Routines dealing with the operations of banded matrices. More...

Data Types
interface	avco

interface	cad1b

interface	cad2b

interface	clipb

interface	csb1b

interface	csb2b

interface	dfco

interface	dfco2

interface	l1ubb

interface	l1ueb

interface	ldltb

interface	ldub

interface	linbv

interface	ltdlbv

interface	u1lbv

interface	u1lbx

interface	u1lby

interface	u1lvb

interface	u1lxb

interface	u1lyb

interface	udlb

interface	udlbv

interface	udlbx

interface	udlby

interface	udlvb

interface	udlxb

interface	udlyb

interface	wrtb

Functions/Subroutines
subroutine, public	avco (na, nb, za, zb, z0, a, b)
	Compute one row of the coefficients for the compact mid-interval interpolation scheme characterized by matrix equation of the form, A.t = B.s (*) Where s is the vector of "source" values, t the staggered "target" values. More...

subroutine, public	cad1b (m1, mah1, mah2, mirror2, a)
	Incorporate operand symmetry and clip near end-1 of a band matrix operator. More...

subroutine, public	cad2b (m1, m2, mah1, mah2, mirror2, a)
	Incorporate symmetry and clip near end-2 of a band matrix. More...

pure subroutine	clib (m1, m2, mah1, mah2, a)
	Clip (set to zero) the unused values in a banded matrix representation. More...

pure subroutine	clib_c (m1, m2, mah1, mah2, a)
	Clip (set to zero) the unused values in a banded matrix representation. More...

pure subroutine	clib_d (m1, m2, mah1, mah2, a)
	Clip (set to zero) the unused values in a banded matrix representation. More...

subroutine, public	csb1b (m1, mah1, mah2, mirror2, a)
	Like cad1b, but for antisymmetric operand. More...

subroutine, public	csb2b (m1, m2, mah1, mah2, mirror2, a)
	Incorporate operand antisymmetry and clip near end-2 of a band matrix. More...

subroutine	davco (na, nb, za, zb, z0, a, b)
	Double precision version of subroutine avco for midpoint interpolation. More...

subroutine	ddfco (na, nb, za, zb, z0, a, b)
	Double precision version of dfco for compact differentiation coefficients. More...

subroutine	ddfco2 (na, nb, za, zb, z0, a, b)
	Double precision version of DFCO2 to get 2nd-derivative coefficients. More...

subroutine, public	dfco (na, nb, za, zb, z0, a, b)
	Compute one row of the coefficients for either the compact differencing or quadrature scheme characterized by matrix equation of the form, A.d = B.c (*) In either case, d is the derivative (or density) of cumulative c. More...

subroutine, public	dfco2 (na, nb, za, zb, z0, a, b)
	Compute one row of the coefficients for either the compact second- differencing scheme characterized by matrix equation of the form, A.d = B.c (*) Where d is the second-derivative of c. More...

subroutine	dl1ubb (m, mah1, mah2, mbh1, mbh2, a, b)
	Double precision version of L1UBB. More...

subroutine	dl1ueb (m, mah1, mah2, mbh1, mbh2, a, b)
	Double precision version of L1UEB. More...

subroutine	dldltb (m, mah1, a)
	[L][D][L^T] factoring of symmetric matrix A (root-free Cholesky). More...

subroutine	dldub (m, mah1, mah2, a)
	[L][D][U] factoring of double precision band-matrix. More...

subroutine	dltdlbv (m, mah1, a, v)
	Like udlbv, except assuming a is the ltdl decomposition of a SYMMETRIC banded matrix, with only the non-upper part provided (to avoid redundancy) More...

subroutine	dudlb (m, mah1, mah2, a)
	[U][D][L] factoring of double precision band matrix A [U] is upper triangular with unit main diagonal [D] is a diagonal matrix [L] is lower triangular with unit main diagonal More...

subroutine	dudlbv (m, mah1, mah2, a, v)
	Back-substitution step of linear inversion involving banded LDU factored matrix and input vector, v. More...

subroutine, public	l1ubb (m, mah1, mah2, mbh1, mbh2, a, b)
	[L][D][U] factoring of band-matrix [A], modify [B] –> [D*-1][B] [L] lower triangular with unit main diagonal [D] diagonal matrix [U] upper triangular with unit main diagonal [B] associated band matrix with same number of rows as [A] lower triangular elements of [A] by [D*-1][L][D], the upper by [U], replace matrix [B] by [D-1][B]. More...

subroutine, public	l1ueb (m, mah1, mah2, mbh1, mbh2, a, b)
	Form the [L][D][U] decomposition of asymmetric band-matrix [A] replace all but row zero of the lower triangular elements of [A] by [D*-1][L][D], the upper by [U], replace matrix [B] by [D-1][B]. More...

subroutine, public	ldltb (m, mah1, a)
	[L][D][L^T] factoring of symmetric band matrix A (root-free Cholesky). More...

subroutine, public	ldub (m, mah1, mah2, a)
	[L][D][U] factoring of single precision band-matrix. More...

