lalg_basic_oct_m Module Reference

Data Types
interface	lalg_axpy
	constant times a vector plus a vector More...
interface	lalg_copy
	Copies a vector x, to a vector y. More...
interface	lalg_gemm
	Matrix-matrix multiplication plus matrix. More...
interface	lalg_gemm_cc
	lalg_gemm with both the (Hermitian) transpose of A and B. More...
interface	lalg_gemm_cn
	The same as above but with (Hermitian) transpose of A. More...
interface	lalg_gemm_nc
	The same as lalg_gemm but with (Hermitian) transpose of B. More...
interface	lalg_gemv
interface	lalg_nrm2
	Returns the euclidean norm of a vector. More...
interface	lalg_scal
	scales a vector by a constant More...
interface	lalg_swap
	swap two vectors More...
interface	lalg_symm
	The following matrix multiplications all expect upper triangular matrices for a. For real matrices, \(A = A^T\), for complex matrices \(A = A^H\). More...
interface	lalg_symv
	Matrix-vector multiplication plus vector. More...
interface	lalg_trmm
	Matrix-matrix multiplication. More...

Functions/Subroutines
subroutine	dgemm_simple (a, b, c, transa, transb, alpha, beta)
	GEMM with a simplified API for two matrices of consistent shape and type. More...
subroutine	swap_1_2 (n1, dx, dy)
subroutine	swap_2_2 (n1, n2, dx, dy)
subroutine	swap_3_2 (n1, n2, n3, dx, dy)
subroutine	swap_4_2 (n1, n2, n3, n4, dx, dy)
subroutine	scal_1_2 (n1, da, dx)
subroutine	scal_2_2 (n1, n2, da, dx)
subroutine	scal_3_2 (n1, n2, n3, da, dx)
subroutine	scal_4_2 (n1, n2, n3, n4, da, dx)
subroutine	axpy_1_2 (n1, da, dx, dy)
subroutine	axpy_2_2 (n1, n2, da, dx, dy)
subroutine	axpy_3_2 (n1, n2, n3, da, dx, dy)
subroutine	axpy_4_2 (n1, n2, n3, n4, da, dx, dy)
subroutine	copy_1_2 (n1, dx, dy)
subroutine	copy_2_2 (n1, n2, dx, dy)
subroutine	copy_3_2 (n1, n2, n3, dx, dy)
subroutine	copy_4_2 (n1, n2, n3, n4, dx, dy)
real(real64) function	nrm2_2 (n, dx)
subroutine	symv_1_2 (n, alpha, a, x, beta, y)
subroutine	symv_2_2 (n1, n2, alpha, a, x, beta, y)
subroutine	gemv_1_2 (m, n, alpha, a, x, beta, y)
subroutine	gemv_2_2 (m1, m2, n, alpha, a, x, beta, y)
subroutine	gemm_1_2 (m, n, k, alpha, a, b, beta, c)
subroutine	gemm_2_2 (m1, m2, n, k, alpha, a, b, beta, c)
subroutine	gemm_cn_1_2 (m, n, k, alpha, a, b, beta, c)
	The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real. More...
subroutine	gemm_cn_2_2 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_nc_1_2 (m, n, k, alpha, a, b, beta, c)
	The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real. More...
subroutine	gemm_nc_2_2 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_cc_1_2 (m, n, k, alpha, a, b, beta, c)
	GEMM when both a and b are (Hermitian) transposes. More...
subroutine	symm_1_2 (m, n, side, alpha, a, b, beta, c)
	The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H. More...
subroutine	trmm_1_2 (m, n, uplo, transa, side, alpha, a, b)
subroutine	swap_1_4 (n1, dx, dy)
subroutine	swap_2_4 (n1, n2, dx, dy)
subroutine	swap_3_4 (n1, n2, n3, dx, dy)
subroutine	swap_4_4 (n1, n2, n3, n4, dx, dy)
subroutine	scal_1_4 (n1, da, dx)
subroutine	scal_2_4 (n1, n2, da, dx)
subroutine	scal_3_4 (n1, n2, n3, da, dx)
subroutine	scal_4_4 (n1, n2, n3, n4, da, dx)
subroutine	scal_5_4 (n1, da, dx)
subroutine	scal_6_4 (n1, n2, da, dx)
subroutine	axpy_1_4 (n1, da, dx, dy)
subroutine	axpy_2_4 (n1, n2, da, dx, dy)
subroutine	axpy_3_4 (n1, n2, n3, da, dx, dy)
subroutine	axpy_4_4 (n1, n2, n3, n4, da, dx, dy)
subroutine	axpy_5_4 (n1, da, dx, dy)
subroutine	axpy_6_4 (n1, n2, da, dx, dy)
subroutine	axpy_7_4 (n1, n2, n3, da, dx, dy)
subroutine	copy_1_4 (n1, dx, dy)
subroutine	copy_2_4 (n1, n2, dx, dy)
subroutine	copy_3_4 (n1, n2, n3, dx, dy)
subroutine	copy_4_4 (n1, n2, n3, n4, dx, dy)
real(real64) function	nrm2_4 (n, dx)
subroutine	symv_1_4 (n, alpha, a, x, beta, y)
subroutine	symv_2_4 (n1, n2, alpha, a, x, beta, y)
subroutine	gemv_1_4 (m, n, alpha, a, x, beta, y)
subroutine	gemv_2_4 (m1, m2, n, alpha, a, x, beta, y)
subroutine	gemm_1_4 (m, n, k, alpha, a, b, beta, c)
subroutine	gemm_2_4 (m1, m2, n, k, alpha, a, b, beta, c)
subroutine	gemm_cn_1_4 (m, n, k, alpha, a, b, beta, c)
	The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real. More...
subroutine	gemm_cn_2_4 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_nc_1_4 (m, n, k, alpha, a, b, beta, c)
	The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real. More...
subroutine	gemm_nc_2_4 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_cc_1_4 (m, n, k, alpha, a, b, beta, c)
	GEMM when both a and b are (Hermitian) transposes. More...
subroutine	symm_1_4 (m, n, side, alpha, a, b, beta, c)
	The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H. More...
subroutine	trmm_1_4 (m, n, uplo, transa, side, alpha, a, b)
subroutine	swap_1_1 (n1, dx, dy)
subroutine	swap_2_1 (n1, n2, dx, dy)
subroutine	swap_3_1 (n1, n2, n3, dx, dy)
subroutine	swap_4_1 (n1, n2, n3, n4, dx, dy)
subroutine	scal_1_1 (n1, da, dx)
subroutine	scal_2_1 (n1, n2, da, dx)
subroutine	scal_3_1 (n1, n2, n3, da, dx)
subroutine	scal_4_1 (n1, n2, n3, n4, da, dx)
subroutine	axpy_1_1 (n1, da, dx, dy)
subroutine	axpy_2_1 (n1, n2, da, dx, dy)
subroutine	axpy_3_1 (n1, n2, n3, da, dx, dy)
subroutine	axpy_4_1 (n1, n2, n3, n4, da, dx, dy)
subroutine	copy_1_1 (n1, dx, dy)
subroutine	copy_2_1 (n1, n2, dx, dy)
subroutine	copy_3_1 (n1, n2, n3, dx, dy)
subroutine	copy_4_1 (n1, n2, n3, n4, dx, dy)
real(real32) function	nrm2_1 (n, dx)
subroutine	symv_1_1 (n, alpha, a, x, beta, y)
subroutine	symv_2_1 (n1, n2, alpha, a, x, beta, y)
subroutine	gemv_1_1 (m, n, alpha, a, x, beta, y)
subroutine	gemv_2_1 (m1, m2, n, alpha, a, x, beta, y)
subroutine	gemm_1_1 (m, n, k, alpha, a, b, beta, c)
subroutine	gemm_2_1 (m1, m2, n, k, alpha, a, b, beta, c)
subroutine	gemm_cn_1_1 (m, n, k, alpha, a, b, beta, c)
	The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real. More...
subroutine	gemm_cn_2_1 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_nc_1_1 (m, n, k, alpha, a, b, beta, c)
	The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real. More...
subroutine	gemm_nc_2_1 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_cc_1_1 (m, n, k, alpha, a, b, beta, c)
	GEMM when both a and b are (Hermitian) transposes. More...
subroutine	symm_1_1 (m, n, side, alpha, a, b, beta, c)
	The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H. More...
subroutine	trmm_1_1 (m, n, uplo, transa, side, alpha, a, b)
subroutine	swap_1_3 (n1, dx, dy)
subroutine	swap_2_3 (n1, n2, dx, dy)
subroutine	swap_3_3 (n1, n2, n3, dx, dy)
subroutine	swap_4_3 (n1, n2, n3, n4, dx, dy)
subroutine	scal_1_3 (n1, da, dx)
subroutine	scal_2_3 (n1, n2, da, dx)
subroutine	scal_3_3 (n1, n2, n3, da, dx)
subroutine	scal_4_3 (n1, n2, n3, n4, da, dx)
subroutine	scal_5_3 (n1, da, dx)
subroutine	scal_6_3 (n1, n2, da, dx)
subroutine	axpy_1_3 (n1, da, dx, dy)
subroutine	axpy_2_3 (n1, n2, da, dx, dy)
subroutine	axpy_3_3 (n1, n2, n3, da, dx, dy)
subroutine	axpy_4_3 (n1, n2, n3, n4, da, dx, dy)
subroutine	axpy_5_3 (n1, da, dx, dy)
subroutine	axpy_6_3 (n1, n2, da, dx, dy)
subroutine	axpy_7_3 (n1, n2, n3, da, dx, dy)
subroutine	copy_1_3 (n1, dx, dy)
subroutine	copy_2_3 (n1, n2, dx, dy)
subroutine	copy_3_3 (n1, n2, n3, dx, dy)
subroutine	copy_4_3 (n1, n2, n3, n4, dx, dy)
real(real32) function	nrm2_3 (n, dx)
subroutine	symv_1_3 (n, alpha, a, x, beta, y)
subroutine	symv_2_3 (n1, n2, alpha, a, x, beta, y)
subroutine	gemv_1_3 (m, n, alpha, a, x, beta, y)
subroutine	gemv_2_3 (m1, m2, n, alpha, a, x, beta, y)
subroutine	gemm_1_3 (m, n, k, alpha, a, b, beta, c)
subroutine	gemm_2_3 (m1, m2, n, k, alpha, a, b, beta, c)
subroutine	gemm_cn_1_3 (m, n, k, alpha, a, b, beta, c)
	The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real. More...
subroutine	gemm_cn_2_3 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_nc_1_3 (m, n, k, alpha, a, b, beta, c)
	The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real. More...
subroutine	gemm_nc_2_3 (m1, m2, n1, n2, k, alpha, a, b, beta, c)
subroutine	gemm_cc_1_3 (m, n, k, alpha, a, b, beta, c)
	GEMM when both a and b are (Hermitian) transposes. More...
subroutine	symm_1_3 (m, n, side, alpha, a, b, beta, c)
	The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H. More...
subroutine	trmm_1_3 (m, n, uplo, transa, side, alpha, a, b)

