. The imaginary parts of the diagonal elements of A are assumed to be zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chemv 

func (Implementation) Chemv(uplo blas.Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)

Chemv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian matrix. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cher 

func (Implementation) Cher(uplo blas.Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int)

Cher performs the Hermitian rank-one operation 

A += alpha * x * xᴴ

where A is an n×n Hermitian matrix, alpha is a real scalar, and x is an n element vector. On entry, the imaginary parts of the diagonal elements of A are ignored and assumed to be zero, on return they will be set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cher2 

func (Implementation) Cher2(uplo blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)

Cher2 performs the Hermitian rank-two operation 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ

where alpha is a scalar, x and y are n element vectors and A is an n×n Hermitian matrix. On entry, the imaginary parts of the diagonal elements are ignored and assumed to be zero. On return they will be set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cher2k 

func (Implementation) Cher2k(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)

Cher2k performs one of the hermitian rank-2k operations 

C = alpha*A*Bᴴ + conj(alpha)*B*Aᴴ + beta*C  if trans == blas.NoTrans
C = alpha*Aᴴ*B + conj(alpha)*Bᴴ*A + beta*C  if trans == blas.ConjTrans

where alpha and beta are scalars with beta real, C is an n×n hermitian matrix and A and B are n×k matrices in the first case and k×n matrices in the second case.

The imaginary parts of the diagonal elements of C are assumed to be zero, and on return they will be set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cherk 

func (Implementation) Cherk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int)

Cherk performs one of the hermitian rank-k operations 

C = alpha*A*Aᴴ + beta*C  if trans == blas.NoTrans
C = alpha*Aᴴ*A + beta*C  if trans == blas.ConjTrans

where alpha and beta are real scalars, C is an n×n hermitian matrix and A is an n×k matrix in the first case and a k×n matrix in the second case.

The imaginary parts of the diagonal elements of C are assumed to be zero, and on return they will be set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chpmv 

func (Implementation) Chpmv(uplo blas.Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int)

Chpmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian matrix in packed form. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chpr 

func (Implementation) Chpr(uplo blas.Uplo, n int, alpha float32, x []complex64, incX int, ap []complex64)

Chpr performs the Hermitian rank-1 operation 

A += alpha * x * xᴴ

where alpha is a real scalar, x is a vector, and A is an n×n hermitian matrix in packed form. On entry, the imaginary parts of the diagonal elements are assumed to be zero, and on return they are set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Chpr2 

func (Implementation) Chpr2(uplo blas.Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64)

Chpr2 performs the Hermitian rank-2 operation 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ

where alpha is a complex scalar, x and y are n element vectors, and A is an n×n Hermitian matrix, supplied in packed form. On entry, the imaginary parts of the diagonal elements are assumed to be zero, and on return they are set to zero.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cscal 

func (Implementation) Cscal(n int, alpha complex64, x []complex64, incX int)

Cscal scales the vector x by a complex scalar alpha. Cscal has no effect if incX < 0.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Csscal 

func (Implementation) Csscal(n int, alpha float32, x []complex64, incX int)

Csscal scales the vector x by a real scalar alpha. Csscal has no effect if incX < 0.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Cswap 

func (Implementation) Cswap(n int, x []complex64, incX int, y []complex64, incY int)

Cswap exchanges the elements of two complex vectors x and y.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Csymm 

func (Implementation) Csymm(side blas.Side, uplo blas.Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

Csymm performs one of the matrix-matrix operations 

C = alpha*A*B + beta*C  if side == blas.Left
C = alpha*B*A + beta*C  if side == blas.Right

where alpha and beta are scalars, A is an m×m or n×n symmetric matrix and B and C are m×n matrices.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Csyr2k 

func (Implementation) Csyr2k(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)

Csyr2k performs one of the symmetric rank-2k operations 

C = alpha*A*Bᵀ + alpha*B*Aᵀ + beta*C  if trans == blas.NoTrans
C = alpha*Aᵀ*B + alpha*Bᵀ*A + beta*C  if trans == blas.Trans

where alpha and beta are scalars, C is an n×n symmetric matrix and A and B are n×k matrices in the first case and k×n matrices in the second case.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Csyrk 

func (Implementation) Csyrk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int)

Csyrk performs one of the symmetric rank-k operations 

C = alpha*A*Aᵀ + beta*C  if trans == blas.NoTrans
C = alpha*Aᵀ*A + beta*C  if trans == blas.Trans

where alpha and beta are scalars, C is an n×n symmetric matrix and A is an n×k matrix in the first case and a k×n matrix in the second case.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctbmv 

func (Implementation) Ctbmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int)

Ctbmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is an n element vector and A is an n×n triangular band matrix, with (k+1) diagonals.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctbsv 

func (Implementation) Ctbsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k int, a []complex64, lda int, x []complex64, incX int)

Ctbsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular band matrix with (k+1) diagonals.

