gblnum.f90 File Reference

General linear algebra routines. More...

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Functions/Subroutines
subroutine	sqminv (v, b, n, nrank, diag, next)
	Matrix inversion.
subroutine	devrot (n, diag, u, v, work, iwork)
	Diagonalization.
subroutine	dbgax (a, x, y, m, n)
	Multiply general M-by-N matrix A and N-vector X.
subroutine	dbavat (v, a, w, n, m)
	A V AT product (similarity).
subroutine	sqmibb (v, b, n, nbdr, nbnd, inv, nrank)
	Bordered band matrix.
subroutine	dbprv (lun, v, n)
	Prints the symmetric N-by-N matrix V.

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Detailed Description

General linear algebra routines.

***** Collection of utility routines from V. Blobel *****

Definition in file gblnum.f90.

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Function/Subroutine Documentation

subroutine dbavat	(	double precision, dimension(*), intent(in)	v,
		double precision, dimension(*), intent(in)	a,
		double precision, dimension(*), intent(out)	w,
		integer, intent(in)	n,
		integer, intent(in)	m
	)

A V AT product (similarity).

Multiply symmetric N-by-N matrix from the left with general M-by-N matrix and from the right with the transposed of the same general matrix to form symmetric M-by-M matrix (used for error propagation).

Parameters:

[in]	V	symmetric N-by-N matrix
[in]	A	general M-by-N matrix
[out]	W	symmetric M-by-M matrix
[in]	M	rows of A
[in]	N	columns of A

Definition at line 463 of file gblnum.f90.

Referenced by gbltraj::gblres(), and test().

subroutine dbgax	(	double precision, dimension(*), intent(in)	a,
		double precision, dimension(*), intent(in)	x,
		double precision, dimension(*), intent(out)	y,
		integer, intent(in)	m,
		integer, intent(in)	n
	)

Multiply general M-by-N matrix A and N-vector X.

Parameters:

[in]	A	general M-by-N matrix (A11 A12 ... A1N A21 A22 ...)
[in]	X	N vector
[out]	Y	= M vector
[in]	M	rows of A
[in]	N	columns of A

Definition at line 427 of file gblnum.f90.

Referenced by gbltraj::gblres().

subroutine dbprv	(	integer, intent(inout)	lun,
		double precision, dimension(*), intent(inout)	v,
		integer, intent(in)	n
	)

Prints the symmetric N-by-N matrix V.

Parameters:

[in]	LUN	output unit
[in]	V	N-by-N matrix V (symmetric storage)
[in]	N	size

Definition at line 788 of file gblnum.f90.

Referenced by test().

subroutine devrot	(	integer, intent(in)	n,
		double precision, dimension(n), intent(out)	diag,
		double precision, dimension(n,n), intent(out)	u,
		double precision, dimension(*), intent(in)	v,
		double precision, dimension(n), intent(out)	work,
		integer, dimension(n), intent(out)	iwork
	)

Diagonalization.

Determination of eigenvalues and eigenvectors of symmetric matrix V by Householder method

Parameters:

[in]	n	size of matrix
[out]	diag	diagonal elements
[out]	u	transformation matrix
[in]	v	symmetric matrix, unchanged
[out]	work	work array
[out]	iwork	work array

Definition at line 182 of file gblnum.f90.

Referenced by gbltraj::gbldat().

subroutine sqmibb	(	double precision, dimension(*), intent(inout)	v,
		double precision, dimension(n), intent(out)	b,
		integer, intent(in)	n,
		integer, intent(in)	nbdr,
		integer, intent(in)	nbnd,
		integer, intent(in)	inv,
		integer, intent(out)	nrank
	)

Bordered band matrix.

Obtain solution of a system of linear equations with symmetric bordered band matrix (V * X = B), on request inverse is calculated. For band part root-free Cholesky decomposition and forward/backward substitution is used.

Use decomposition in border and band part for block matrix algebra:

| A  Ct |   | x1 |   | b1 |        , A  is the border part
|       | * |    | = |    |        , Ct is the mixed part
| C  D  |   | x2 |   | b2 |        , D  is the band part

Explicit inversion of D is avoided by using solution X of D*X=C (X=D^-1*C, obtained from Cholesky decomposition and forward/backward substitution)

| x1 |   | E*b1 - E*Xt*b2 |        , E^-1 = A-Ct*D^-1*C = A-Ct*X
|    | = |                |
| x2 |   |  x   - X*x1    |        , x is solution of D*x=b2 (x=D^-1*b2)

Inverse matrix is:

|  E   -E*Xt          |
|                     |            , only band part of (D^-1 + X*E*Xt)
| -X*E  D^-1 + X*E*Xt |              is calculated for inv=1

Parameters:

[in,out]	V	symmetric N-by-N matrix in symmetric storage mode (V(1) = V11, V(2) = V12, V(3) = V22, V(4) = V13, ...), replaced by inverse matrix
[in,out]	B	N-vector, replaced by solution vector
[in]	N	size of V, B
[in]	NBDR	border size
[in]	NBND	band width
[in]	INV	=1 calculate band part of inverse (for pulls), >1 calculate complete inverse
[out]	NRANK	rank of matrix V

Definition at line 557 of file gblnum.f90.

References dbcdec(), and sqminv().

Referenced by gbltraj::gblfit().

subroutine sqminv	(	double precision, dimension(*), intent(inout)	v,
		double precision, dimension(n), intent(out)	b,
		integer, intent(in)	n,
		integer, intent(out)	nrank,
		double precision, dimension(n), intent(out)	diag,
		integer, dimension(n), intent(out)	next
	)

Matrix inversion.

Obtain solution of a system of linear equations with symmetric matrix (V * X = B) and the inverse.

Method of solution is by elimination selecting the pivot on the diagonal each stage. The rank of the matrix is returned in NRANK. For NRANK ne N, all remaining rows and cols of the resulting matrix V and the corresponding elements of B are set to zero.

Parameters:

[in,out]	V	symmetric N-by-N matrix in symmetric storage mode (V(1) = V11, V(2) = V12, V(3) = V22, V(4) = V13, ...), replaced by inverse matrix
[in,out]	B	N-vector, replaced by solution vector
[in]	N	size of V, B
[out]	NRANK	rank of matrix V
[out]	DIAG	double precision scratch array
[out]	NEXT	integer aux array

Definition at line 58 of file gblnum.f90.

Referenced by sqmibb().