Function/Subroutine Documentation

dgemm_simple()

subroutine lalg_basic_oct_m::dgemm_simple ( real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:,:), intent(in), contiguous  b, real(real64), dimension(:,:), intent(inout), contiguous  c, character(len=1), intent(in), optional  transa, character(len=1), intent(in), optional  transb, real(real64), intent(in), optional  alpha, real(real64), intent(in), optional  beta  )

private

GEMM with a simplified API for two matrices of consistent shape and type.

GEMM 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 ) = x**t

operating on all elements of both matrices. If all defaults are used, the routine performs \(C = A B\). See the official [lapack](https: documentation for more details.

Parameters

[in,out]	c	If not summing to c, it does not need to be
[in]	transb	Transpose a and b
[in]	alpha	Scale the product, op( A )*op( B )
[in]	beta	Scale input value of c.

Definition at line 355 of file lalg_basic.F90.

swap_1_2()

subroutine lalg_basic_oct_m::swap_1_2 ( integer, intent(in)  n1, real(real64), dimension(:), intent(inout), contiguous  dx, real(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

BLAS level I

Definition at line 442 of file lalg_basic.F90.

swap_2_2()

subroutine lalg_basic_oct_m::swap_2_2 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), dimension(:,:), intent(inout), contiguous  dx, real(real64), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 459 of file lalg_basic.F90.

swap_3_2()

subroutine lalg_basic_oct_m::swap_3_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real64), dimension(:,:,:), intent(inout), contiguous  dx, real(real64), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 485 of file lalg_basic.F90.

swap_4_2()

subroutine lalg_basic_oct_m::swap_4_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real64), dimension(:,:,:,:), intent(inout), contiguous  dx, real(real64), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 506 of file lalg_basic.F90.

scal_1_2()

subroutine lalg_basic_oct_m::scal_1_2 ( integer, intent(in)  n1, real(real64), intent(in)  da, real(real64), dimension(:), intent(inout), contiguous  dx  )

private

---

scales a vector by a constant

Definition at line 533 of file lalg_basic.F90.

