Module oc_lsqr_mod

1.

Purpose simple LSQR solver

$$\fbox {$ \displaystyle \mathcal L\bold m\approx \bold D $}$$

		 $\bold m= 0$ 
		 $\bold U= \bold D$				$\b = \sqrt{\parallel \bold U\parallel^2 }$		$\bold U=\frac{1}{\b}\bold U$ 
		 $\bold v= \mathcal L^*\bold U$				$\alpha= \sqrt{\parallel \bold v\parallel^2 }$		$\bold v=\frac{1}{\alpha}\bold v$ 
		 $\bold w= \bold v$ 
		 $\bar\rho =\alpha$		$\bar\phi = \b$ 
		 iterate { 
		 		  $\bold U= -\alpha\bold U$		$\bold U= \bold U+\mathcal L\bold v$ 
		 		  $\b = \sqrt{\parallel \bold U\parallel^2 }$		$\bold U=\frac{1}{\b}\bold U$
		 		  $\bold v= -\b \bold v$		$\bold v= \bold v+\mathcal L^*\bold U$ 
		 		  $\alpha= \sqrt{\parallel \bold v\parallel^2 }$		$\bold v=\frac{1}{\alpha}\bold v$
		 		  $\rho = \sqrt{\bar\rho^2 + \b^2}$ 
		 		  $c=\frac{\bar\rho}{\rho}$ $\bar\rho=-c\alpha$ 
		 		  $s=\frac{\b}{\rho}$ $\theta = s\alpha$ 
		 		  $\phi = c\bar\phi$ $\bar\phi=s\bar\phi$ 
		 		  $t_1=\frac{\phi}{\rho}$ $t_2=-\frac{\theta}{\rho}$
		 		  $\bold m= \bold m+ t_1 \bold w$ 
		 		  $\bold w= \bold v+ t_2 \bold w$ 
		 		 }

2.

Functions and subroutines

(a)

subroutine oc_lsqr_init(niter,maxmem,verb,movie)

Purpose: initialize the simple LSQR solver

• niter: iterations number
• verb: verbose flag (optional)
• movie: movie output flag (optional)

(b)

subroutine oc_lsqr( L, x_,yy_,op1 ...op9)

Purpose: simple LSQR solver

• L: out-of-core linear operator