subroutine, public	linbv (m, mah1, mah2, a, v)
	Solve LINear system with square Banded-matrix and vector V. More...

subroutine, public	ltdlbv (m, mah1, a, v)
	Like udlbv, except assuming a is the ldlt decomposition of a SYMMETRIC banded matrix, with only the non-upper part provided (to avoid redundancy) More...

subroutine	tavco (xa, xb, a, b)
	Simplified computation of compact midpoint interpolation coefficients. More...

subroutine	tdfco (xa, xb, a, b)
	Simplified computation of compact differencing coefficients to get derivatives d from cumulatives c, or vice-versa. More...

subroutine	tdfco2 (xa, xb, a, b)
	Simplified computation of compact 2nd-derivative coefficients. More...

subroutine, public	u1lbv (m, mah1, mah2, a, v)
	Back-substitution step ((U*-1)(L**-1)) of linear inversion involving special Banded matrix and right-Vector. More...

subroutine, public	u1lbx (mx, mah1, mah2, my, a, v)
	Special back-substitution step of parallel linear inversion involving Banded matrix and X-right-Vectors. More...

subroutine, public	u1lby (my, mah1, mah2, mx, a, v)
	Special Back-substitution step of parallel linear inversion involving Banded matrix and Y-right-Vectors. More...

subroutine, public	u1lvb (m, mah1, mah2, v, a)
	Special Back-substitution step of linear inversion involving left-Vector and Banded matrix. More...

subroutine, public	u1lxb (mx, mah1, mah2, my, v, a)
	Special Back-substitution step of parallel linear inversion involving Banded matrix and X-left-Vectors. More...

subroutine, public	u1lyb (my, mah1, mah2, mx, v, a)
	Special Back-substitution step of parallel linear inversion involving special Banded matrix and Y-left-Vectors. More...

subroutine, public	udlb (m, mah1, mah2, a)
	[U][D][L] factoring of single precision band matrix A [U] is upper triangular with unit main diagonal [D] is a diagonal matrix [L] is lower triangular with unit main diagonal More...

subroutine, public	udlbv (m, mah1, mah2, a, v)
	Back-substitution step of linear inversion involving banded LDU factored matrix and input vector, v. More...

subroutine, public	udlbx (mx, mah1, mah2, my, a, v)
	Back-substitution step of parallel linear inversion involving Banded matrix and X-Vectors. More...

subroutine, public	udlby (my, mah1, mah2, mx, a, v)
	Back-substitution step of parallel linear inversion involving Banded matrix and Y-Vectors. More...

subroutine, public	udlvb (m, mah1, mah2, v, a)
	Back-substitution step of linear inversion involving row-Vector and Banded matrix. More...

subroutine, public	udlxb (mx, mah1, mah2, my, v, a)
	Back-substitution step of parallel linear inversion involving Banded matrix and row-X-Vectors. More...

subroutine, public	udlyb (my, mah1, mah2, mx, v, a)
	BACk-substitution step of parallel linear inversion involving Banded matrix and row-Y-Vectors. More...

subroutine, public	wrtb (m1, m2, mah1, mah2, a)
	Convenient routine for interactively writing out the real contents of a band matrix. More...

Variables
real(dp), parameter	zero =0
	Double precision real zero. More...

Detailed Description

Routines dealing with the operations of banded matrices.

The three special routines allow the construction of compact or conventional interpolation and differencing stencils to a general order of accuracy. These are:

avco() Averaging, or interpolating;
dfco() Differentiating (once);
dfco2() Differentiating (twice).

Other routines provide the tools for applying compact schemes, and for the construction and application of recursive filters.

Last modified (Purser): January 6th 2005 added nonredundant ldltb and ltdlbv routines for symmetric matrices, and remove obsolescent routines.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994/1999

Function/Subroutine Documentation

◆ avco()

subroutine, public pmat2::avco	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(sp), dimension(na), intent(in)	za,
		real(sp), dimension(nb), intent(in)	zb,
		real(sp), intent(in)	z0,
		real(sp), dimension(na), intent(out)	a,
		real(sp), dimension(nb), intent(out)	b
	)

Compute one row of the coefficients for the compact mid-interval interpolation scheme characterized by matrix equation of the form, A.t = B.s (*) Where s is the vector of "source" values, t the staggered "target" values.

Parameters

[in]	na	number of t-points operated on by this row of the A of (*)
[in]	nb	number of s-points operated on by this row of the B of (*)
[in]	za	coordinates of t-points used in this row of (*)
[in]	zb	coordinates of s-points used in this row of (*)
[in]	z0	nominal point of application of this row of (*)
[out]	a	the NA coefficients A for this scheme
[out]	b	the NB coefficients B for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 100 of file pmat2.f90.

References pietc::u0, and pietc::u1.

◆ cad1b()

subroutine, public pmat2::cad1b	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mirror2,
		real(sp), dimension(0:m1-1,-mah1:mah2), intent(inout)	a
	)

Incorporate operand symmetry and clip near end-1 of a band matrix operator.