On entry, x contains the values of b, and the solution 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.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctpmv 

func (Implementation) Ctpmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, ap []complex64, x []complex64, incX int)

Ctpmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is an n element vector and A is an n×n triangular matrix, supplied in packed form.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctpsv 

func (Implementation) Ctpsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, ap []complex64, x []complex64, incX int)

Ctpsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular matrix in packed form.

On entry, x contains the values of b, and the solution 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.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctrmm 

func (Implementation) Ctrmm(side blas.Side, uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)

Ctrmm performs one of the matrix-matrix operations 

B = alpha * op(A) * B  if side == blas.Left,
B = alpha * B * op(A)  if side == blas.Right,

where alpha is a scalar, B is an m×n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of 

op(A) = A   if trans == blas.NoTrans,
op(A) = Aᵀ  if trans == blas.Trans,
op(A) = Aᴴ  if trans == blas.ConjTrans.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctrmv 

func (Implementation) Ctrmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, a []complex64, lda int, x []complex64, incX int)

Ctrmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is a vector, and A is an n×n triangular matrix.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctrsm 

func (Implementation) Ctrsm(side blas.Side, uplo blas.Uplo, transA blas.Transpose, diag blas.Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)

Ctrsm solves one of the matrix equations 

op(A) * X = alpha * B  if side == blas.Left,
X * op(A) = alpha * B  if side == blas.Right,

where alpha is a scalar, X and B are m×n matrices, A is a unit or non-unit, upper or lower triangular matrix and op(A) is one of 

op(A) = A   if transA == blas.NoTrans,
op(A) = Aᵀ  if transA == blas.Trans,
op(A) = Aᴴ  if transA == blas.ConjTrans.

On return the matrix X is overwritten on B.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Ctrsv 

func (Implementation) Ctrsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, a []complex64, lda int, x []complex64, incX int)

Ctrsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular matrix.

On entry, x contains the values of b, and the solution 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.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Dasum 

func (Implementation) Dasum(n int, x []float64, incX int) float64

Dasum computes the sum of the absolute values of the elements of x. 

\sum_i |x[i]|

Dasum returns 0 if incX is negative.

func (Implementation) Daxpy 

func (Implementation) Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)

Daxpy adds alpha times x to y 

y[i] += alpha * x[i] for all i

func (Implementation) Dcopy 

func (Implementation) Dcopy(n int, x []float64, incX int, y []float64, incY int)

Dcopy copies the elements of x into the elements of y. 

y[i] = x[i] for all i

func (Implementation) Ddot 

func (Implementation) Ddot(n int, x []float64, incX int, y []float64, incY int) float64

Ddot computes the dot product of the two vectors 

\sum_i x[i]*y[i]

func (Implementation) Dgbmv 

func (Implementation) Dgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dgbmv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if tA == blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if tA == blas.Trans or blas.ConjTrans

where A is an m×n band matrix with kL sub-diagonals and kU super-diagonals, x and y are vectors, and alpha and beta are scalars.

func (Implementation) Dgemm 

func (Implementation) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dgemm performs one of the matrix-matrix operations 

C = alpha * A * B + beta * C
C = alpha * Aᵀ * B + beta * C
C = alpha * A * Bᵀ + beta * C
C = alpha * Aᵀ * Bᵀ + beta * C

where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or B are transposed.

func (Implementation) Dgemv 

func (Implementation) Dgemv(tA blas.Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dgemv computes 

y = alpha * A * x + beta * y   if tA = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if tA = blas.Trans or blas.ConjTrans

where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.

func (Implementation) Dger 

func (Implementation) Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)

Dger performs the rank-one operation 

A += alpha * x * yᵀ

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

func (Implementation) Dnrm2 

func (Implementation) Dnrm2(n int, x []float64, incX int) float64

Dnrm2 computes the Euclidean norm of a vector, 

sqrt(\sum_i x[i] * x[i]).

This function returns 0 if incX is negative.

func (Implementation) Drot 

func (Implementation) Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64)

Drot applies a plane transformation. 

x[i] = c * x[i] + s * y[i]
y[i] = c * y[i] - s * x[i]

func (Implementation) Drotg 

func (Implementation) Drotg(a, b float64) (c, s, r, z float64)

Drotg computes a plane rotation 

⎡  c s ⎤ ⎡ a ⎤ = ⎡ r ⎤
⎣ -s c ⎦ ⎣ b ⎦   ⎣ 0 ⎦

satisfying c^2 + s^2 = 1.

