NAG Library Routine Document

F07FNF (ZPOSV)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A$ is stored.

If $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A$ is stored.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

2:     N – INTEGERInput

On entry: $n$, the number of linear equations, i.e., the order of the matrix $A$.

Constraint: $\mathbf{N}\ge 0$.

3:     NRHS – INTEGERInput

On entry: $r$, the number of right-hand sides, i.e., the number of columns of the matrix $B$.

Constraint: $\mathbf{NRHS}\ge 0$.

4:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the $n$ by $n$ Hermitian matrix $A$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: if $\mathbf{INFO}=\mathbf{0}$, the factor $U$ or $L$ from the Cholesky factorization $A=U^{\mathrm{H}}U$ or $A=L{L}^{\mathrm{H}}$.

5:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F07FNF (ZPOSV) is called.

Constraint: $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

6:     B(LDB,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{NRHS}\right)$.

To solve the equations $Ax=b$, where $b$ is a single right-hand side, B may be supplied as a one-dimensional array with length $\mathbf{LDB}=\max \left(1,\mathbf{N}\right)$.

On entry: the $n$ by $r$ right-hand side matrix $B$.

On exit: if $\mathbf{INFO}=\mathbf{0}$, the $n$ by $r$ solution matrix $X$.

7:     LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F07FNF (ZPOSV) is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

8:     INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, the $i$th argument had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{INFO}>0$

If $\mathbf{INFO}=i$, the leading minor of order $i$ of $A$ is not positive definite, so the factorization could not be completed, and the solution has not been computed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f07fnfe.f90)

9.2  Program Data

Program Data (f07fnfe.d)

9.3  Program Results

Program Results (f07fnfe.r)