Parameters

[in]	m1	Size of implied full matrix
[in]	mah1	Left semi-bandwidths (subdiagonals) of A.
[in]	mah2	Right semi-bandwidths (superdiagonals) of A.
[in]	mirror2	2*location of symmetry axis relative to end-1 operand element.
[in,out]	a	Input operator, output as symmetrized and clipped at end-1 Note: although m2 is not used here, it IS used in companion routines cad2b and csb2b; it is retained in the interests of uniformity.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 426 of file pmat2.f90.

◆ cad2b()

subroutine, public pmat2::cad2b	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mirror2,
		real(sp), dimension(1-m1:0,m1-m2-mah1:m1-m2+mah2), intent(inout)	a
	)

Incorporate symmetry and clip near end-2 of a band matrix.

Parameters

[in]	m1	Number of rows of full matrix A
[in]	m2	Number of columns of implied full matrix A
[in]	mah1	Left semi-bandwidths (subdiagonals) of A.
[in]	mah2	Right semi-bandwidths (superdiagonals) of A.
[in]	mirror2	2*location of symmetry axis relative to end-2 operand element.
[in,out]	a	Input operator, output as symmetrized and clipped at end-2.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 477 of file pmat2.f90.

◆ clib()

pure subroutine pmat2::clib	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m1,-mah1:mah2), intent(inout)	a
	)

private

Clip (set to zero) the unused values in a banded matrix representation.

Parameters

[in]	m1	number of matrix rows
[in]	m2	number of matrix columns
[in]	mah1	number of subdiagonals
[in]	mah2	number of superdiagonals
[in,out]	a	single precision matrix elements, stored compactly as rows

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 370 of file pmat2.f90.

◆ clib_c()

pure subroutine pmat2::clib_c	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		complex(dpc), dimension(m1,-mah1:mah2), intent(inout)	a
	)

Clip (set to zero) the unused values in a banded matrix representation.

Parameters

[in]	m1	number of matrix rows
[in]	m2	number of matrix columns
[in]	mah1	number of subdiagonals
[in]	mah2	number of superdiagonals
[in]	a	complex matrix elements, stored compactly as rows

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 406 of file pmat2.f90.

References pietc::c0.

◆ clib_d()

pure subroutine pmat2::clib_d	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(dp), dimension(m1,-mah1:mah2), intent(inout)	a
	)

Clip (set to zero) the unused values in a banded matrix representation.

Parameters

[in]	m1	number of matrix rows
[in]	m2	number of matrix columns
[in]	mah1	number of subdiagonals
[in]	mah2	number of superdiagonals
[in]	a	double precision matrix elements, stored compactly as rows

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 388 of file pmat2.f90.

References pietc::u0.

◆ csb1b()

subroutine, public pmat2::csb1b	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mirror2,
		real(sp), dimension(0:m1-1,-mah1:mah2), intent(inout)	a
	)

Like cad1b, but for antisymmetric operand.

Parameters

[in]	m1	Size of implied full matrix
[in]	mah1	Left semi-bandwidths (subdiagonals) of A.
[in]	mah2	Right semi-bandwidths (superdiagonals) of A.
[in]	mirror2	2*location of symmetry axis relative to end-1 operand element.
[in,out]	a	Input operator, output as clipped antisymmetric at end-1.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 451 of file pmat2.f90.

◆ csb2b()

subroutine, public pmat2::csb2b	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mirror2,
		real(sp), dimension(1-m1:0,m1-m2-mah1:m1-m2+mah2), intent(inout)	a
	)

Incorporate operand antisymmetry and clip near end-2 of a band matrix.

Parameters

[in]	m1	Number of rows of matrix A
[in]	m2	Number of columns of matrix A
[in]	mah1	Left semi-bandwidths (subdiagonals) of A.
[in]	mah2	Right semi-bandwidths (superdiagonals) of A.
[in]	mirror2	2*location of symmetry axis relative to end-2 operand element.
[in,out]	a	Input operator, output as antisymmetrized and clipped at end-2.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 504 of file pmat2.f90.

◆ davco()

subroutine pmat2::davco	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(dp), dimension(na), intent(in)	za,
		real(dp), dimension(nb), intent(in)	zb,
		real(dp), intent(in)	z0,
		real(dp), dimension(na), intent(out)	a,
		real(dp), dimension(nb), intent(out)	b
	)

Double precision version of subroutine avco for midpoint interpolation.

Parameters

[in]	na	number of target points involved in formula
[in]	nb	number of source points involved in formula
[in]	za	coordinates of target points
[in]	zb	coordinates of source points
[in]	z0	nominal point of application of compact interpolation formula
[out]	a	the coefficients A for this scheme
[out]	b	the coefficients B for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 134 of file pmat2.f90.

References pietc::u0, and pietc::u1.

Referenced by tavco().