The computation uses the formulas 

sigma = sgn(a)    if |a| >  |b|
      = sgn(b)    if |b| >= |a|
r = sigma*sqrt(a^2 + b^2)
c = 1; s = 0      if r = 0
c = a/r; s = b/r  if r != 0
c >= 0            if |a| > |b|

The subroutine also computes 

z = s    if |a| > |b|,
  = 1/c  if |b| >= |a| and c != 0
  = 1    if c = 0

This allows c and s to be reconstructed from z as follows: 

If z = 1, set c = 0, s = 1.
If |z| < 1, set c = sqrt(1 - z^2) and s = z.
If |z| > 1, set c = 1/z and s = sqrt(1 - c^2).

NOTE: There is a discrepancy between the reference implementation and the BLAS technical manual regarding the sign for r when a or b are zero. Drotg agrees with the definition in the manual and other common BLAS implementations.

func (Implementation) Drotm 

func (Implementation) Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams)

Drotm applies the modified Givens rotation to the 2×n matrix.

func (Implementation) Drotmg 

func (Implementation) Drotmg(d1, d2, x1, y1 float64) (p blas.DrotmParams, rd1, rd2, rx1 float64)

Drotmg computes the modified Givens rotation. See http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html for more details.

func (Implementation) Dsbmv 

func (Implementation) Dsbmv(ul blas.Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dsbmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric band matrix with k super-diagonals, x and y are vectors, and alpha and beta are scalars.

func (Implementation) Dscal 

func (Implementation) Dscal(n int, alpha float64, x []float64, incX int)

Dscal scales x by alpha. 

x[i] *= alpha

Dscal has no effect if incX < 0.

func (Implementation) Dsdot 

func (Implementation) Dsdot(n int, x []float32, incX int, y []float32, incY int) float64

Dsdot computes the dot product of the two vectors 

\sum_i x[i]*y[i]

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Dspmv 

func (Implementation) Dspmv(ul blas.Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int)

Dspmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha and beta are scalars.

func (Implementation) Dspr 

func (Implementation) Dspr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, ap []float64)

Dspr performs the symmetric rank-one operation 

A += alpha * x * xᵀ

where A is an n×n symmetric matrix in packed format, x is a vector, and alpha is a scalar.

func (Implementation) Dspr2 

func (Implementation) Dspr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, ap []float64)

Dspr2 performs the symmetric rank-2 update 

A += alpha * x * yᵀ + alpha * y * xᵀ

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha is a scalar.

func (Implementation) Dswap 

func (Implementation) Dswap(n int, x []float64, incX int, y []float64, incY int)

Dswap exchanges the elements of two vectors. 

x[i], y[i] = y[i], x[i] for all i

func (Implementation) Dsymm 

func (Implementation) Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dsymm performs one of the matrix-matrix operations 

C = alpha * A * B + beta * C  if side == blas.Left
C = alpha * B * A + beta * C  if side == blas.Right

where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha is a scalar.

func (Implementation) Dsymv 

func (Implementation) Dsymv(ul blas.Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)

Dsymv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric matrix, x and y are vectors, and alpha and beta are scalars.

func (Implementation) Dsyr 

func (Implementation) Dsyr(ul blas.Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)

Dsyr performs the symmetric rank-one update 

A += alpha * x * xᵀ

where A is an n×n symmetric matrix, and x is a vector.

func (Implementation) Dsyr2 

func (Implementation) Dsyr2(ul blas.Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)

Dsyr2 performs the symmetric rank-two update 

A += alpha * x * yᵀ + alpha * y * xᵀ

where A is an n×n symmetric matrix, x and y are vectors, and alpha is a scalar.

func (Implementation) Dsyr2k 

func (Implementation) Dsyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)

Dsyr2k performs one of the symmetric rank 2k operations 

C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C  if tA == blas.NoTrans
C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C  if tA == blas.Trans or tA == blas.ConjTrans

where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and alpha and beta are scalars.

func (Implementation) Dsyrk 

func (Implementation) Dsyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)

Dsyrk performs one of the symmetric rank-k operations 

C = alpha * A * Aᵀ + beta * C  if tA == blas.NoTrans
C = alpha * Aᵀ * A + beta * C  if tA == blas.Trans or tA == blas.ConjTrans

where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and beta are scalars.

func (Implementation) Dtbmv 

func (Implementation) Dtbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)

Dtbmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular band matrix with k+1 diagonals, and x is a vector.

func (Implementation) Dtbsv 

func (Implementation) Dtbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float64, lda int, x []float64, incX int)

Dtbsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or tA == blas.ConjTrans

where A is an n×n triangular band matrix with k+1 diagonals, and x and b are vectors.