scal_2_2()

subroutine lalg_basic_oct_m::scal_2_2 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), intent(in)  da, real(real64), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 550 of file lalg_basic.F90.

scal_3_2()

subroutine lalg_basic_oct_m::scal_3_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real64), intent(in)  da, real(real64), dimension(:, :, :), intent(inout), contiguous  dx  )

private

Definition at line 575 of file lalg_basic.F90.

scal_4_2()

subroutine lalg_basic_oct_m::scal_4_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real64), intent(in)  da, real(real64), dimension(:, :, :, :), intent(inout), contiguous  dx  )

private

Definition at line 594 of file lalg_basic.F90.

axpy_1_2()

subroutine lalg_basic_oct_m::axpy_1_2 ( integer, intent(in)  n1, real(real64), intent(in)  da, real(real64), dimension(:), intent(in), contiguous  dx, real(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

constant times a vector plus a vector

Definition at line 618 of file lalg_basic.F90.

axpy_2_2()

subroutine lalg_basic_oct_m::axpy_2_2 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), intent(in)  da, real(real64), dimension(:, :), intent(in), contiguous  dx, real(real64), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 647 of file lalg_basic.F90.

axpy_3_2()

subroutine lalg_basic_oct_m::axpy_3_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real64), intent(in)  da, real(real64), dimension(:, :, :), intent(in), contiguous  dx, real(real64), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 686 of file lalg_basic.F90.

axpy_4_2()

subroutine lalg_basic_oct_m::axpy_4_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real64), intent(in)  da, real(real64), dimension(:, :, :, :), intent(in), contiguous  dx, real(real64), dimension(:, :, :, :), intent(inout), contiguous  dy  )

private

Definition at line 718 of file lalg_basic.F90.

copy_1_2()

subroutine lalg_basic_oct_m::copy_1_2 ( integer, intent(in)  n1, real(real64), dimension(:), intent(in), contiguous  dx, real(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

Copies a vector x, to a vector y

Definition at line 756 of file lalg_basic.F90.

copy_2_2()

subroutine lalg_basic_oct_m::copy_2_2 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), dimension(:,:), intent(in), contiguous  dx, real(real64), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 779 of file lalg_basic.F90.

copy_3_2()

subroutine lalg_basic_oct_m::copy_3_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real64), dimension(:,:,:), intent(in), contiguous  dx, real(real64), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 810 of file lalg_basic.F90.

copy_4_2()

subroutine lalg_basic_oct_m::copy_4_2 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real64), dimension(:,:,:,:), intent(in), contiguous  dx, real(real64), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 835 of file lalg_basic.F90.

nrm2_2()

real(real64) function lalg_basic_oct_m::nrm2_2 ( integer, intent(in)  n, real(real64), dimension(:), intent(in)  dx  )

private

---

Returns the euclidean norm of a vector

Definition at line 866 of file lalg_basic.F90.

symv_1_2()

subroutine lalg_basic_oct_m::symv_1_2 ( integer, intent(in)  n, real(real64), intent(in)  alpha, real(real64), dimension(:, :), intent(in), contiguous  a, real(real64), dimension(:), intent(in), contiguous  x, real(real64), intent(in)  beta, real(real64), dimension(:), intent(inout), contiguous  y  )

private

---

BLAS level II

Matrix-vector multiplication plus vector.

Definition at line 894 of file lalg_basic.F90.

symv_2_2()

subroutine lalg_basic_oct_m::symv_2_2 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), intent(in)  alpha, real(real64), dimension(:, :, :), intent(in), contiguous  a, real(real64), dimension(:), intent(in), contiguous  x, real(real64), intent(in)  beta, real(real64), dimension(:, :), intent(inout), contiguous  y  )

private

Definition at line 912 of file lalg_basic.F90.

gemv_1_2()

subroutine lalg_basic_oct_m::gemv_1_2 ( integer, intent(in)  m, integer, intent(in)  n, real(real64), intent(in)  alpha, real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:), intent(in), contiguous  x, real(real64), intent(in)  beta, real(real64), dimension(:), intent(inout), contiguous  y  )

private

Definition at line 934 of file lalg_basic.F90.

gemv_2_2()

subroutine lalg_basic_oct_m::gemv_2_2 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, real(real64), intent(in)  alpha, real(real64), dimension(:,:,:), intent(in), contiguous  a, real(real64), dimension(:), intent(in), contiguous  x, real(real64), intent(in)  beta, real(real64), dimension(:,:), intent(inout), contiguous  y  )

private

Definition at line 956 of file lalg_basic.F90.

gemm_1_2()

subroutine lalg_basic_oct_m::gemm_1_2 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:,:), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:,:), intent(inout), contiguous  c  )

private

---

BLAS level III

Matrix-matrix multiplication plus matrix.

Definition at line 989 of file lalg_basic.F90.

gemm_2_2()

subroutine lalg_basic_oct_m::gemm_2_2 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:, :, :), intent(in), contiguous  a, real(real64), dimension(:, :), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:, :, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(m1, m2, k)
[in]	b	b(k, n)
[in,out]	c	c(m1, m2, n)

Definition at line 1010 of file lalg_basic.F90.

gemm_cn_1_2()

subroutine lalg_basic_oct_m::gemm_cn_1_2 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:,:), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:,:), intent(inout), contiguous  c  )

private

The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real.

Parameters

[in]	a	a(k, m)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 1036 of file lalg_basic.F90.

gemm_cn_2_2()

subroutine lalg_basic_oct_m::gemm_cn_2_2 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:, :, :), intent(in), contiguous  a, real(real64), dimension(:, :, :), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 1057 of file lalg_basic.F90.

gemm_nc_1_2()

subroutine lalg_basic_oct_m::gemm_nc_1_2 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:,:), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:,:), intent(inout), contiguous  c  )

private

The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real.

Parameters

[in]	a	a(m, k)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 1084 of file lalg_basic.F90.

gemm_nc_2_2()

subroutine lalg_basic_oct_m::gemm_nc_2_2 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:, :, :), intent(in), contiguous  a, real(real64), dimension(:, :, :), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 1105 of file lalg_basic.F90.

gemm_cc_1_2()

subroutine lalg_basic_oct_m::gemm_cc_1_2 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real64), intent(in)  alpha, real(real64), dimension(:,:), intent(in), contiguous  a, real(real64), dimension(:,:), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:,:), intent(inout), contiguous  c  )

private

GEMM when both a and b are (Hermitian) transposes.

\[ \mathbf{C} = \mathbf{A}^\dagger \mathbf{B}^\dagger \]

Note that one can equivalently perform:

\[ \mathbf{C} = \left[\mathbf{B} \mathbf{A} \right]^\dagger \]

It might be more efficient to replace the implementation with the second operation defined above - requires testing.