◆ ddfco()

subroutine pmat2::ddfco	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(dp), dimension(na), intent(in)	za,
		real(dp), dimension(nb), intent(in)	zb,
		real(dp), intent(in)	z0,
		real(dp), dimension(na), intent(out)	a,
		real(dp), dimension(nb), intent(out)	b
	)

Double precision version of dfco for compact differentiation coefficients.

Parameters

[in]	na	number of A coefficients multiplying derivatives
[in]	nb	number of B coefficients multiplying cumulatives
[in]	za	coordinates of the density (d) points
[in]	zb	coordinates of the cumulative (c) points
[in]	z0	nominal point of application of the compact formula
[in]	a	the A-coefficients for this scheme
[in]	b	the B-coefficients for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 225 of file pmat2.f90.

References pietc::u0, and pietc::u1.

Referenced by tdfco().

◆ ddfco2()

subroutine pmat2::ddfco2	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(dp), dimension(na), intent(in)	za,
		real(dp), dimension(nb), intent(in)	zb,
		real(dp), intent(in)	z0,
		real(dp), dimension(na), intent(out)	a,
		real(dp), dimension(nb), intent(out)	b
	)

Double precision version of DFCO2 to get 2nd-derivative coefficients.

Parameters

[in]	na	number of 2nd-derivative (d) points in compact formula
[in]	nb	number of source points (c)
[in]	za	coordinates of 2nd-derivative points
[in]	zb	coordinates of source points
[in]	z0	nominal coordinate of application
[in]	a	coefficients A for derivative points
[in]	b	coefficients B for source points

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 318 of file pmat2.f90.

References pietc::u0, and pietc::u1.

Referenced by tdfco2().

◆ dfco()

subroutine, public pmat2::dfco	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(sp), dimension(na), intent(in)	za,
		real(sp), dimension(nb), intent(in)	zb,
		real(sp), intent(in)	z0,
		real(sp), dimension(na), intent(out)	a,
		real(sp), dimension(nb), intent(out)	b
	)

Compute one row of the coefficients for either the compact differencing or quadrature scheme characterized by matrix equation of the form, A.d = B.c (*) In either case, d is the derivative (or density) of cumulative c.

Parameters

[in]	na	number of d-points operated on by this row of the A of (*)
[in]	nb	number of c-points operated on by this row of the B of (*)
[in]	za	coordinates of d-points used in this row of (*)
[in]	zb	coordinates of c-points used in this row of (*)
[in]	z0	nominal point of application of this row of (*)
[in]	A	the A-coefficients for this scheme
[in]	B	the B-coefficients for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 190 of file pmat2.f90.

◆ dfco2()

subroutine, public pmat2::dfco2	(	integer(spi), intent(in)	na,
		integer(spi), intent(in)	nb,
		real(sp), dimension(na), intent(in)	za,
		real(sp), dimension(nb), intent(in)	zb,
		real(sp), intent(in)	z0,
		real(sp), dimension(na), intent(out)	a,
		real(sp), dimension(nb), intent(out)	b
	)

Compute one row of the coefficients for either the compact second- differencing scheme characterized by matrix equation of the form, A.d = B.c (*) Where d is the second-derivative of c.

Parameters

[in]	na	number of d-points operated on by this row of the A of (*)
[in]	nb	number of c-points operated on by this row of the B of (*)
[in]	za	coordinates of d-points used in this row of (*)
[in]	zb	coordinates of c-points used in this row of (*)
[in]	z0	nominal point of application of this row of (*)
[in]	a	the NA coefficients A for this scheme
[in]	b	the NB coefficients B for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 283 of file pmat2.f90.

◆ dl1ubb()

subroutine pmat2::dl1ubb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mbh1,
		integer(spi), intent(in)	mbh2,
		real(dp), dimension(m,-mah1:mah2), intent(inout)	a,
		real(dp), dimension(m,-mbh1:mbh2), intent(inout)	b
	)

Double precision version of L1UBB.

Parameters

[in]	m	Number of rows of A and B
[in]	mah1	left half-width of fortran array A
[in]	mah2	right half-width of fortran array A
[in]	mbh1	left half-width of fortran array B
[in]	mbh2	left half-width of fortran array B
[in,out]	a	Input double precision band matrix A; output factors encoded as [D*-1 L * D]+[U-I]
[in,out]	b	Input double precision band matrix B; output [D**-1 B]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 771 of file pmat2.f90.

References pietc::u0, and pietc::u1.

◆ dl1ueb()

subroutine pmat2::dl1ueb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mbh1,
		integer(spi), intent(in)	mbh2,
		real(dp), dimension(0:,-mah1:), intent(inout)	a,
		real(dp), dimension(:,-mbh1:), intent(inout)	b
	)

Double precision version of L1UEB.

Parameters

[in]	m	number of rows of band matrices A and B
[in]	mah1	number of subdiagonals of A
[in]	mah2	number of superdiagonals of A
[in]	mbh1	number of subdiagonals of B
[in]	mbh2	number of superdiagonals of B
[in,out]	a	Input matrix A; output encoded L, D, U, factors
[in,out]	b	Input matrix B; output D*-1 B

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 855 of file pmat2.f90.