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 (Implementation) Dtpmv 

func (Implementation) Dtpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int)

Dtpmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix in packed format, and x is a vector.

func (Implementation) Dtpsv 

func (Implementation) Dtpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float64, x []float64, incX int)

Dtpsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix in packed format, and x and b are vectors.

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 (Implementation) Dtrmm 

func (Implementation) Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)

Dtrmm performs one of the matrix-matrix operations 

B = alpha * A * B   if tA == blas.NoTrans and side == blas.Left
B = alpha * Aᵀ * B  if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
B = alpha * B * A   if tA == blas.NoTrans and side == blas.Right
B = alpha * B * Aᵀ  if tA == blas.Trans or blas.ConjTrans, and side == 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 (Implementation) Dtrmv 

func (Implementation) Dtrmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)

Dtrmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix, and x is a vector.

func (Implementation) Dtrsm 

func (Implementation) Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)

Dtrsm solves one of the matrix equations 

A * X = alpha * B   if tA == blas.NoTrans and side == blas.Left
Aᵀ * X = alpha * B  if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
X * A = alpha * B   if tA == blas.NoTrans and side == blas.Right
X * Aᵀ = alpha * B  if tA == blas.Trans or blas.ConjTrans, and side == 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, X contains the values of B, and the result is stored in-place into X.

No check is made that A is invertible.

func (Implementation) Dtrsv 

func (Implementation) Dtrsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float64, lda int, x []float64, incX int)

Dtrsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix, and x and b are vectors.

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 (Implementation) Dzasum 

func (Implementation) Dzasum(n int, x []complex128, incX int) float64

Dzasum returns the sum of the absolute values of the elements of x 

\sum_i |Re(x[i])| + |Im(x[i])|

Dzasum returns 0 if incX is negative.

func (Implementation) Dznrm2 

func (Implementation) Dznrm2(n int, x []complex128, incX int) float64

Dznrm2 computes the Euclidean norm of the complex vector x, 

‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).

This function returns 0 if incX is negative.

func (Implementation) Icamax 

func (Implementation) Icamax(n int, x []complex64, incX int) int

Icamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|. Icamax returns -1 if n is 0 or incX is negative.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Idamax 

func (Implementation) Idamax(n int, x []float64, incX int) int

Idamax returns the index of an element of x with the largest absolute value. If there are multiple such indices the earliest is returned. Idamax returns -1 if n == 0.

func (Implementation) Isamax 

func (Implementation) Isamax(n int, x []float32, incX int) int

Isamax returns the index of an element of x with the largest absolute value. If there are multiple such indices the earliest is returned. Isamax returns -1 if n == 0.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Izamax 

func (Implementation) Izamax(n int, x []complex128, incX int) int

Izamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|. Izamax returns -1 if n is 0 or incX is negative.

func (Implementation) Sasum 

func (Implementation) Sasum(n int, x []float32, incX int) float32

Sasum computes the sum of the absolute values of the elements of x. 

\sum_i |x[i]|

Sasum returns 0 if incX is negative.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Saxpy 

func (Implementation) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int)

Saxpy adds alpha times x to y 

y[i] += alpha * x[i] for all i

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Scasum 

func (Implementation) Scasum(n int, x []complex64, incX int) float32

Scasum returns the sum of the absolute values of the elements of x 

\sum_i |Re(x[i])| + |Im(x[i])|

Scasum returns 0 if incX is negative.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Scnrm2 

func (Implementation) Scnrm2(n int, x []complex64, incX int) float32

Scnrm2 computes the Euclidean norm of the complex vector x, 

‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).

This function returns 0 if incX is negative.

Complex64 implementations are autogenerated and not directly tested.

func (Implementation) Scopy 

func (Implementation) Scopy(n int, x []float32, incX int, y []float32, incY int)

Scopy copies the elements of x into the elements of y. 

y[i] = x[i] for all i

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sdot 

func (Implementation) Sdot(n int, x []float32, incX int, y []float32, incY int) float32

Sdot computes the dot product of the two vectors 

\sum_i x[i]*y[i]

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sdsdot 

func (Implementation) Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32

Sdsdot computes the dot product of the two vectors plus a constant 

alpha + \sum_i x[i]*y[i]

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sgbmv 

func (Implementation) Sgbmv(tA blas.Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Sgbmv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if tA == blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if tA == blas.Trans or blas.ConjTrans

where A is an m×n band matrix with kL sub-diagonals and kU super-diagonals, x and y are vectors, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sgemm 

func (Implementation) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Sgemm performs one of the matrix-matrix operations 

