blas

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An interface to level 1, 2 and 3 BLAS linear algebra routines.

Documentation

Naming conventions for routines

Every routine in the BLAS library comes in four flavors, each prefixed by the letters S, D, C, and Z, respectively. Each letter indicates the format of input data:

S stands for single-precision (32-bit IEEE floating point numbers),
D stands for double-precision (64-bit IEEE floating point numbers),
C stands for complex numbers (represented by pairs of 32-bit IEEE floating point numbers),
Z stands for double complex numbers (represented by pairs of 64-bit IEEE floating point numbers)

In addition, each BLAS routine in this egg comes in three flavors:

Safe, pure

Safe routines check the sizes of their input arguments. For example, if a routine is supplied arguments that indicate that an input matrix is of dimensions M-by-N, then the argument corresponding to that matrix is checked that it is of size M * N.

Pure routines do not alter their arguments in any way. A new matrix or vector is allocated for the return value of the routine.

Safe, destructive (suffix: !)

Destructive routines can modify some or all of their arguments. They are given names ending in exclamation mark. Please consult the BLAS documentation to determine which functions modify their input arguments.

Unsafe, destructive (prefix: unsafe-, suffix: !)

Unsafe routines do not check the sizes of their input arguments. They invoke the corresponding BLAS routines directly. Unsafe routines do not have pure variants.

For example, function xGEMM (matrix-matrix multiplication) comes in the following variants:

BLAS name	Safe, pure	Safe, destructive	Unsafe, destructive
SGEMM	sgemm	sgemm!	unsafe-sgemm!
DGEMM	dgemm	dgemm!	unsafe-dgemm!
CGEMM	cgemm	cgemm!	unsafe-cgemm!
ZGEMM	zgemm	zgemm!	unsafe-zgemm!

Vector copy routines

scopy:procedure

dcopy:procedure

ccopy:procedure

zcopy:procedure: These procedures return a copy of given input SRFI-4 vector. The returned vector is allocated with the corresponding SRFI-4 constructor, and the input vector is copied to it by the corresponding BLAS copy procedure.

BLAS level 1 routines

Conventions

The BLAS level 1 procedures in this egg differ from the actual routines they invoke by the position of the vector increment arguments (INCX and INCY). In this egg, these arguments are optional; the default value of INCX and INCY is 1.

In the procedure signatures below, these optional arguments are indicated by [ and ] (square brackets).

Apply plane rotation

srot:procedure

drot:procedure

xROT applies a plane rotation matrix to a sequence of ordered pairs: (x_i , y_i), for i = 1, 2, ..., n.

X and Y are vector of dimensions (N-1) * abs(incx) + 1 and (N-1) * abs(incy) + 1, respectively.

C and S are respectively the cosine and sine of the plane of rotation.

Scale vector

sscal:procedure

dscal:procedure

cscal:procedure

zscal:procedure: xSCAL scales a vector with a scalar: x := alpha * x.

Swap the elements of two vectors

sswap:procedure

dswap:procedure

cswap:procedure

zswap:procedure: xSWAP interchanges the elements of two vectors: x <-> y.

Real vector dot product

sdot:procedure

ddot:procedure: xDOT computes the dot product of two vectors of real values: dot := x'*y = \Sum_{i=1}^{n} (x_i * y_i).

Complex vector dot product

cdotu:procedure

zdotu:procedure: xDOTU computes the dot product of two vectors of complex values: dotu := x'*y = \Sum_{i=1}^{n} (x_i * y_i).

Hermitian vector dot product

cdotc:procedure

zdotc:procedure: xDOTC computes the dot product of the conjugates of two complex vectors: dotu := conjg(x')*y = \Sum_{i=1}^{n} (conjg(x_i) * y_i), for i = 1, 2, ..., n.

Vector multiply-add

saxpy:procedure

daxpy:procedure

caxpy:procedure

zaxpy:procedure: xAXPY adds a scalar multiple of a vector to another vector: y := alpha * x + y.

Vector multiply-add with optional offset

siaxpy:procedure

diaxpy:procedure

ciaxpy:procedure

ziaxpy:procedure: xIAXPY adds a scalar multiple of a vector to another vector, where the beginning of each vector argument can be offset: y[yofs:n] := alpha * x[xofs:n] + y[yofs:n].

Euclidean norm of a vector

snrm2:procedure

dnrm2:procedure

cnrm2:procedure

znrm2:procedure: xNRM2 computes the Euclidean (L2) norm of a vector.