References pietc::u0, and pietc::u1.

◆ dldltb()

subroutine pmat2::dldltb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		real(dp), dimension(m,-mah1:0), intent(inout)	a
	)

[L]*[D]*[L^T] factoring of symmetric matrix A (root-free Cholesky).

[L] is lower triangular with unit main diagonal [D] is a diagonal matrix

Parameters

[in]	m	size of symmetric matrix A
[in]	mah1	semi-bandwidth of matrix A
[in,out]	a	input lower (left) part of symmetric A; output its factors encoded as [L-I]+[D**-1]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 645 of file pmat2.f90.

References pietc::u0, and pietc::u1.

◆ dldub()

subroutine pmat2::dldub	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(dp), dimension(m,-mah1:mah2), intent(inout)	a
	)

[L]*[D]*[U] factoring of double precision band-matrix.

[L] is lower triangular with unit main diagonal [D] is a diagonal matrix [U] is upper triangular with unit main diagonal

Parameters

[in]	m	The number of rows of array A
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in,out]	a	input as the asymmetric band matrix, [A]. On output, it contains the factors in the encoding, [L-I]+[D**-1]+[U-I], I=identity.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 571 of file pmat2.f90.

References pietc::u0, and pietc::u1.

Referenced by dudlb().

◆ dltdlbv()

subroutine pmat2::dltdlbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		real(dp), dimension(m,-mah1:0), intent(in)	a,
		real(dp), dimension(m), intent(inout)	v
	)

private

Like udlbv, except assuming a is the ltdl decomposition of a SYMMETRIC banded matrix, with only the non-upper part provided (to avoid redundancy)

Parameters

[in]	m	the number of rows assumed for A and for V
[in]	mah1	the left half-bandwidth of fortran array A
[in,out]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB
[in,out]	v	input as right-hand-side vector, output as solution vector

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 980 of file pmat2.f90.

◆ dudlb()

subroutine pmat2::dudlb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(dp), dimension(m,-mah1:mah2), intent(inout)	a
	)

private

[U]*[D]*[L] factoring of double precision band matrix A [U] is upper triangular with unit main diagonal [D] is a diagonal matrix [L] is lower triangular with unit main diagonal

Parameters

[in]	m	number of rows of A
[in]	mah1	number of subdiagonals of A
[in]	mah2	number of superdiagonals of A
[in,out]	a	Input double precision band matrix A; output its factors encoded as [U-I]+[D**-1]+[L-I]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 704 of file pmat2.f90.

References dldub().

◆ dudlbv()

subroutine pmat2::dudlbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(dp), dimension(m,-mah1:mah2), intent(in)	a,
		real(dp), dimension(m), intent(inout)	v
	)

private

Back-substitution step of linear inversion involving banded LDU factored matrix and input vector, v.

Output vector is [U**-1]*[D**-1]*[L**-1]*v

Parameters

[in]	m	the number of rows assumed for A and for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	a	encodes the LDU factorization of the linear-system matrix, as supplied by subroutine LDUB, in double precision
[in,out]	v	input as right-hand-side vector, output as solution vector

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 921 of file pmat2.f90.

◆ l1ubb()

subroutine, public pmat2::l1ubb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mbh1,
		integer(spi), intent(in)	mbh2,
		real(sp), dimension(m,-mah1:mah2), intent(inout)	a,
		real(sp), dimension(m,-mbh1:mbh2), intent(inout)	b
	)

[L]*[D]*[U] factoring of band-matrix [A], modify [B] –> [D**-1]*[B] [L] lower triangular with unit main diagonal [D] diagonal matrix [U] upper triangular with unit main diagonal [B] associated band matrix with same number of rows as [A] lower triangular elements of [A] by [D**-1]*[L]*[D], the upper by [U], replace matrix [B] by [D**-1]*[B].

Parameters

[in]	m	Number of rows of A and B
[in]	mah1	number of subdiagonals of A
[in]	mah2	number of superdiagonals of A
[in]	mbh1	number of subdiagonals of B
[in]	mbh2	number of superdiagonals of B
[in,out]	a	input as band matrix, output as lower and upper triangulars with 1s implicitly assumed to lie on the main diagonal. The product of these triangular matrices is [D*-1][A], where [D] is a diagonal matrix.
[in,out]	b	Input single precision band matrix B; output [D**-1 B]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 733 of file pmat2.f90.

◆ l1ueb()

subroutine, public pmat2::l1ueb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mbh1,
		integer(spi), intent(in)	mbh2,
		real(sp), dimension(0:m,-mah1:mah2), intent(inout)	a,
		real(sp), dimension(m,-mbh1:mbh2), intent(inout)	b
	)

Form the [L]*[D]*[U] decomposition of asymmetric band-matrix [A] replace all but row zero of the lower triangular elements of [A] by [D**-1]*[L]*[D], the upper by [U], replace matrix [B] by [D**-1]*[B].