Parameters

[in]	a	a(k, m)
[in]	b	b(n, k)
[in,out]	c	c(m, n)

Definition at line 1143 of file lalg_basic.F90.

symm_1_2()

subroutine lalg_basic_oct_m::symm_1_2 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  side, real(real64), intent(in)  alpha, real(real64), dimension(:, :), intent(in), contiguous  a, real(real64), dimension(:, :), intent(in), contiguous  b, real(real64), intent(in)  beta, real(real64), dimension(:, :), intent(inout), contiguous  c  )

private

The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H.

Definition at line 1168 of file lalg_basic.F90.

trmm_1_2()

subroutine lalg_basic_oct_m::trmm_1_2 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  uplo, character(1), intent(in)  transa, character(1), intent(in)  side, real(real64), intent(in)  alpha, real(real64), dimension(:, :), intent(in), contiguous  a, real(real64), dimension(:, :), intent(inout), contiguous  b  )

private

---

Matrix-matrix multiplication.

Definition at line 1200 of file lalg_basic.F90.

swap_1_4()

subroutine lalg_basic_oct_m::swap_1_4 ( integer, intent(in)  n1, complex(real64), dimension(:), intent(inout), contiguous  dx, complex(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

BLAS level I

Definition at line 1275 of file lalg_basic.F90.

swap_2_4()

subroutine lalg_basic_oct_m::swap_2_4 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real64), dimension(:,:), intent(inout), contiguous  dx, complex(real64), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 1292 of file lalg_basic.F90.

swap_3_4()

subroutine lalg_basic_oct_m::swap_3_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real64), dimension(:,:,:), intent(inout), contiguous  dx, complex(real64), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 1318 of file lalg_basic.F90.

swap_4_4()

subroutine lalg_basic_oct_m::swap_4_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real64), dimension(:,:,:,:), intent(inout), contiguous  dx, complex(real64), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 1339 of file lalg_basic.F90.

scal_1_4()

subroutine lalg_basic_oct_m::scal_1_4 ( integer, intent(in)  n1, complex(real64), intent(in)  da, complex(real64), dimension(:), intent(inout), contiguous  dx  )

private

---

scales a vector by a constant

Definition at line 1366 of file lalg_basic.F90.

scal_2_4()

subroutine lalg_basic_oct_m::scal_2_4 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real64), intent(in)  da, complex(real64), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 1383 of file lalg_basic.F90.

scal_3_4()

subroutine lalg_basic_oct_m::scal_3_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real64), intent(in)  da, complex(real64), dimension(:, :, :), intent(inout), contiguous  dx  )

private

Definition at line 1408 of file lalg_basic.F90.

scal_4_4()

subroutine lalg_basic_oct_m::scal_4_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real64), intent(in)  da, complex(real64), dimension(:, :, :, :), intent(inout), contiguous  dx  )

private

Definition at line 1427 of file lalg_basic.F90.

scal_5_4()

subroutine lalg_basic_oct_m::scal_5_4 ( integer, intent(in)  n1, real(real64), intent(in)  da, complex(real64), dimension(:), intent(inout), contiguous  dx  )

private

Definition at line 1448 of file lalg_basic.F90.

scal_6_4()

subroutine lalg_basic_oct_m::scal_6_4 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), intent(in)  da, complex(real64), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 1465 of file lalg_basic.F90.

axpy_1_4()

subroutine lalg_basic_oct_m::axpy_1_4 ( integer, intent(in)  n1, complex(real64), intent(in)  da, complex(real64), dimension(:), intent(in), contiguous  dx, complex(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

constant times a vector plus a vector

Definition at line 1496 of file lalg_basic.F90.

axpy_2_4()

subroutine lalg_basic_oct_m::axpy_2_4 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real64), intent(in)  da, complex(real64), dimension(:, :), intent(in), contiguous  dx, complex(real64), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 1525 of file lalg_basic.F90.

axpy_3_4()

subroutine lalg_basic_oct_m::axpy_3_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real64), intent(in)  da, complex(real64), dimension(:, :, :), intent(in), contiguous  dx, complex(real64), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 1564 of file lalg_basic.F90.

axpy_4_4()

subroutine lalg_basic_oct_m::axpy_4_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real64), intent(in)  da, complex(real64), dimension(:, :, :, :), intent(in), contiguous  dx, complex(real64), dimension(:, :, :, :), intent(inout), contiguous  dy  )

private

Definition at line 1596 of file lalg_basic.F90.

axpy_5_4()

subroutine lalg_basic_oct_m::axpy_5_4 ( integer, intent(in)  n1, real(real64), intent(in)  da, complex(real64), dimension(:), intent(in), contiguous  dx, complex(real64), dimension(:), intent(inout), contiguous  dy  )

private

Definition at line 1631 of file lalg_basic.F90.

axpy_6_4()

subroutine lalg_basic_oct_m::axpy_6_4 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real64), intent(in)  da, complex(real64), dimension(:, :), intent(in), contiguous  dx, complex(real64), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 1656 of file lalg_basic.F90.

axpy_7_4()

subroutine lalg_basic_oct_m::axpy_7_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real64), intent(in)  da, complex(real64), dimension(:, :, :), intent(in), contiguous  dx, complex(real64), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 1692 of file lalg_basic.F90.

copy_1_4()

subroutine lalg_basic_oct_m::copy_1_4 ( integer, intent(in)  n1, complex(real64), dimension(:), intent(in), contiguous  dx, complex(real64), dimension(:), intent(inout), contiguous  dy  )

private

---

Copies a vector x, to a vector y

Definition at line 1725 of file lalg_basic.F90.

copy_2_4()

subroutine lalg_basic_oct_m::copy_2_4 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real64), dimension(:,:), intent(in), contiguous  dx, complex(real64), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 1748 of file lalg_basic.F90.

copy_3_4()

subroutine lalg_basic_oct_m::copy_3_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real64), dimension(:,:,:), intent(in), contiguous  dx, complex(real64), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 1779 of file lalg_basic.F90.

copy_4_4()

subroutine lalg_basic_oct_m::copy_4_4 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real64), dimension(:,:,:,:), intent(in), contiguous  dx, complex(real64), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 1804 of file lalg_basic.F90.

nrm2_4()

real(real64) function lalg_basic_oct_m::nrm2_4 ( integer, intent(in)  n, complex(real64), dimension(:), intent(in)  dx  )

private

---

Returns the euclidean norm of a vector

Definition at line 1835 of file lalg_basic.F90.

symv_1_4()

subroutine lalg_basic_oct_m::symv_1_4 ( integer, intent(in)  n, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :), intent(in), contiguous  a, complex(real64), dimension(:), intent(in), contiguous  x, complex(real64), intent(in)  beta, complex(real64), dimension(:), intent(inout), contiguous  y  )

private

---

BLAS level II

Matrix-vector multiplication plus vector.