Sum of absolute values of the elements in a vector

sasum:procedure

dasum:procedure

casum:procedure

zasum:procedure: xASUM sums the absolute values of the elements in a vector.

Sum of absolute values of the elements in a vector

samax:procedure

damax:procedure

camax:procedure

zamax:procedure: xAMAX searches a vector for the first occurrence of its maximum absolute value, and returns the index of that element.

BLAS level 2 routines

Conventions

The BLAS level 2 procedures in this egg differ from the actual routines they invoke by the position of the leading dimension argument (LDA) and the vector increment arguments (INCX and INCY). In this egg, these arguments are optional; the default value of LDAis the largest matrix dimension, depending on the semantics of the respective operation, and the default value of INCX and INCY is 1.

In the procedure signatures below, these optional arguments are indicated by [ and ] (square brackets).

Argument ORDER is one of RowMajor or ColMajor to indicate that the input and output matrices are in row-major or column-major form, respectively.

Where present, argument TRANS can be one of NoTrans or Trans to indicate whether the input matrix is to be transposed or not.

Where present, argument UPLO can be one of Upper or Lower to indicate whether the upper or lower triangular part of an input symmetric matrix is to referenced,or to specify the type of an input triangular matrix.

Where present, argument DIAG can be one of NonUnit or Unit to indicate whether an input triangular matrix is unit triangular or not.

General matrix-vector multiply-add

sgemv:procedure

dgemv:procedure

cgemv:procedure

zgemv:procedure

xGEMV performs the matrix-vector multiply-add operation of the form y := alpha*op( A )*x + beta*y, where op( X ) is one of op( A ) = A or op( A ) = A'.

ALPHA and BETA are scalars, and A is an M x N matrix.

X is a vector of size (1 + ( N - 1 ) * abs(INCX)) when argument TRANS is NoTrans, and (1 + ( M - 1 ) * abs(INCX)) otherwise. Y is a vector of size (1 + ( M - 1 ) * abs(INCY)) when argument TRANS is NoTrans, and (1 + ( N - 1 ) * abs(INCY)) otherwise.

Banded matrix-vector multiply-add

sgbmv:procedure

dgbmv:procedure

cgbmv:procedure

zgbmv:procedure

xGBMV performs the matrix-vector multiply-add operation of the form y := alpha*op( A )*x + beta*y, where op( X ) is one of op( A ) = A or op( A ) = A'.

ALPHA and BETA are scalars, and A is an M x N banded matrix, with KL sub-diagonals and KU super-diagonals.

Hermitian matrix-vector multiply-add

chemv:procedure

zhemv:procedure

xHEMV performs the matrix-vector multiply-add operation of the form y := alpha*op( A )*x + beta*y, where op( X ) is one of op( A ) = A or op( A ) = A'.

ALPHA and BETA are scalars, and A is an N x N Hermitian matrix.

X and Y are N element vectors.

Hermitian banded matrix-vector multiply-add

chbmv:procedure

zhbmv:procedure

xHBMV performs the matrix-vector multiply-add operation of the form y := alpha*op( A )*x + beta*y, where op( X ) is one of op( A ) = A or op( A ) = A'.

ALPHA and BETA are scalars, and A is an N x N Hermitian banded matrix, with K super-diagonals.

X and Y are N element vectors.

Symmetric matrix-vector multiply-add

ssymv:procedure

dsymv:procedure

xSYMV performs matrix-vector multiply-add operation of the form y := alpha*A*x + beta*y.

ALPHA and BETA are scalars, and A is an N x N symmetric matrix.

X and Y are N element vectors.

Banded symmetric matrix-vector multiply-add

ssbmv:procedure

dsbmv:procedure

xSBMV performs matrix-vector multiply-add operation of the form y := alpha*A*B + beta*y.

ALPHA and BETA are scalars, and A is an N x N symmetric banded matrix, with K super-diagonals.

X and Y are N element vectors.

Triangular matrix-vector multiply-add

strmv:procedure

dtrmv:procedure

ctrmv:procedure

ztrmv:procedure

xTRMV performs matrix-vector multiply-add operation of the form y := alpha*op( A )*x, where op ( A ) = A or op ( A ) = A'

ALPHA and BETA are scalars, and A is an N x N upper or lower triangular matrix.

X is a vector of length (1 + (n - 1) * abs(INCX)).