This is a special adaptation of L1UBB used to process quadrature weights for QEDBV etc in which the initial quadrature value is provided as input instead of being implicitly assumed zero (which is the case for QZDBV etc).

Parameters

[in]	m	number of rows of B, one less than the rows of A (which has "row 0")
[in]	mah1	left half-width of fortran array A
[in]	mah2	right half-width of fortran array A
[in]	mbh1	left half-width of fortran array B
[in]	mbh2	right half-width of fortran array B
[in,out]	a	input as band matrix, output as lower and upper triangulars with 1s implicitly assumed to lie on the main diagonal. The product of these triangular matrices is [D*-1][A], where [D] is a diagonal matrix.
[in,out]	b	in as band matrix, out as same but premultiplied by diagonal [D**-1]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1998

Definition at line 818 of file pmat2.f90.

◆ ldltb()

subroutine, public pmat2::ldltb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		real(sp), dimension(m,-mah1:0), intent(inout)	a
	)

[L]*[D]*[L^T] factoring of symmetric band matrix A (root-free Cholesky).

[L] is lower triangular with unit main diagonal [D] is a diagonal matrix.

Parameters

[in]	m	size of symmetric matrix A
[in]	mah1	semi-bandwidth of matrix A
[in,out]	a	input lower (left) part of symmetric A; output its factors encoded as [L-I]+[D**-1]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 609 of file pmat2.f90.

◆ ldub()

subroutine, public pmat2::ldub	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m,-mah1:mah2), intent(inout)	a
	)

[L]*[D]*[U] factoring of single precision band-matrix.

[L] is lower triangular with unit main diagonal [D] is a diagonal matrix [U] is upper triangular with unit main diagonal

Parameters

[in]	m	The number of rows of array A
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in,out]	a	input as the asymmetric band matrix, [A]. On output, it contains the factors in the encoding, [L-I]+[D**-1]+[U-I], I=identity.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 532 of file pmat2.f90.

◆ linbv()

subroutine, public pmat2::linbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m,-mah1:mah2), intent(inout)	a,
		real(sp), dimension(m), intent(inout)	v
	)

Solve LINear system with square Banded-matrix and vector V.

Parameters

[in]	m	order of matrix A
[in]	mah1	left half-bandwidth of A
[in]	mah2	right half-bandwidth of A
[in,out]	a	system matrix on input, its [L][D-1][U] factorization on exit
[in,out]	v	vector of right-hand-sides on input, solution vector on exit

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1323 of file pmat2.f90.

◆ ltdlbv()

subroutine, public pmat2::ltdlbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		real(sp), dimension(m,-mah1:0), intent(in)	a,
		real(sp), dimension(m), intent(inout)	v
	)

Like udlbv, except assuming a is the ldlt decomposition of a SYMMETRIC banded matrix, with only the non-upper part provided (to avoid redundancy)

Parameters

[in]	m	the number of rows assumed for A and for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	a	encodes the LDL^T factorization of the linear-system matrix, as supplied by subroutine LDLTB
[in,out]	v	input as right-hand-side vector, output as solution vector

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 950 of file pmat2.f90.

◆ tavco()

subroutine pmat2::tavco	(	real(dp), dimension(:), intent(in)	xa,
		real(dp), dimension(:), intent(in)	xb,
		real(dp), dimension(:), intent(out)	a,
		real(dp), dimension(:), intent(out)	b
	)

Simplified computation of compact midpoint interpolation coefficients.

Parameters

[in]	xa	coordinates of target points relative to point of application
[in]	xb	coordinates of source points relative to point of application
[out]	a	the coefficients A for this scheme
[out]	b	the coefficients B for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 165 of file pmat2.f90.

References davco(), and zero.

◆ tdfco()

subroutine pmat2::tdfco	(	real(dp), dimension(:), intent(in)	xa,
		real(dp), dimension(:), intent(in)	xb,
		real(dp), dimension(:), intent(out)	a,
		real(dp), dimension(:), intent(out)	b
	)

Simplified computation of compact differencing coefficients to get derivatives d from cumulatives c, or vice-versa.

Parameters

[in]	xa	coordinates, relative to point of application, of d values
[in]	xb	coordinates, relatuve to point of application, of c values
[in]	a	the coefficients, A, for this scheme
[in]	b	the coefficients, B, for this scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 258 of file pmat2.f90.

References ddfco(), and zero.

◆ tdfco2()

subroutine pmat2::tdfco2	(	real(dp), dimension(:), intent(in)	xa,
		real(dp), dimension(:), intent(in)	xb,
		real(dp), dimension(:), intent(out)	a,
		real(dp), dimension(:), intent(out)	b
	)

Simplified computation of compact 2nd-derivative coefficients.

Parameters

[in]	xa	Relative coordinates of derivatives
[in]	xb	Relative coordinates of source points
[out]	a	coefficients A for the derivatives in compact scheme
[out]	b	coefficients B for source values in the compact scheme

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 350 of file pmat2.f90.

