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 Go to latest Published: Oct 18, 2016 License: Apache-2.0 Imports: 8 Imported by: 0

Documentation

Overview

Package native 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. Please note that the treatment of NaN values is not specified, and differs among the BLAS implementations. github.com/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.

Please 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) 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 computes 

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

where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and m and n refer to the size of the full dense matrix it represents. 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 computes 

C = beta * C + alpha * A * B.

tA and tB specify whether A or B are transposed. A, B, and C are m×n dense matrices.

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 * A^T * 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 is a scalar.

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 * y^T

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 the plane rotation 

 _    _      _ _       _ _
| c  s |    | a |     | r |
| -s c |  * | b |   = | 0 |
 ‾    ‾      ‾ ‾       ‾ ‾

where 

r = ±(a^2 + b^2)
c = a/r, the cosine of the plane rotation
s = b/r, the sine of the plane rotation

NOTE: There is a discrepancy between the refence 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 

y = alpha * A * x + beta * y

where A is an n×n symmetric banded matrix, 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, a []float64, x []float64, incX int, beta float64, y []float64, incY int)

Dspmv performs 

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, a []float64)

Dspr computes the rank-one operation 

a += alpha * x * x^T

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 * y^T + alpha * y * x^T

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

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 

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 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 computes 

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 rank-one update 

a += alpha * x * x^T

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 * y^T + alpha * y * x^T

where A is a symmetric n×n 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 the symmetric rank 2k operation 

C = alpha * A * B^T + alpha * B * A^T + beta * C

where C is an n×n symmetric matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. 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 the symmetric rank-k operation 

C = alpha * A * A^T + beta*C

C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. 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 computes 

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

where A is an n×n triangular banded matrix with k 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 

A * x = b

where A is an n×n triangular banded matrix with k diagonals 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 (Implementation) Dtpmv 

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

Dtpmv computes 

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

where A is an n×n unit 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 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or 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 (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 

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

where A is an n×n triangular matrix, and B is an m×n matrix.

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 computes 

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

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 

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

where A is an n×n triangular matrix, x is an m×n matrix, 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 

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

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 (Implementation) Idamax 

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

Idamax returns the index of the largest element of x. If there are multiple such indices the earliest is returned. Idamax returns -1 if incX is negative or if n == 0.

func (Implementation) Isamax 

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

Isamax returns the index of the largest element of x. If there are multiple such indices the earliest is returned. Idamax returns -1 if incX is negative or if n == 0.

Float32 implementations are autogenerated and not directly tested.

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) 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 computes 

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

where a is an m×n band matrix kL subdiagonals and kU super-diagonals, and m and n refer to the size of the full dense matrix it represents. 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 computes 

C = beta * C + alpha * A * B.

tA and tB specify whether A or B are transposed. A, B, and C are m×n dense matrices.

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 * A^T * 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 is a scalar.

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 * y^T

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 the plane rotation 

 _    _      _ _       _ _
| c  s |    | a |     | r |
| -s c |  * | b |   = | 0 |
 ‾    ‾      ‾ ‾       ‾ ‾

where 

r = ±(a^2 + b^2)
c = a/r, the cosine of the plane rotation
s = b/r, the sine of the plane rotation

NOTE: There is a discrepancy between the refence implementation and the BLAS technical manual regarding the sign for r when a or b are zero. Srotg 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 

y = alpha * A * x + beta * y

where A is an n×n symmetric banded matrix, 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, a []float32, x []float32, incX int, beta float32, y []float32, incY int)

Sspmv performs 

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, a []float32)

Sspr computes the rank-one operation 

a += alpha * x * x^T

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 * y^T + alpha * y * x^T

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

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 

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 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 computes 

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 rank-one update 

a += alpha * x * x^T

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 * y^T + alpha * y * x^T

where A is a symmetric n×n 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 the symmetric rank 2k operation 

C = alpha * A * B^T + alpha * B * A^T + beta * C

where C is an n×n symmetric matrix. A and B are n×k matrices if tA == NoTrans and k×n otherwise. 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 the symmetric rank-k operation 

C = alpha * A * A^T + beta*C

C is an n×n symmetric matrix. A is an n×k matrix if tA == blas.NoTrans, and a k×n matrix otherwise. 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 computes 

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

where A is an n×n triangular banded matrix with k 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 

A * x = b

where A is an n×n triangular banded matrix with k diagonals 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.

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 computes 

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

where A is an n×n unit 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 

A * x = b if tA == blas.NoTrans
A^T * x = b if tA == blas.Trans or 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.

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 

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

where A is an n×n triangular matrix, and B is an m×n matrix.

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 computes 

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

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 

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

where A is an n×n triangular matrix, x is an m×n matrix, 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 

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

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.

Float32 implementations are autogenerated and not directly tested.

Source Files

View all Source files

Directories

Path Synopsis
internal
math32
Package math32 provides float32 versions of standard library math package routines used by gonum/blas/native.
 Package math32 provides float32 versions of standard library math package routines used by gonum/blas/native.

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