Stability	Experimental
Safe Haskell	None
Language	Haskell98

Blas.Specialized.ComplexDouble.Unsafe

Contents

Level 1: vector-vector operations
- Basic operations
- Norm operations
Level 2: matrix-vector operations
Level 3: matrix-matrix operations

Description

Generic interface to Blas using unsafe foreign calls. Refer to the GHC documentation for more information regarding appropriate use of safe and unsafe foreign calls.

The functions here are named in a similar fashion to the original Blas interface, with the type-dependent letter(s) removed. Some functions have been merged with others to allow the interface to work on both real and complex numbers. If you can't a particular function, try looking for its corresponding complex equivalent (e.g. symv is a special case of hemv applied to real numbers).

Note: although complex versions of rot and rotg exist in many implementations, they are not part of the official Blas standard and therefore not included here. If you really need them, submit a ticket so we can try to come up with a solution.

The documentation here is still incomplete. Consult the official documentation for more information.

Notation:

⋅ denotes dot product (without any conjugation).
* denotes complex conjugation.
⊤ denotes transpose.
† denotes conjugate transpose (Hermitian conjugate).

Conventions:

All scalars are denoted with lowercase Greek letters
All vectors are denoted with lowercase Latin letters and are assumed to be column vectors (unless transposed).
All matrices are denoted with uppercase Latin letters.

Since: 0.1.1

Synopsis

Level 1: vector-vector operations

Basic operations

swap :: Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Swap two vectors:

(x, y) ← (y, x)

scal :: Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Multiply a vector by a scalar.

x ← α x

copy :: Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Copy a vector into another vector:

y ← x

axpy :: Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Add a scalar-vector product to a vector.

y ← α x + y

dotu :: Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO (Complex Double) Source

Calculate the bilinear dot product of two vectors:

x ⋅ y ≡ ∑[i] x[i] y[i]

dotc :: Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO (Complex Double) Source

Calculate the sesquilinear dot product of two vectors.

x* ⋅ y ≡ ∑[i] x[i]* y[i]

Norm operations

nrm2 :: Int -> Ptr (Complex Double) -> Int -> IO Double Source

Calculate the Euclidean (L²) norm of a vector:

‖x‖₂ ≡ √(∑[i] x[i]²)

asum :: Int -> Ptr (Complex Double) -> Int -> IO Double Source

Calculate the Manhattan (L¹) norm, equal to the sum of the magnitudes of the elements:

‖x‖₁ = ∑[i] |x[i]|

iamax :: Int -> Ptr (Complex Double) -> Int -> IO Int Source

Calculate the index of the element with the maximum magnitude (absolute value).

Level 2: matrix-vector operations

Multiplication

gemv :: Order -> Transpose -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a general matrix-vector update.

y ← α T(A) x + β y

gbmv :: Order -> Transpose -> Int -> Int -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a general banded matrix-vector update.

y ← α T(A) x + β y

hemv :: Order -> Uplo -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a hermitian matrix-vector update.

y ← α A x + β y

hbmv :: Order -> Uplo -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a hermitian banded matrix-vector update.

y ← α A x + β y

hpmv :: Order -> Uplo -> Int -> Complex Double -> Ptr (Complex Double) -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a hermitian packed matrix-vector update.

y ← α A x + β y

Triangular operations

trmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Multiply a triangular matrix by a vector.

x ← T(A) x

tbmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Multiply a triangular banded matrix by a vector.

x ← T(A) x

tpmv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr (Complex Double) -> Ptr (Complex Double) -> Int -> IO () Source

Multiply a triangular packed matrix by a vector.

x ← T(A) x

trsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Multiply an inverse triangular matrix by a vector.

x ← T(A⁻¹) x

tbsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Multiply an inverse triangular banded matrix by a vector.

x ← T(A⁻¹) x

tpsv :: Order -> Uplo -> Transpose -> Diag -> Int -> Ptr (Complex Double) -> Ptr (Complex Double) -> Int -> IO () Source

Multiply an inverse triangular packed matrix by a vector.

x ← T(A⁻¹) x

Rank updates

geru :: Order -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform an unconjugated rank-1 update of a general matrix.

A ← α x y⊤ + A

gerc :: Order -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform a conjugated rank-1 update of a general matrix.

A ← α x y† + A

her :: Order -> Uplo -> Int -> Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform a rank-1 update of a Hermitian matrix.

A ← α x y† + A

hpr :: Order -> Uplo -> Int -> Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> IO () Source

Perform a rank-1 update of a Hermitian packed matrix.

A ← α x y† + A

her2 :: Order -> Uplo -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform a rank-2 update of a Hermitian matrix.