Definition at line 1863 of file lalg_basic.F90.

symv_2_4()

subroutine lalg_basic_oct_m::symv_2_4 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :, :), intent(in), contiguous  a, complex(real64), dimension(:), intent(in), contiguous  x, complex(real64), intent(in)  beta, complex(real64), dimension(:, :), intent(inout), contiguous  y  )

private

Definition at line 1881 of file lalg_basic.F90.

gemv_1_4()

subroutine lalg_basic_oct_m::gemv_1_4 ( integer, intent(in)  m, integer, intent(in)  n, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:), intent(in), contiguous  a, complex(real64), dimension(:), intent(in), contiguous  x, complex(real64), intent(in)  beta, complex(real64), dimension(:), intent(inout), contiguous  y  )

private

Definition at line 1903 of file lalg_basic.F90.

gemv_2_4()

subroutine lalg_basic_oct_m::gemv_2_4 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:,:), intent(in), contiguous  a, complex(real64), dimension(:), intent(in), contiguous  x, complex(real64), intent(in)  beta, complex(real64), dimension(:,:), intent(inout), contiguous  y  )

private

Definition at line 1925 of file lalg_basic.F90.

gemm_1_4()

subroutine lalg_basic_oct_m::gemm_1_4 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:), intent(in), contiguous  a, complex(real64), dimension(:,:), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:,:), intent(inout), contiguous  c  )

private

---

BLAS level III

Matrix-matrix multiplication plus matrix.

Definition at line 1958 of file lalg_basic.F90.

gemm_2_4()

subroutine lalg_basic_oct_m::gemm_2_4 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :, :), intent(in), contiguous  a, complex(real64), dimension(:, :), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:, :, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(m1, m2, k)
[in]	b	b(k, n)
[in,out]	c	c(m1, m2, n)

Definition at line 1979 of file lalg_basic.F90.

gemm_cn_1_4()

subroutine lalg_basic_oct_m::gemm_cn_1_4 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:), intent(in), contiguous  a, complex(real64), dimension(:,:), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:,:), intent(inout), contiguous  c  )

private

The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real.

Parameters

[in]	a	a(k, m)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 2005 of file lalg_basic.F90.

gemm_cn_2_4()

subroutine lalg_basic_oct_m::gemm_cn_2_4 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :, :), intent(in), contiguous  a, complex(real64), dimension(:, :, :), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 2026 of file lalg_basic.F90.

gemm_nc_1_4()

subroutine lalg_basic_oct_m::gemm_nc_1_4 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:), intent(in), contiguous  a, complex(real64), dimension(:,:), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:,:), intent(inout), contiguous  c  )

private

The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real.

Parameters

[in]	a	a(m, k)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 2053 of file lalg_basic.F90.

gemm_nc_2_4()

subroutine lalg_basic_oct_m::gemm_nc_2_4 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :, :), intent(in), contiguous  a, complex(real64), dimension(:, :, :), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 2074 of file lalg_basic.F90.

gemm_cc_1_4()

subroutine lalg_basic_oct_m::gemm_cc_1_4 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real64), intent(in)  alpha, complex(real64), dimension(:,:), intent(in), contiguous  a, complex(real64), dimension(:,:), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:,:), intent(inout), contiguous  c  )

private

GEMM when both a and b are (Hermitian) transposes.

\[ \mathbf{C} = \mathbf{A}^\dagger \mathbf{B}^\dagger \]

Note that one can equivalently perform:

\[ \mathbf{C} = \left[\mathbf{B} \mathbf{A} \right]^\dagger \]

It might be more efficient to replace the implementation with the second operation defined above - requires testing.

Parameters

[in]	a	a(k, m)
[in]	b	b(n, k)
[in,out]	c	c(m, n)

Definition at line 2112 of file lalg_basic.F90.

symm_1_4()

subroutine lalg_basic_oct_m::symm_1_4 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  side, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :), intent(in), contiguous  a, complex(real64), dimension(:, :), intent(in), contiguous  b, complex(real64), intent(in)  beta, complex(real64), dimension(:, :), intent(inout), contiguous  c  )

private

The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H.

Definition at line 2137 of file lalg_basic.F90.

trmm_1_4()

subroutine lalg_basic_oct_m::trmm_1_4 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  uplo, character(1), intent(in)  transa, character(1), intent(in)  side, complex(real64), intent(in)  alpha, complex(real64), dimension(:, :), intent(in), contiguous  a, complex(real64), dimension(:, :), intent(inout), contiguous  b  )

private

---

Matrix-matrix multiplication.

Definition at line 2169 of file lalg_basic.F90.

swap_1_1()

subroutine lalg_basic_oct_m::swap_1_1 ( integer, intent(in)  n1, real(real32), dimension(:), intent(inout), contiguous  dx, real(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

BLAS level I

Definition at line 2244 of file lalg_basic.F90.

swap_2_1()

subroutine lalg_basic_oct_m::swap_2_1 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), dimension(:,:), intent(inout), contiguous  dx, real(real32), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 2261 of file lalg_basic.F90.

swap_3_1()

subroutine lalg_basic_oct_m::swap_3_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real32), dimension(:,:,:), intent(inout), contiguous  dx, real(real32), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 2287 of file lalg_basic.F90.

swap_4_1()

subroutine lalg_basic_oct_m::swap_4_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real32), dimension(:,:,:,:), intent(inout), contiguous  dx, real(real32), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 2308 of file lalg_basic.F90.

scal_1_1()

subroutine lalg_basic_oct_m::scal_1_1 ( integer, intent(in)  n1, real(real32), intent(in)  da, real(real32), dimension(:), intent(inout), contiguous  dx  )

private

---

scales a vector by a constant

Definition at line 2335 of file lalg_basic.F90.

scal_2_1()

subroutine lalg_basic_oct_m::scal_2_1 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), intent(in)  da, real(real32), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 2352 of file lalg_basic.F90.