Banded triangular matrix-vector multiply-add

stbmv:procedure

dtbmv:procedure

ctbmv:procedure

ztbmv:procedure

xTBMV performs matrix-vector multiply-add operation of the form y := alpha*A*B + beta*y, where op ( A ) = A or op ( A ) = A'

ALPHA and BETA are scalars, and A is an N x N upper or lower triangular banded matrix, with K+1 diagonals.

X is a vector of length (1 + (n - 1) * abs(INCX)).

Triangular matrix equation solve

strsv:procedure

dtrsv:procedure

ctrsv:procedure

ztrsv:procedure

xTRSV solves one of the systems of equations A*x = b or A'*x = b.

ALPHA and BETA are scalars, A is a upper or lower triangular matrix, and B is a N element vector.

Banded triangular matrix equation solve

stbsv:procedure

dtbsv:procedure

ctbsv:procedure

ztbsv:procedure

xTBSV solves one of the systems of equations A*x = b or A'*x = b.

ALPHA and BETA are scalars, A is a upper or lower banded triangular matrix with K+1 diagonals, and B is a N element vector.

Rank 1 operation

sger:procedure

dger:procedure

xGER performs the rank 1 operation A := alpha*x*y' + A.

ALPHA is a scalar, X is an M element vector, Y is an N element vector, and A is an M x N matrix.

Rank 1 operation with optional offset

siger:procedure

diger:procedure

xIGER performs the rank 1 operation A := alpha*x[xofs:M]*y'[yofs:N] + A.

ALPHA is a scalar, X is an M element vector, Y is an N element vector, and A is an M x N matrix.

Rank 1 operation on complex matrices and vectors

cgeru:procedure

zgeru:procedure

xGERU performs the rank 1 operation A := alpha*x*y' + A.

ALPHA is a scalar, X is an M element vector, Y is an N element vector, and A is an M x N matrix.

Rank 1 operation on complex matrices and vectors

cgerc:procedure

zgerc:procedure

xGERC performs the rank 1 operation A := alpha*x*conjg(y') + A.

ALPHA is a scalar, X is an M element vector, Y is an N element vector, and A is an M x N matrix.

Hermitian rank 1 operation

cher:procedure

zher:procedure

xHER performs the Hermitian rank 1 operation A := alpha*x*conjg(x') + A.

ALPHA is a scalar, X is an N element vector, and A is an N x N Hermitian matrix.

Hermitian rank 2 operation

cher2:procedure

zher2:procedure

xHER2 performs the Hermitian rank 2 operation A := alpha*x*conjg(y') + conjg(alpha)*y*conjg(x') + A.

ALPHA is a scalar, X and Y are N element vectors, and A is an N x N Hermitian matrix.

Symmetric rank 1 operation

ssyr:procedure

dsyr:procedure

xSYR performs the symmetric rank 1 operation A := alpha*x*x' + A.

ALPHA is a scalar, X is an N element vector, and A is an N x N symmetric matrix.

Symmetric rank 2 operation

ssyr2:procedure

dsyr2:procedure

xSYR2 performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A.

ALPHA is a scalar, X and Y are N element vectors, and A is an N x N symmetric matrix.

BLAS level 3 routines

Conventions

The BLAS level 3 procedures in this egg differ from the actual routines they invoke by the position of the leading dimension arguments (LDA, LDB, and LDC). In this egg, these arguments are optional, and their default values are set to the largest matrix dimension, depending on the semantics of the respective operation.

In the procedure signatures below, these optional arguments are indicated by [ and ] (square brackets).

Argument ORDER is one of RowMajor or ColMajor to indicate that the input and output matrices are in row-major or column-major form, respectively.

Where present, arguments TRANS, TRANSA, TRANSB can be one of NoTrans or Trans to indicate whether the respective input matrices are to be transposed or not.

Where present, argument SIDE can be one of Left or Right to indicate whether an input symmetric matrix appears on the left or right in the respective operation.

Where present, argument DIAG can be one of NonUnit or Unit to indicate whether an input triangular matrix is unit triangular or not.

General matrix multiply-add

sgemm:procedure

dgemm:procedure

cgemm:procedure

zgemm:procedure

xGEMM performs matrix-matrix multiply-add operation of the form C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X'.

ALPHA and BETA are scalars, and A, B and C are matrices, with op( A ) an M x K matrix, op( B ) a K x N matrix and C an M x N matrix.