C = alpha * A * B + beta * C
C = alpha * Aᵀ * B + beta * C
C = alpha * A * Bᵀ + beta * C
C = alpha * Aᵀ * Bᵀ + beta * C

where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or B are transposed.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sgemv 

func (Implementation) Sgemv(tA blas.Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Sgemv computes 

y = alpha * A * x + beta * y   if tA = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if tA = blas.Trans or blas.ConjTrans

where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sger 

func (Implementation) Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)

Sger performs the rank-one operation 

A += alpha * x * yᵀ

where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Snrm2 

func (Implementation) Snrm2(n int, x []float32, incX int) float32

Snrm2 computes the Euclidean norm of a vector, 

sqrt(\sum_i x[i] * x[i]).

This function returns 0 if incX is negative.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Srot 

func (Implementation) Srot(n int, x []float32, incX int, y []float32, incY int, c float32, s float32)

Srot applies a plane transformation. 

x[i] = c * x[i] + s * y[i]
y[i] = c * y[i] - s * x[i]

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Srotg 

func (Implementation) Srotg(a, b float32) (c, s, r, z float32)

Srotg computes a plane rotation 

⎡  c s ⎤ ⎡ a ⎤ = ⎡ r ⎤
⎣ -s c ⎦ ⎣ b ⎦   ⎣ 0 ⎦

satisfying c^2 + s^2 = 1.

The computation uses the formulas 

sigma = sgn(a)    if |a| >  |b|
      = sgn(b)    if |b| >= |a|
r = sigma*sqrt(a^2 + b^2)
c = 1; s = 0      if r = 0
c = a/r; s = b/r  if r != 0
c >= 0            if |a| > |b|

The subroutine also computes 

z = s    if |a| > |b|,
  = 1/c  if |b| >= |a| and c != 0
  = 1    if c = 0

This allows c and s to be reconstructed from z as follows: 

If z = 1, set c = 0, s = 1.
If |z| < 1, set c = sqrt(1 - z^2) and s = z.
If |z| > 1, set c = 1/z and s = sqrt(1 - c^2).

NOTE: There is a discrepancy between the reference implementation and the BLAS technical manual regarding the sign for r when a or b are zero. Drotg agrees with the definition in the manual and other common BLAS implementations.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Srotm 

func (Implementation) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams)

Srotm applies the modified Givens rotation to the 2×n matrix.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Srotmg 

func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32)

Srotmg computes the modified Givens rotation. See http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html for more details.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssbmv 

func (Implementation) Ssbmv(ul blas.Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Ssbmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric band matrix with k super-diagonals, x and y are vectors, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sscal 

func (Implementation) Sscal(n int, alpha float32, x []float32, incX int)

Sscal scales x by alpha. 

x[i] *= alpha

Sscal has no effect if incX < 0.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sspmv 

func (Implementation) Sspmv(ul blas.Uplo, n int, alpha float32, ap []float32, x []float32, incX int, beta float32, y []float32, incY int)

Sspmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sspr 

func (Implementation) Sspr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, ap []float32)

Sspr performs the symmetric rank-one operation 

A += alpha * x * xᵀ

where A is an n×n symmetric matrix in packed format, x is a vector, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sspr2 

func (Implementation) Sspr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, ap []float32)

Sspr2 performs the symmetric rank-2 update 

A += alpha * x * yᵀ + alpha * y * xᵀ

where A is an n×n symmetric matrix in packed format, x and y are vectors, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Sswap 

func (Implementation) Sswap(n int, x []float32, incX int, y []float32, incY int)

Sswap exchanges the elements of two vectors. 

x[i], y[i] = y[i], x[i] for all i

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssymm 

func (Implementation) Ssymm(s blas.Side, ul blas.Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Ssymm performs one of the matrix-matrix operations 

C = alpha * A * B + beta * C  if side == blas.Left
C = alpha * B * A + beta * C  if side == blas.Right

where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssymv 

func (Implementation) Ssymv(ul blas.Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)

Ssymv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where A is an n×n symmetric matrix, x and y are vectors, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssyr 

func (Implementation) Ssyr(ul blas.Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int)

Ssyr performs the symmetric rank-one update 

A += alpha * x * xᵀ

where A is an n×n symmetric matrix, and x is a vector.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssyr2 

func (Implementation) Ssyr2(ul blas.Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)

Ssyr2 performs the symmetric rank-two update 

A += alpha * x * yᵀ + alpha * y * xᵀ

where A is an n×n symmetric matrix, x and y are vectors, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssyr2k 

func (Implementation) Ssyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)