A ← α x y† + y (α x)† + A

hpr2 :: Order -> Uplo -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> IO () Source

Perform a rank-2 update of a Hermitian packed matrix.

A ← α x y† + y (α x)† + A

Level 3: matrix-matrix operations

Multiplication

gemm Source

Arguments

:: Order	Layout of all the matrices.
-> Transpose	The operation `T` to be applied to `A`.
-> Transpose	The operation `U` to be applied to `B`.
-> Int	Number of rows of `T(A)` and `C`.
-> Int	Number of columns of `U(B)` and `C`.
-> Int	Number of columns of `T(A)` and number of rows of `U(B)`.
-> Complex Double	Scaling factor `α` of the product.
-> Ptr (Complex Double)	Pointer to a matrix `A`.
-> Int	Stride of the major dimension of `A`.
-> Ptr (Complex Double)	Pointer to a matrix `B`.
-> Int	Stride of the major dimension of `B`.
-> Complex Double	Scaling factor `β` of the original `C`.
-> Ptr (Complex Double)	Pointer to a mutable matrix `C`.
-> Int	Stride of the major dimension of `C`.
-> IO ()

Perform a general matrix-matrix update.

C ← α T(A) U(B) + β C

symm Source

Arguments

:: Order	Layout of all the matrices.
-> Side	Side that `A` appears in the product.
-> Uplo	The part of `A` that is used.
-> Int	Number of rows of `C`.
-> Int	Number of columns of `C`.
-> Complex Double	Scaling factor `α` of the product.
-> Ptr (Complex Double)	Pointer to a symmetric matrix `A`.
-> Int	Stride of the major dimension of `A`.
-> Ptr (Complex Double)	Pointer to a matrix `B`.
-> Int	Stride of the major dimension of `B`.
-> Complex Double	Scaling factor `α` of the original `C`.
-> Ptr (Complex Double)	Pointer to a mutable matrix `C`.
-> Int	Stride of the major dimension of `C`.
-> IO ()

Perform a symmetric matrix-matrix update.

C ← α A B + β C    or    C ← α B A + β C

where A is symmetric. The matrix A must be in an unpacked format, although the routine will only access half of it as specified by the Uplo argument.

hemm Source

Arguments

:: Order	Layout of all the matrices.
-> Side	Side that `A` appears in the product.
-> Uplo	The part of `A` that is used.
-> Int	Number of rows of `C`.
-> Int	Number of columns of `C`.
-> Complex Double	Scaling factor `α` of the product.
-> Ptr (Complex Double)	Pointer to a Hermitian matrix `A`.
-> Int	Stride of the major dimension of `A`.
-> Ptr (Complex Double)	Pointer to a matrix `B`.
-> Int	Stride of the major dimension of `B`.
-> Complex Double	Scaling factor `α` of the original `C`.
-> Ptr (Complex Double)	Pointer to a mutable matrix `C`.
-> Int	Stride of the major dimension of `C`.
-> IO ()

Perform a Hermitian matrix-matrix update.

C ← α A B + β C    or    C ← α B A + β C

where A is Hermitian. The matrix A must be in an unpacked format, although the routine will only access half of it as specified by the Uplo argument.

Rank updates

syrk :: Order -> Uplo -> Transpose -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a symmetric rank-k update.

C ← α A A⊤ + β C    or    C ← α A⊤ A + β C

herk :: Order -> Uplo -> Transpose -> Int -> Int -> Double -> Ptr (Complex Double) -> Int -> Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a Hermitian rank-k update.

C ← α A A† + β C    or    C ← α A† A + β C

syr2k :: Order -> Uplo -> Transpose -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a symmetric rank-2k update.

C ← α A B⊤ + α* B A⊤ + β C    or    C ← α A⊤ B + α* B⊤ A + β C

her2k :: Order -> Uplo -> Transpose -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> Double -> Ptr (Complex Double) -> Int -> IO () Source

Perform a Hermitian rank-2k update.

C ← α A B† + α* B A† + β C    or    C ← α A† B + α* B† A + β C

Triangular operations

trmm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform a triangular matrix-matrix multiplication.

B ← α T(A) B    or    B ← α B T(A)

where A is triangular.

trsm :: Order -> Side -> Uplo -> Transpose -> Diag -> Int -> Int -> Complex Double -> Ptr (Complex Double) -> Int -> Ptr (Complex Double) -> Int -> IO () Source

Perform an inverse triangular matrix-matrix multiplication.

B ← α T(A⁻¹) B    or    B ← α B T(A⁻¹)

where A is triangular.