References ddfco2(), and zero.

◆ u1lbv()

subroutine, public pmat2::u1lbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m,-mah1:mah2), intent(in)	a,
		real(sp), dimension(m), intent(inout)	v
	)

Back-substitution step ((U**-1)*(L**-1)) of linear inversion involving special Banded matrix and right-Vector.

Parameters

[in]	m	the number of rows assumed for A and for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	a	encodes the [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB
[in,out]	v	input as right-hand-side vector, output as solution vector

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1155 of file pmat2.f90.

◆ u1lbx()

subroutine, public pmat2::u1lbx	(	integer(spi), intent(in)	mx,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	my,
		real(sp), dimension(mx,-mah1:mah2), intent(in)	a,
		real(sp), dimension(mx,my), intent(inout)	v
	)

Special back-substitution step of parallel linear inversion involving Banded matrix and X-right-Vectors.

Parameters

[in]	mx	the number of rows assumed for A and length of X-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	my	number of parallel X-vectors inverted
[in]	a	encodes the [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB
[in,out]	v	input as right-hand-side vectors, output as solution vectors

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1186 of file pmat2.f90.

◆ u1lby()

subroutine, public pmat2::u1lby	(	integer(spi), intent(in)	my,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mx,
		real(sp), dimension(my,-mah1:mah2), intent(in)	a,
		real(sp), dimension(mx,my), intent(inout)	v
	)

Special Back-substitution step of parallel linear inversion involving Banded matrix and Y-right-Vectors.

Parameters

[in]	my	the number of rows assumed for A and length of Y-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	mx	number of parallel Y-vectors inverted
[in]	a	encodes the [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB
[in,out]	v	input as right-hand-side vectors, output as solution vectors

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1214 of file pmat2.f90.

◆ u1lvb()

subroutine, public pmat2::u1lvb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m), intent(inout)	v,
		real(sp), dimension(m,-mah1:mah2), intent(in)	a
	)

Special Back-substitution step of linear inversion involving left-Vector and Banded matrix.

Parameters

[in]	m	the number of rows assumed for A and columns for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in,out]	v	input as right-hand-side row-vector, output as solution vector
[in]	a	encodes the special [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1240 of file pmat2.f90.

◆ u1lxb()

subroutine, public pmat2::u1lxb	(	integer(spi), intent(in)	mx,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	my,
		real(sp), dimension(mx,my), intent(inout)	v,
		real(sp), dimension(mx,-mah1:mah2), intent(in)	a
	)

Special Back-substitution step of parallel linear inversion involving Banded matrix and X-left-Vectors.

Parameters

[in]	mx	the number of rows assumed for A and length of X-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	my	number of parallel X-vectors inverted
[in]	v	input as right-hand-side vectors, output as solution vectors
[in]	a	encodes the special [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1271 of file pmat2.f90.

◆ u1lyb()

subroutine, public pmat2::u1lyb	(	integer(spi), intent(in)	my,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mx,
		real(sp), dimension(mx,my), intent(inout)	v,
		real(sp), dimension(my,-mah1:mah2), intent(in)	a
	)

Special Back-substitution step of parallel linear inversion involving special Banded matrix and Y-left-Vectors.

Parameters

[in]	my	the number of rows assumed for A and length of Y-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	mx	number of parallel Y-vectors inverted
[in,out]	v	input as right-hand-side vectors, output as solution vectors
[in]	a	encodes the [L]*[U] factorization of the linear-system matrix, as supplied by subroutine L1UBB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1996

Definition at line 1299 of file pmat2.f90.

◆ udlb()

subroutine, public pmat2::udlb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m,-mah1:mah2), intent(inout)	a
	)

[U]*[D]*[L] factoring of single precision band matrix A [U] is upper triangular with unit main diagonal [D] is a diagonal matrix [L] is lower triangular with unit main diagonal

Parameters

[in]	m	number of rows of A
[in]	mah1	number of subdiagonals of A
[in]	mah2	number of superdiagonals of A
[in,out]	a	Input single precision band matrix A; output its factors encoded as [U-I]+[D**-1]+[L-I]

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 683 of file pmat2.f90.

◆ udlbv()

subroutine, public pmat2::udlbv	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m,-mah1:mah2), intent(in)	a,
		real(sp), dimension(m), intent(inout)	v
	)

Back-substitution step of linear inversion involving banded LDU factored matrix and input vector, v.

Output vector is [U**-1]*[D**-1]*[L**-1]*v

Parameters

[in]	m	the number of rows assumed for A and for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	a	encodes the LDU factorization of the linear-system matrix, as supplied by subroutine LDUB, in single precision
[in,out]	v	input as right-hand-side vector, output as solution vector

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 892 of file pmat2.f90.

◆ udlbx()

subroutine, public pmat2::udlbx	(	integer(spi), intent(in)	mx,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	my,
		real(sp), dimension(mx,-mah1:mah2), intent(in)	a,
		real(sp), dimension(mx,my), intent(inout)	v
	)

Back-substitution step of parallel linear inversion involving Banded matrix and X-Vectors.