Ssyr2k performs one of the symmetric rank 2k operations 

C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C  if tA == blas.NoTrans
C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C  if tA == blas.Trans or tA == blas.ConjTrans

where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Ssyrk 

func (Implementation) Ssyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int)

Ssyrk performs one of the symmetric rank-k operations 

C = alpha * A * Aᵀ + beta * C  if tA == blas.NoTrans
C = alpha * Aᵀ * A + beta * C  if tA == blas.Trans or tA == blas.ConjTrans

where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and beta are scalars.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Stbmv 

func (Implementation) Stbmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int)

Stbmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular band matrix with k+1 diagonals, and x is a vector.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Stbsv 

func (Implementation) Stbsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n, k int, a []float32, lda int, x []float32, incX int)

Stbsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or tA == blas.ConjTrans

where A is an n×n triangular band matrix with k+1 diagonals, and x and b are vectors.

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.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Stpmv 

func (Implementation) Stpmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float32, x []float32, incX int)

Stpmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix in packed format, and x is a vector.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Stpsv 

func (Implementation) Stpsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, ap []float32, x []float32, incX int)

Stpsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix in packed format, and x and b are vectors.

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.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Strmm 

func (Implementation) Strmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)

Strmm performs one of the matrix-matrix operations 

B = alpha * A * B   if tA == blas.NoTrans and side == blas.Left
B = alpha * Aᵀ * B  if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
B = alpha * B * A   if tA == blas.NoTrans and side == blas.Right
B = alpha * B * Aᵀ  if tA == blas.Trans or blas.ConjTrans, and side == blas.Right

where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is a scalar.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Strmv 

func (Implementation) Strmv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int)

Strmv performs one of the matrix-vector operations 

x = A * x   if tA == blas.NoTrans
x = Aᵀ * x  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix, and x is a vector.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Strsm 

func (Implementation) Strsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)

Strsm solves one of the matrix equations 

A * X = alpha * B   if tA == blas.NoTrans and side == blas.Left
Aᵀ * X = alpha * B  if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
X * A = alpha * B   if tA == blas.NoTrans and side == blas.Right
X * Aᵀ = alpha * B  if tA == blas.Trans or blas.ConjTrans, and side == 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, X contains the values of B, and the result is stored in-place into X.

No check is made that A is invertible.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Strsv 

func (Implementation) Strsv(ul blas.Uplo, tA blas.Transpose, d blas.Diag, n int, a []float32, lda int, x []float32, incX int)

Strsv solves one of the systems of equations 

A * x = b   if tA == blas.NoTrans
Aᵀ * x = b  if tA == blas.Trans or blas.ConjTrans

where A is an n×n triangular matrix, and x and b are vectors.

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.

Float32 implementations are autogenerated and not directly tested.

func (Implementation) Zaxpy 

func (Implementation) Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)

Zaxpy adds alpha times x to y: 

y[i] += alpha * x[i] for all i

func (Implementation) Zcopy 

func (Implementation) Zcopy(n int, x []complex128, incX int, y []complex128, incY int)

Zcopy copies the vector x to vector y.

func (Implementation) Zdotc 

func (Implementation) Zdotc(n int, x []complex128, incX int, y []complex128, incY int) complex128

Zdotc computes the dot product 

xᴴ · y

of two complex vectors x and y.

func (Implementation) Zdotu 

func (Implementation) Zdotu(n int, x []complex128, incX int, y []complex128, incY int) complex128

Zdotu computes the dot product 

xᵀ · y

of two complex vectors x and y.

func (Implementation) Zdscal 

func (Implementation) Zdscal(n int, alpha float64, x []complex128, incX int)

Zdscal scales the vector x by a real scalar alpha. Zdscal has no effect if incX < 0.

func (Implementation) Zgbmv 

func (Implementation) Zgbmv(trans blas.Transpose, m, n, kL, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

Zgbmv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if trans = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if trans = blas.Trans
y = alpha * Aᴴ * x + beta * y  if trans = blas.ConjTrans

where alpha and beta are scalars, x and y are vectors, and A is an m×n band matrix with kL sub-diagonals and kU super-diagonals.

func (Implementation) Zgemm 

func (Implementation) Zgemm(tA, tB blas.Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

Zgemm performs one of the matrix-matrix operations 

C = alpha * op(A) * op(B) + beta * C

where op(X) is one of 

op(X) = X  or  op(X) = Xᵀ  or  op(X) = Xᴴ,

alpha and beta are scalars, and A, B and C are matrices, with op(A) an m×k matrix, op(B) a k×n matrix and C an m×n matrix.

func (Implementation) Zgemv 

func (Implementation) Zgemv(trans blas.Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