scal_3_1()

subroutine lalg_basic_oct_m::scal_3_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real32), intent(in)  da, real(real32), dimension(:, :, :), intent(inout), contiguous  dx  )

private

Definition at line 2377 of file lalg_basic.F90.

scal_4_1()

subroutine lalg_basic_oct_m::scal_4_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real32), intent(in)  da, real(real32), dimension(:, :, :, :), intent(inout), contiguous  dx  )

private

Definition at line 2396 of file lalg_basic.F90.

axpy_1_1()

subroutine lalg_basic_oct_m::axpy_1_1 ( integer, intent(in)  n1, real(real32), intent(in)  da, real(real32), dimension(:), intent(in), contiguous  dx, real(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

constant times a vector plus a vector

Definition at line 2420 of file lalg_basic.F90.

axpy_2_1()

subroutine lalg_basic_oct_m::axpy_2_1 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), intent(in)  da, real(real32), dimension(:, :), intent(in), contiguous  dx, real(real32), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 2449 of file lalg_basic.F90.

axpy_3_1()

subroutine lalg_basic_oct_m::axpy_3_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real32), intent(in)  da, real(real32), dimension(:, :, :), intent(in), contiguous  dx, real(real32), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 2488 of file lalg_basic.F90.

axpy_4_1()

subroutine lalg_basic_oct_m::axpy_4_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real32), intent(in)  da, real(real32), dimension(:, :, :, :), intent(in), contiguous  dx, real(real32), dimension(:, :, :, :), intent(inout), contiguous  dy  )

private

Definition at line 2520 of file lalg_basic.F90.

copy_1_1()

subroutine lalg_basic_oct_m::copy_1_1 ( integer, intent(in)  n1, real(real32), dimension(:), intent(in), contiguous  dx, real(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

Copies a vector x, to a vector y

Definition at line 2558 of file lalg_basic.F90.

copy_2_1()

subroutine lalg_basic_oct_m::copy_2_1 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), dimension(:,:), intent(in), contiguous  dx, real(real32), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 2581 of file lalg_basic.F90.

copy_3_1()

subroutine lalg_basic_oct_m::copy_3_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real32), dimension(:,:,:), intent(in), contiguous  dx, real(real32), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 2612 of file lalg_basic.F90.

copy_4_1()

subroutine lalg_basic_oct_m::copy_4_1 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, real(real32), dimension(:,:,:,:), intent(in), contiguous  dx, real(real32), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 2637 of file lalg_basic.F90.

nrm2_1()

real(real32) function lalg_basic_oct_m::nrm2_1 ( integer, intent(in)  n, real(real32), dimension(:), intent(in)  dx  )

private

---

Returns the euclidean norm of a vector

Definition at line 2668 of file lalg_basic.F90.

symv_1_1()

subroutine lalg_basic_oct_m::symv_1_1 ( integer, intent(in)  n, real(real32), intent(in)  alpha, real(real32), dimension(:, :), intent(in), contiguous  a, real(real32), dimension(:), intent(in), contiguous  x, real(real32), intent(in)  beta, real(real32), dimension(:), intent(inout), contiguous  y  )

private

---

BLAS level II

Matrix-vector multiplication plus vector.

Definition at line 2696 of file lalg_basic.F90.

symv_2_1()

subroutine lalg_basic_oct_m::symv_2_1 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), intent(in)  alpha, real(real32), dimension(:, :, :), intent(in), contiguous  a, real(real32), dimension(:), intent(in), contiguous  x, real(real32), intent(in)  beta, real(real32), dimension(:, :), intent(inout), contiguous  y  )

private

Definition at line 2714 of file lalg_basic.F90.

gemv_1_1()

subroutine lalg_basic_oct_m::gemv_1_1 ( integer, intent(in)  m, integer, intent(in)  n, real(real32), intent(in)  alpha, real(real32), dimension(:,:), intent(in), contiguous  a, real(real32), dimension(:), intent(in), contiguous  x, real(real32), intent(in)  beta, real(real32), dimension(:), intent(inout), contiguous  y  )

private

Definition at line 2736 of file lalg_basic.F90.

gemv_2_1()

subroutine lalg_basic_oct_m::gemv_2_1 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, real(real32), intent(in)  alpha, real(real32), dimension(:,:,:), intent(in), contiguous  a, real(real32), dimension(:), intent(in), contiguous  x, real(real32), intent(in)  beta, real(real32), dimension(:,:), intent(inout), contiguous  y  )

private

Definition at line 2758 of file lalg_basic.F90.

gemm_1_1()

subroutine lalg_basic_oct_m::gemm_1_1 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:,:), intent(in), contiguous  a, real(real32), dimension(:,:), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:,:), intent(inout), contiguous  c  )

private

---

BLAS level III

Matrix-matrix multiplication plus matrix.

Definition at line 2791 of file lalg_basic.F90.

gemm_2_1()

subroutine lalg_basic_oct_m::gemm_2_1 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:, :, :), intent(in), contiguous  a, real(real32), dimension(:, :), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:, :, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(m1, m2, k)
[in]	b	b(k, n)
[in,out]	c	c(m1, m2, n)

Definition at line 2812 of file lalg_basic.F90.

gemm_cn_1_1()

subroutine lalg_basic_oct_m::gemm_cn_1_1 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:,:), intent(in), contiguous  a, real(real32), dimension(:,:), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:,:), intent(inout), contiguous  c  )

private

The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real.

Parameters

[in]	a	a(k, m)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 2838 of file lalg_basic.F90.

gemm_cn_2_1()

subroutine lalg_basic_oct_m::gemm_cn_2_1 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:, :, :), intent(in), contiguous  a, real(real32), dimension(:, :, :), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 2859 of file lalg_basic.F90.

gemm_nc_1_1()

subroutine lalg_basic_oct_m::gemm_nc_1_1 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:,:), intent(in), contiguous  a, real(real32), dimension(:,:), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:,:), intent(inout), contiguous  c  )

private

The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real.

Parameters

[in]	a	a(m, k)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 2886 of file lalg_basic.F90.

gemm_nc_2_1()

subroutine lalg_basic_oct_m::gemm_nc_2_1 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:, :, :), intent(in), contiguous  a, real(real32), dimension(:, :, :), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 2907 of file lalg_basic.F90.

gemm_cc_1_1()

subroutine lalg_basic_oct_m::gemm_cc_1_1 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, real(real32), intent(in)  alpha, real(real32), dimension(:,:), intent(in), contiguous  a, real(real32), dimension(:,:), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:,:), intent(inout), contiguous  c  )

private

GEMM when both a and b are (Hermitian) transposes.

\[ \mathbf{C} = \mathbf{A}^\dagger \mathbf{B}^\dagger \]

Note that one can equivalently perform:

\[ \mathbf{C} = \left[\mathbf{B} \mathbf{A} \right]^\dagger \]

It might be more efficient to replace the implementation with the second operation defined above - requires testing.