Symmetric matrix multiply-add

ssymm:procedure

dsymm:procedure

csymm:procedure

zsymm:procedure

xSYMM performs matrix-matrix multiply-add operation of the form C := alpha*A*B + beta*C or C := alpha*B*A + beta*C.

ALPHA and BETA are scalars, A is a symmetric matrix, and B and C are M x N matrices.

Symmetric rank k operation

ssyrk:procedure

dsyrk:procedure

csyrk:procedure

zsyrk:procedure

xSYRK performs one of the symmetric rank k operations

{{C := alpha*A*A' + beta*C}} or {{C := alpha*A'*A + beta*C}}.

ALPHA and BETA are scalars, A is an N x K or K x N matrix, and C is an N x N symmetric matrix.

Hermitian rank k operation

cherk:procedure

zherk:procedure

xHERK performs one of the hermitian rank k operations C := alpha*A*conjg(A') + beta*C or C := alpha*conjg(A')*A + beta*C.

ALPHA and BETA are scalars, A is an N x K or K x N matrix, and C is an N x N hermitian matrix.

Symmetric rank 2k operation

ssyr2k:procedure

dsyr2k:procedure

csyr2k:procedure

zsyr2k:procedure

xSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B' + beta*C or C := alpha*B'*A + beta*C.

ALPHA and BETA are scalars, A and B are N x K or K x N matrices, and C is an N x N symmetric matrix.

Hermitian rank 2k operation

cher2k:procedure

zher2k:procedure

xHER2K performs one of the hermitian rank 2k operations C := alpha*A*conjg(B') + beta*C or C := alpha*conjg(B')*A + beta*C.

ALPHA and BETA are scalars, A and B are N x K or K x N matrices, and C is an N x N hermitian matrix.

Triangular matrix multiply

strmm:procedure

dtrmm:procedure

ctrmm:procedure

ztrmm:procedure

xTRMM performs matrix-matrix multiply operation of the form B := alpha*op( A )*B or B := alpha*B*op( A ).

ALPHA is a scalar, A is an upper or lower triangular matrix, and B is an M x N matrix.

Triangular matrix equation solve

strsm:procedure

dtrsm:procedure

ctrsm:procedure

ztrsm:procedure

xTRSM solves one of the matrix equations

{{op( A )*X = alpha*B}} or {{X*op( A ) = alpha*B}}.

op( A ) is one of op( A ) = A or op( A ) = A'.

ALPHA and BETA are scalars, A is a upper or lower triangular matrix, and B is a M x N matrix.

Examples

(use srfi-4 blas)

(define order ColMajor)
(define transa NoTrans)

(define m 4)
(define n 4)

(define alpha 1)
(define beta 0)

(define a				; column-major order!
  (f64vector 1 2 3 4
	     1 1 1 1
	     3 4 5 6
	     5 6 7 8) )

(define x (f64vector 1 2 1 1))
(define y (f64vector 0 0 0 0))
   
(dgemv! order transa m n alpha a x beta y)

(print y)

4.1: Fixed use of memq [thanks to Moritz Heidkamp]
4.0: Using bind instead of easyffi
3.1: Updated test script to return proper exit code
3.0: Eliminated reduntant blas: prefix from names of exported symbols
2.8: Eliminated use of noop
2.7: Switched to wiki documentation
2.6: Ported to Chicken 4
2.5: Build script updated for better cross-platform compatibility
2.4: Added iger procedures; fixed a bug in the default arguments of level 2 routines
2.3: Added iaxpy procedures; fixed a bug in the default arguments of level 1 routines
2.2: Fixed a bug in the renaming of C routines
2.1: Added eggdoc property to meta file
2.0: An overhaul of the library to introduce safe, unsafe, and pure variants of each routine
1.8: Added icopy procedures [by Ivan Raikov]
1.7: Support for Mac OS X added [by Will Farr]
1.6: Fixed bug in blas library test code
1.5: Added support for CLAPACK [by Ivan Raikov]
1.4: Added support for atlas CBLAS library [by Stu Glaser]
1.3: Tries to find a proper CBLAS library (currently only GSL)
1.2: Adapted to new FFI macro-names
1.1: Adapted to new setup scheme

License

Copyright (c) 2003-2006, Felix L. Winkelmann 
Copyright (c) 2007-2014 Ivan Raikov

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

  Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

  Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.

  Neither the name of the author nor the names of its contributors may
be used to endorse or promote products derived from this software
without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE.

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