Zgemv performs one of the matrix-vector operations 

y = alpha * A * x + beta * y   if trans = blas.NoTrans
y = alpha * Aᵀ * x + beta * y  if trans = blas.Trans
y = alpha * Aᴴ * x + beta * y  if trans = blas.ConjTrans

where alpha and beta are scalars, x and y are vectors, and A is an m×n dense matrix.

func (Implementation) Zgerc 

func (Implementation) Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

Zgerc performs the rank-one operation 

A += alpha * x * yᴴ

where A is an m×n dense matrix, alpha is a scalar, x is an m element vector, and y is an n element vector.

func (Implementation) Zgeru 

func (Implementation) Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

Zgeru performs the rank-one operation 

A += alpha * x * yᵀ

where A is an m×n dense matrix, alpha is a scalar, x is an m element vector, and y is an n element vector.

func (Implementation) Zhbmv 

func (Implementation) Zhbmv(uplo blas.Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

Zhbmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian band matrix with k super-diagonals. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

func (Implementation) Zhemm 

func (Implementation) Zhemm(side blas.Side, uplo blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

Zhemm performs one of the matrix-matrix operations 

C = alpha*A*B + beta*C  if side == blas.Left
C = alpha*B*A + beta*C  if side == blas.Right

where alpha and beta are scalars, A is an m×m or n×n hermitian matrix and B and C are m×n matrices. The imaginary parts of the diagonal elements of A are assumed to be zero.

func (Implementation) Zhemv 

func (Implementation) Zhemv(uplo blas.Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)

Zhemv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian matrix. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

func (Implementation) Zher 

func (Implementation) Zher(uplo blas.Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)

Zher performs the Hermitian rank-one operation 

A += alpha * x * xᴴ

where A is an n×n Hermitian matrix, alpha is a real scalar, and x is an n element vector. On entry, the imaginary parts of the diagonal elements of A are ignored and assumed to be zero, on return they will be set to zero.

func (Implementation) Zher2 

func (Implementation) Zher2(uplo blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)

Zher2 performs the Hermitian rank-two operation 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ

where alpha is a scalar, x and y are n element vectors and A is an n×n Hermitian matrix. On entry, the imaginary parts of the diagonal elements are ignored and assumed to be zero. On return they will be set to zero.

func (Implementation) Zher2k 

func (Implementation) Zher2k(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)

Zher2k performs one of the hermitian rank-2k operations 

C = alpha*A*Bᴴ + conj(alpha)*B*Aᴴ + beta*C  if trans == blas.NoTrans
C = alpha*Aᴴ*B + conj(alpha)*Bᴴ*A + beta*C  if trans == blas.ConjTrans

where alpha and beta are scalars with beta real, C is an n×n hermitian matrix and A and B are n×k matrices in the first case and k×n matrices in the second case.

The imaginary parts of the diagonal elements of C are assumed to be zero, and on return they will be set to zero.

func (Implementation) Zherk 

func (Implementation) Zherk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int)

Zherk performs one of the hermitian rank-k operations 

C = alpha*A*Aᴴ + beta*C  if trans == blas.NoTrans
C = alpha*Aᴴ*A + beta*C  if trans == blas.ConjTrans

where alpha and beta are real scalars, C is an n×n hermitian matrix and A is an n×k matrix in the first case and a k×n matrix in the second case.

The imaginary parts of the diagonal elements of C are assumed to be zero, and on return they will be set to zero.

func (Implementation) Zhpmv 

func (Implementation) Zhpmv(uplo blas.Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int)

Zhpmv performs the matrix-vector operation 

y = alpha * A * x + beta * y

where alpha and beta are scalars, x and y are vectors, and A is an n×n Hermitian matrix in packed form. The imaginary parts of the diagonal elements of A are ignored and assumed to be zero.

func (Implementation) Zhpr 

func (Implementation) Zhpr(uplo blas.Uplo, n int, alpha float64, x []complex128, incX int, ap []complex128)

Zhpr performs the Hermitian rank-1 operation 

A += alpha * x * xᴴ

where alpha is a real scalar, x is a vector, and A is an n×n hermitian matrix in packed form. On entry, the imaginary parts of the diagonal elements are assumed to be zero, and on return they are set to zero.

func (Implementation) Zhpr2 

func (Implementation) Zhpr2(uplo blas.Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128)

Zhpr2 performs the Hermitian rank-2 operation 

A += alpha * x * yᴴ + conj(alpha) * y * xᴴ

where alpha is a complex scalar, x and y are n element vectors, and A is an n×n Hermitian matrix, supplied in packed form. On entry, the imaginary parts of the diagonal elements are assumed to be zero, and on return they are set to zero.

