NAG Library Function Document

nag_real_cholesky_skyline_solve (f04mcc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{selct}$ – Nag_SolveSystemInput

On entry: selct must specify the type of system to be solved, as follows:

• if $\mathbf{selct}=\mathrm{Nag\_LDLTX}$: solve ${LDL}^{TX}=B$;
• if $\mathbf{selct}=\mathrm{Nag\_LDX}$: solve $LDX=B$;
• if $\mathbf{selct}=\mathrm{Nag\_DLTX}$: solve ${DL}^{\mathrm{T}}X=B$;
• if $\mathbf{selct}=\mathrm{Nag\_LLTX}$: solve ${LL}^{\mathrm{T}}X=B$;
• if $\mathbf{selct}=\mathrm{Nag\_LX}$: solve $LX=B$;
• if $\mathbf{selct}=\mathrm{Nag\_LTX}$: solve $L^{\mathrm{T}}X=B$.

Constraint: $\mathbf{selct}=\mathrm{Nag\_LDLTX}$, $\mathrm{Nag\_LDX}$, $\mathrm{Nag\_DLTX}$, $\mathrm{Nag\_LLTX}$, $\mathrm{Nag\_LX}$ or $\mathrm{Nag\_LTX}$.

2:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $L$.

Constraint: $\mathbf{n}\ge 1$.

3:    $\mathbf{nrhs}$ – IntegerInput

On entry: $r$, the number of right-hand sides.

Constraint: $\mathbf{nrhs}\ge 1$.

4:    $\mathbf{al}\left[\mathbf{lal}\right]$ – const doubleInput

On entry: the elements within the envelope of the lower triangular matrix $L$, taken in row by row order, as returned by nag_real_cholesky_skyline (f01mcc). The unit diagonal elements of $L$ must be stored explicitly.

5:    $\mathbf{lal}$ – IntegerInput

On entry: the dimension of the array al.

Constraint: $\mathbf{lal}\ge \mathbf{row}\left[0\right]+\mathbf{row}\left[1\right]+\cdots +\mathbf{row}\left[n-1\right]$.

6:    $\mathbf{d}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the diagonal elements of the diagonal matrix $D$. d is not referenced if $\mathbf{selct}=\mathrm{Nag\_LLTX}$, $\mathrm{Nag\_LX}$ or $\mathrm{Nag\_LTX}$

7:    $\mathbf{row}\left[\mathbf{n}\right]$ – const IntegerInput

On entry: $\mathbf{row}\left[i\right]$ must contain the width of row $i$ of $L$, i.e., the number of elements between the first (left-most) nonzero element and the element on the diagonal, inclusive.

Constraint: $1\le \mathbf{row}\left[i\right]\le i+1$ for $i=0,1,\dots ,n-1$.

8:    $\mathbf{b}\left[\mathbf{n}\times \mathbf{tdb}\right]$ – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix $B$ is stored in $\mathbf{b}\left[\left(i-1\right)\times \mathbf{tdb}+j-1\right]$.

On entry: the $n$ by $r$ right-hand side matrix $B$. See also Section 9.

9:    $\mathbf{tdb}$ – IntegerInput

On entry: the stride separating matrix column elements in the array b.

Constraint: $\mathbf{tdb}\ge \mathbf{nrhs}$.

10:  $\mathbf{x}\left[\mathbf{n}\times \mathbf{tdx}\right]$ – doubleOutput

Note: the $\left(i,j\right)$th element of the matrix $X$ is stored in $\mathbf{x}\left[\left(i-1\right)\times \mathbf{tdx}+j-1\right]$.

On exit: the $n$ by $r$ solution matrix $X$. See also Section 9.

11:  $\mathbf{tdx}$ – IntegerInput

On entry: the stride separating matrix column elements in the array x.

Constraint: $\mathbf{tdx}\ge \mathbf{nrhs}$.

12:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_GT

On entry, $\mathbf{row}\left[i\right]=〈\mathit{\text{value}}〉$ while $i=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{row}\left[i\right]\le i+1$.

NE_2_INT_ARG_LT

On entry, $\mathbf{lal}=〈\mathit{\text{value}}〉$ while $\mathbf{row}\left[0\right]+\cdots +\mathbf{row}\left[n-1\right]=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{lal}\ge \mathbf{row}\left[0\right]+\cdots +\mathbf{row}\left[n-1\right]$.

On entry, $\mathbf{tdb}=〈\mathit{\text{value}}〉$ while $\mathbf{nrhs}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdb}\ge \mathbf{nrhs}$.

On entry, $\mathbf{tdx}=〈\mathit{\text{value}}〉$ while $\mathbf{nrhs}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdx}\ge \mathbf{nrhs}$.

NE_BAD_PARAM

On entry, argument selct had an illegal value.

NE_INT_ARG_LT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

On entry, $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrhs}\ge 1$.

On entry, $\mathbf{row}\left[〈\mathit{\text{value}}〉\right]$ must not be less than 1: $\mathbf{row}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

NE_NOT_UNIT_DIAG

The lower triangular matrix $L$ has at least one diagonal element which is not equal to unity. The first non-unit element has been located in the array $\mathbf{al}\left[〈\mathit{\text{value}}〉\right]$.

NE_ZERO_DIAG

The diagonal matrix $D$ is singular as it has at least one zero element. The first zero element has been located in the array $\mathbf{d}\left[〈\mathit{\text{value}}〉\right]$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f04mcce.c)

10.2

Program Data

Program Data (f04mcce.d)

10.3

Program Results

Program Results (f04mcce.r)