Parameters

[in]	mx	the number of rows assumed for A and length of X-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	my	number of parallel X-vectors inverted
[in]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB or, if N=NA, by LDUB
[in,out]	v	input as right-hand-side vectors, output as solution vectors

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1011 of file pmat2.f90.

◆ udlby()

subroutine, public pmat2::udlby	(	integer(spi), intent(in)	my,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mx,
		real(sp), dimension(my,-mah1:mah2), intent(in)	a,
		real(sp), dimension(mx,my), intent(inout)	v
	)

Back-substitution step of parallel linear inversion involving Banded matrix and Y-Vectors.

Parameters

[in]	my	the number of rows assumed for A and length of Y-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	mx	number of parallel Y-vectors inverted
[in]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB or, if N=NA, by LDUB
[in,out]	v	input as right-hand-side vectors, output as solution vectors

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1040 of file pmat2.f90.

◆ udlvb()

subroutine, public pmat2::udlvb	(	integer(spi), intent(in)	m,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m), intent(inout)	v,
		real(sp), dimension(m,-mah1:mah2), intent(in)	a
	)

Back-substitution step of linear inversion involving row-Vector and Banded matrix.

Parameters

[in]	m	the number of rows assumed for A and columns for V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in,out]	v	input as right-hand-side row-vector, output as solution vector
[in]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1067 of file pmat2.f90.

◆ udlxb()

subroutine, public pmat2::udlxb	(	integer(spi), intent(in)	mx,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	my,
		real(sp), dimension(mx,my), intent(inout)	v,
		real(sp), dimension(mx,-mah1:mah2), intent(in)	a
	)

Back-substitution step of parallel linear inversion involving Banded matrix and row-X-Vectors.

Parameters

[in]	mx	the number of rows assumed for A and length of X-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	my	number of parallel X-vectors inverted
[in,out]	v	input as right-hand-side vectors, output as solution vectors
[in]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1099 of file pmat2.f90.

◆ udlyb()

subroutine, public pmat2::udlyb	(	integer(spi), intent(in)	my,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		integer(spi), intent(in)	mx,
		real(sp), dimension(mx,my), intent(inout)	v,
		real(sp), dimension(my,-mah1:mah2), intent(in)	a
	)

BACk-substitution step of parallel linear inversion involving Banded matrix and row-Y-Vectors.

Parameters

[in]	my	the number of rows assumed for A and length of Y-vectors stored in V
[in]	mah1	the left half-bandwidth of fortran array A
[in]	mah2	the right half-bandwidth of fortran array A
[in]	mx	number of parallel Y-vectors inverted
[in,out]	v	input as right-hand-side vectors, output as solution vectors
[in]	a	encodes the (L)(D-1)(U) factorization of the linear-system matrix, as supplied by subroutine LDUB

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1994

Definition at line 1128 of file pmat2.f90.

◆ wrtb()

subroutine, public pmat2::wrtb	(	integer(spi), intent(in)	m1,
		integer(spi), intent(in)	m2,
		integer(spi), intent(in)	mah1,
		integer(spi), intent(in)	mah2,
		real(sp), dimension(m1,-mah1:mah2), intent(in)	a
	)

Convenient routine for interactively writing out the real contents of a band matrix.

Parameters

[in]	m1	number of rows of full matrix
[in]	m2	number of columns of full matrix
[in]	mah1	number of sub-diagonals
[in]	mah2	number of super-diagonals
[in]	a	contents of single precision real band matrix.

Author: R. J. Purser, Tsukasa Fujita (JMA)

Date: 1999

Definition at line 1341 of file pmat2.f90.

Variable Documentation

◆ zero

real(dp), parameter pmat2::zero =0

private

Double precision real zero.

Definition at line 54 of file pmat2.f90.

Referenced by tavco(), tdfco(), and tdfco2().

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ avco()

◆ cad1b()

◆ cad2b()

◆ clib()

◆ clib_c()

◆ clib_d()

◆ csb1b()

◆ csb2b()

◆ davco()

◆ ddfco()

◆ ddfco2()

◆ dfco()

◆ dfco2()

◆ dl1ubb()

◆ dl1ueb()

◆ dldltb()

◆ dldub()

◆ dltdlbv()

◆ dudlb()

◆ dudlbv()

◆ l1ubb()

◆ l1ueb()

◆ ldltb()

◆ ldub()

◆ linbv()

◆ ltdlbv()

◆ tavco()

◆ tdfco()

◆ tdfco2()

◆ u1lbv()

◆ u1lbx()

◆ u1lby()

◆ u1lvb()

◆ u1lxb()

◆ u1lyb()

◆ udlb()

◆ udlbv()

◆ udlbx()

◆ udlby()

◆ udlvb()

◆ udlxb()

◆ udlyb()

◆ wrtb()

Variable Documentation

◆ zero