func (Implementation) Zscal 

func (Implementation) Zscal(n int, alpha complex128, x []complex128, incX int)

Zscal scales the vector x by a complex scalar alpha. Zscal has no effect if incX < 0.

func (Implementation) Zswap 

func (Implementation) Zswap(n int, x []complex128, incX int, y []complex128, incY int)

Zswap exchanges the elements of two complex vectors x and y.

func (Implementation) Zsymm 

func (Implementation) Zsymm(side blas.Side, uplo blas.Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

Zsymm performs one of the matrix-matrix operations 

C = alpha*A*B + beta*C  if side == blas.Left
C = alpha*B*A + beta*C  if side == blas.Right

where alpha and beta are scalars, A is an m×m or n×n symmetric matrix and B and C are m×n matrices.

func (Implementation) Zsyr2k 

func (Implementation) Zsyr2k(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)

Zsyr2k performs one of the symmetric rank-2k operations 

C = alpha*A*Bᵀ + alpha*B*Aᵀ + beta*C  if trans == blas.NoTrans
C = alpha*Aᵀ*B + alpha*Bᵀ*A + beta*C  if trans == blas.Trans

where alpha and beta are scalars, C is an n×n symmetric matrix and A and B are n×k matrices in the first case and k×n matrices in the second case.

func (Implementation) Zsyrk 

func (Implementation) Zsyrk(uplo blas.Uplo, trans blas.Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)

Zsyrk performs one of the symmetric rank-k operations 

C = alpha*A*Aᵀ + beta*C  if trans == blas.NoTrans
C = alpha*Aᵀ*A + beta*C  if trans == blas.Trans

where alpha and beta are scalars, C is an n×n symmetric matrix and A is an n×k matrix in the first case and a k×n matrix in the second case.

func (Implementation) Ztbmv 

func (Implementation) Ztbmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int)

Ztbmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is an n element vector and A is an n×n triangular band matrix, with (k+1) diagonals.

func (Implementation) Ztbsv 

func (Implementation) Ztbsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k int, a []complex128, lda int, x []complex128, incX int)

Ztbsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular band matrix with (k+1) diagonals.

On entry, x contains the values of b, and the solution 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 (Implementation) Ztpmv 

func (Implementation) Ztpmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, ap []complex128, x []complex128, incX int)

Ztpmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is an n element vector and A is an n×n triangular matrix, supplied in packed form.

func (Implementation) Ztpsv 

func (Implementation) Ztpsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, ap []complex128, x []complex128, incX int)

Ztpsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular matrix in packed form.

On entry, x contains the values of b, and the solution 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 (Implementation) Ztrmm 

func (Implementation) Ztrmm(side blas.Side, uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)

Ztrmm performs one of the matrix-matrix operations 

B = alpha * op(A) * B  if side == blas.Left,
B = alpha * B * op(A)  if side == blas.Right,

where alpha is a scalar, B is an m×n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of 

op(A) = A   if trans == blas.NoTrans,
op(A) = Aᵀ  if trans == blas.Trans,
op(A) = Aᴴ  if trans == blas.ConjTrans.

func (Implementation) Ztrmv 

func (Implementation) Ztrmv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, a []complex128, lda int, x []complex128, incX int)

Ztrmv performs one of the matrix-vector operations 

x = A * x   if trans = blas.NoTrans
x = Aᵀ * x  if trans = blas.Trans
x = Aᴴ * x  if trans = blas.ConjTrans

where x is a vector, and A is an n×n triangular matrix.

func (Implementation) Ztrsm 

func (Implementation) Ztrsm(side blas.Side, uplo blas.Uplo, transA blas.Transpose, diag blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)

Ztrsm solves one of the matrix equations 

op(A) * X = alpha * B  if side == blas.Left,
X * op(A) = alpha * B  if side == blas.Right,

where alpha is a scalar, X and B are m×n matrices, A is a unit or non-unit, upper or lower triangular matrix and op(A) is one of 

op(A) = A   if transA == blas.NoTrans,
op(A) = Aᵀ  if transA == blas.Trans,
op(A) = Aᴴ  if transA == blas.ConjTrans.

On return the matrix X is overwritten on B.

func (Implementation) Ztrsv 

func (Implementation) Ztrsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n int, a []complex128, lda int, x []complex128, incX int)

Ztrsv solves one of the systems of equations 

A * x = b   if trans == blas.NoTrans
Aᵀ * x = b  if trans == blas.Trans
Aᴴ * x = b  if trans == blas.ConjTrans

where b and x are n element vectors and A is an n×n triangular matrix.

On entry, x contains the values of b, and the solution 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.

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