Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.

Syntax

lapack_int LAPACKE_sgetrs (int matrix_layout , char trans , lapack_int n , lapack_int nrhs , const float * a , lapack_int lda , const lapack_int * ipiv , float * b , lapack_int ldb );

lapack_int LAPACKE_dgetrs (int matrix_layout , char trans , lapack_int n , lapack_int nrhs , const double * a , lapack_int lda , const lapack_int * ipiv , double * b , lapack_int ldb );

lapack_int LAPACKE_cgetrs (int matrix_layout , char trans , lapack_int n , lapack_int nrhs , const lapack_complex_float * a , lapack_int lda , const lapack_int * ipiv , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zgetrs (int matrix_layout , char trans , lapack_int n , lapack_int nrhs , const lapack_complex_double * a , lapack_int lda , const lapack_int * ipiv , lapack_complex_double * b , lapack_int ldb );

Include Files

  • mkl.h

Description

The routine solves for X the following systems of linear equations:

A*X = B

if trans='N',

AT*X = B

if trans='T',

AH*X = B

if trans='C' (for complex matrices only).

Before calling this routine, you must call ?getrf to compute the LU factorization of A.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

trans

Must be 'N' or 'T' or 'C'.

Indicates the form of the equations:

If trans = 'N', then A*X = B is solved for X.

If trans = 'T', then AT*X = B is solved for X.

If trans = 'C', then AH*X = B is solved for X.

n

The order of A; the number of rows in B(n 0).

nrhs

The number of right-hand sides; nrhs 0.

a

Array of size max(1, lda*n).

The array a contains LU factorization of matrix A resulting from the call of ?getrf.

b

Array of size max(1,ldb*nrhs) for column major layout, and max(1,ldb*n) for row major layout.

The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

lda

The leading dimension of a; lda max(1, n).

ldb

The leading dimension of b; ldb max(1, n) for column major layout and ldbnrhs for row major layout.

ipiv

Array, size at least max(1, n). The ipiv array, as returned by ?getrf.

Output Parameters

b

Overwritten by the solution matrix X.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

Application Notes

For each right-hand side b, the computed solution is the exact solution of a perturbed system of equations (A + E)x = b, where

|E|  c(n)ε P|L||U|

c(n) is a modest linear function of n, and ε is the machine precision.

If x0 is the true solution, the computed solution x satisfies this error bound:


Equation

where cond(A,x)= || |A-1||A| |x| || / ||x|| ||A-1|| ||A|| = κ(A).

Note that cond(A,x) can be much smaller than κ(A); the condition number of AT and AH might or might not be equal to κ(A).

The approximate number of floating-point operations for one right-hand side vector b is 2n2 for real flavors and 8n2 for complex flavors.

To estimate the condition number κ(A), call ?gecon.

To refine the solution and estimate the error, call ?gerfs.

Para obtener información más completa sobre las optimizaciones del compilador, consulte nuestro Aviso de optimización.
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