Parameters

[in]	a	a(k, m)
[in]	b	b(n, k)
[in,out]	c	c(m, n)

Definition at line 2945 of file lalg_basic.F90.

symm_1_1()

subroutine lalg_basic_oct_m::symm_1_1 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  side, real(real32), intent(in)  alpha, real(real32), dimension(:, :), intent(in), contiguous  a, real(real32), dimension(:, :), intent(in), contiguous  b, real(real32), intent(in)  beta, real(real32), dimension(:, :), intent(inout), contiguous  c  )

private

The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H.

Definition at line 2970 of file lalg_basic.F90.

trmm_1_1()

subroutine lalg_basic_oct_m::trmm_1_1 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  uplo, character(1), intent(in)  transa, character(1), intent(in)  side, real(real32), intent(in)  alpha, real(real32), dimension(:, :), intent(in), contiguous  a, real(real32), dimension(:, :), intent(inout), contiguous  b  )

private

---

Matrix-matrix multiplication.

Definition at line 3002 of file lalg_basic.F90.

swap_1_3()

subroutine lalg_basic_oct_m::swap_1_3 ( integer, intent(in)  n1, complex(real32), dimension(:), intent(inout), contiguous  dx, complex(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

BLAS level I

Definition at line 3077 of file lalg_basic.F90.

swap_2_3()

subroutine lalg_basic_oct_m::swap_2_3 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real32), dimension(:,:), intent(inout), contiguous  dx, complex(real32), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 3094 of file lalg_basic.F90.

swap_3_3()

subroutine lalg_basic_oct_m::swap_3_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real32), dimension(:,:,:), intent(inout), contiguous  dx, complex(real32), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 3120 of file lalg_basic.F90.

swap_4_3()

subroutine lalg_basic_oct_m::swap_4_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real32), dimension(:,:,:,:), intent(inout), contiguous  dx, complex(real32), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 3141 of file lalg_basic.F90.

scal_1_3()

subroutine lalg_basic_oct_m::scal_1_3 ( integer, intent(in)  n1, complex(real32), intent(in)  da, complex(real32), dimension(:), intent(inout), contiguous  dx  )

private

---

scales a vector by a constant

Definition at line 3168 of file lalg_basic.F90.

scal_2_3()

subroutine lalg_basic_oct_m::scal_2_3 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real32), intent(in)  da, complex(real32), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 3185 of file lalg_basic.F90.

scal_3_3()

subroutine lalg_basic_oct_m::scal_3_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real32), intent(in)  da, complex(real32), dimension(:, :, :), intent(inout), contiguous  dx  )

private

Definition at line 3210 of file lalg_basic.F90.

scal_4_3()

subroutine lalg_basic_oct_m::scal_4_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real32), intent(in)  da, complex(real32), dimension(:, :, :, :), intent(inout), contiguous  dx  )

private

Definition at line 3229 of file lalg_basic.F90.

scal_5_3()

subroutine lalg_basic_oct_m::scal_5_3 ( integer, intent(in)  n1, real(real32), intent(in)  da, complex(real32), dimension(:), intent(inout), contiguous  dx  )

private

Definition at line 3250 of file lalg_basic.F90.

scal_6_3()

subroutine lalg_basic_oct_m::scal_6_3 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), intent(in)  da, complex(real32), dimension(:, :), intent(inout), contiguous  dx  )

private

Definition at line 3267 of file lalg_basic.F90.

axpy_1_3()

subroutine lalg_basic_oct_m::axpy_1_3 ( integer, intent(in)  n1, complex(real32), intent(in)  da, complex(real32), dimension(:), intent(in), contiguous  dx, complex(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

constant times a vector plus a vector

Definition at line 3298 of file lalg_basic.F90.

axpy_2_3()

subroutine lalg_basic_oct_m::axpy_2_3 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real32), intent(in)  da, complex(real32), dimension(:, :), intent(in), contiguous  dx, complex(real32), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 3327 of file lalg_basic.F90.

axpy_3_3()

subroutine lalg_basic_oct_m::axpy_3_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real32), intent(in)  da, complex(real32), dimension(:, :, :), intent(in), contiguous  dx, complex(real32), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 3366 of file lalg_basic.F90.

axpy_4_3()

subroutine lalg_basic_oct_m::axpy_4_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real32), intent(in)  da, complex(real32), dimension(:, :, :, :), intent(in), contiguous  dx, complex(real32), dimension(:, :, :, :), intent(inout), contiguous  dy  )

private

Definition at line 3398 of file lalg_basic.F90.

axpy_5_3()

subroutine lalg_basic_oct_m::axpy_5_3 ( integer, intent(in)  n1, real(real32), intent(in)  da, complex(real32), dimension(:), intent(in), contiguous  dx, complex(real32), dimension(:), intent(inout), contiguous  dy  )

private

Definition at line 3433 of file lalg_basic.F90.

axpy_6_3()

subroutine lalg_basic_oct_m::axpy_6_3 ( integer, intent(in)  n1, integer, intent(in)  n2, real(real32), intent(in)  da, complex(real32), dimension(:, :), intent(in), contiguous  dx, complex(real32), dimension(:, :), intent(inout), contiguous  dy  )

private

Definition at line 3458 of file lalg_basic.F90.

axpy_7_3()

subroutine lalg_basic_oct_m::axpy_7_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, real(real32), intent(in)  da, complex(real32), dimension(:, :, :), intent(in), contiguous  dx, complex(real32), dimension(:, :, :), intent(inout), contiguous  dy  )

private

Definition at line 3494 of file lalg_basic.F90.

copy_1_3()

subroutine lalg_basic_oct_m::copy_1_3 ( integer, intent(in)  n1, complex(real32), dimension(:), intent(in), contiguous  dx, complex(real32), dimension(:), intent(inout), contiguous  dy  )

private

---

Copies a vector x, to a vector y

Definition at line 3527 of file lalg_basic.F90.

copy_2_3()

subroutine lalg_basic_oct_m::copy_2_3 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real32), dimension(:,:), intent(in), contiguous  dx, complex(real32), dimension(:,:), intent(inout), contiguous  dy  )

private

Definition at line 3550 of file lalg_basic.F90.

copy_3_3()

subroutine lalg_basic_oct_m::copy_3_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, complex(real32), dimension(:,:,:), intent(in), contiguous  dx, complex(real32), dimension(:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 3581 of file lalg_basic.F90.

copy_4_3()

subroutine lalg_basic_oct_m::copy_4_3 ( integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  n3, integer, intent(in)  n4, complex(real32), dimension(:,:,:,:), intent(in), contiguous  dx, complex(real32), dimension(:,:,:,:), intent(inout), contiguous  dy  )

private

Definition at line 3606 of file lalg_basic.F90.

nrm2_3()

real(real32) function lalg_basic_oct_m::nrm2_3 ( integer, intent(in)  n, complex(real32), dimension(:), intent(in)  dx  )

private

---

Returns the euclidean norm of a vector

Definition at line 3637 of file lalg_basic.F90.

symv_1_3()

subroutine lalg_basic_oct_m::symv_1_3 ( integer, intent(in)  n, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :), intent(in), contiguous  a, complex(real32), dimension(:), intent(in), contiguous  x, complex(real32), intent(in)  beta, complex(real32), dimension(:), intent(inout), contiguous  y  )

private

---

BLAS level II

Matrix-vector multiplication plus vector.

Definition at line 3665 of file lalg_basic.F90.

symv_2_3()

subroutine lalg_basic_oct_m::symv_2_3 ( integer, intent(in)  n1, integer, intent(in)  n2, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :, :), intent(in), contiguous  a, complex(real32), dimension(:), intent(in), contiguous  x, complex(real32), intent(in)  beta, complex(real32), dimension(:, :), intent(inout), contiguous  y  )

private

Definition at line 3683 of file lalg_basic.F90.

gemv_1_3()

subroutine lalg_basic_oct_m::gemv_1_3 ( integer, intent(in)  m, integer, intent(in)  n, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:), intent(in), contiguous  a, complex(real32), dimension(:), intent(in), contiguous  x, complex(real32), intent(in)  beta, complex(real32), dimension(:), intent(inout), contiguous  y  )

private

Definition at line 3705 of file lalg_basic.F90.

gemv_2_3()

subroutine lalg_basic_oct_m::gemv_2_3 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:,:), intent(in), contiguous  a, complex(real32), dimension(:), intent(in), contiguous  x, complex(real32), intent(in)  beta, complex(real32), dimension(:,:), intent(inout), contiguous  y  )

private

Definition at line 3727 of file lalg_basic.F90.

gemm_1_3()

subroutine lalg_basic_oct_m::gemm_1_3 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:), intent(in), contiguous  a, complex(real32), dimension(:,:), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:,:), intent(inout), contiguous  c  )

private

---

BLAS level III

Matrix-matrix multiplication plus matrix.

Definition at line 3760 of file lalg_basic.F90.

gemm_2_3()

subroutine lalg_basic_oct_m::gemm_2_3 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :, :), intent(in), contiguous  a, complex(real32), dimension(:, :), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:, :, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(m1, m2, k)
[in]	b	b(k, n)
[in,out]	c	c(m1, m2, n)

Definition at line 3781 of file lalg_basic.F90.

gemm_cn_1_3()

subroutine lalg_basic_oct_m::gemm_cn_1_3 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:), intent(in), contiguous  a, complex(real32), dimension(:,:), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:,:), intent(inout), contiguous  c  )

private

The same as above but with (Hermitian) transpose of a. Note, in this also works when a and b are real.

Parameters

[in]	a	a(k, m)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 3807 of file lalg_basic.F90.

gemm_cn_2_3()

subroutine lalg_basic_oct_m::gemm_cn_2_3 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :, :), intent(in), contiguous  a, complex(real32), dimension(:, :, :), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 3828 of file lalg_basic.F90.

gemm_nc_1_3()

subroutine lalg_basic_oct_m::gemm_nc_1_3 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:), intent(in), contiguous  a, complex(real32), dimension(:,:), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:,:), intent(inout), contiguous  c  )

private

The same as gemm but with (Hermitian) transpose of b. Note, in this also works when a and b are real.

Parameters

[in]	a	a(m, k)
[in]	b	b(k, n)
[in,out]	c	c(m, n)

Definition at line 3855 of file lalg_basic.F90.

gemm_nc_2_3()

subroutine lalg_basic_oct_m::gemm_nc_2_3 ( integer, intent(in)  m1, integer, intent(in)  m2, integer, intent(in)  n1, integer, intent(in)  n2, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :, :), intent(in), contiguous  a, complex(real32), dimension(:, :, :), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:, :), intent(inout), contiguous  c  )

private

Parameters

[in]	a	a(k, m2, m1)
[in]	b	b(k, n2, n1)
[in,out]	c	c(m1*m2, n1*n2)

Definition at line 3876 of file lalg_basic.F90.

gemm_cc_1_3()

subroutine lalg_basic_oct_m::gemm_cc_1_3 ( integer, intent(in)  m, integer, intent(in)  n, integer, intent(in)  k, complex(real32), intent(in)  alpha, complex(real32), dimension(:,:), intent(in), contiguous  a, complex(real32), dimension(:,:), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:,:), intent(inout), contiguous  c  )

private

GEMM when both a and b are (Hermitian) transposes.

\[ \mathbf{C} = \mathbf{A}^\dagger \mathbf{B}^\dagger \]

Note that one can equivalently perform:

\[ \mathbf{C} = \left[\mathbf{B} \mathbf{A} \right]^\dagger \]

It might be more efficient to replace the implementation with the second operation defined above - requires testing.

Parameters

[in]	a	a(k, m)
[in]	b	b(n, k)
[in,out]	c	c(m, n)

Definition at line 3914 of file lalg_basic.F90.

symm_1_3()

subroutine lalg_basic_oct_m::symm_1_3 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  side, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :), intent(in), contiguous  a, complex(real32), dimension(:, :), intent(in), contiguous  b, complex(real32), intent(in)  beta, complex(real32), dimension(:, :), intent(inout), contiguous  c  )

private

The following matrix multiplications all expect upper triangular matrices for a. For real matrices, a = a^T, for complex matrices a = a^H.

Definition at line 3939 of file lalg_basic.F90.

trmm_1_3()

subroutine lalg_basic_oct_m::trmm_1_3 ( integer, intent(in)  m, integer, intent(in)  n, character(1), intent(in)  uplo, character(1), intent(in)  transa, character(1), intent(in)  side, complex(real32), intent(in)  alpha, complex(real32), dimension(:, :), intent(in), contiguous  a, complex(real32), dimension(:, :), intent(inout), contiguous  b  )

private

---

Matrix-matrix multiplication.

Definition at line 3971 of file lalg_basic.F90.