timing_zauxiliary.c 15.6 KB
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/**
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 *
 * @file timing_zauxiliary.c
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 *
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 * @copyright 2009-2014 The University of Tennessee and The University of
 *                      Tennessee Research Foundation. All rights reserved.
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 * @copyright 2012-2019 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria,
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 *                      Univ. Bordeaux. All rights reserved.
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 *
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 ***
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 *
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 * @version 0.9.2
 * @author Mathieu Faverge
 * @date 2015-03-24
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 * @precisions normal z -> c d s
 *
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 */
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#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
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#include <chameleon.h>
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#include <coreblas/cblas.h>
#include <coreblas/lapacke.h>
#include <coreblas.h>
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#include "timing_zauxiliary.h"
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/*-------------------------------------------------------------------
 * Check the orthogonality of Q
 */

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int z_check_orthogonality(int M, int N, int LDQ, CHAMELEON_Complex64_t *Q)
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{
    double alpha, beta;
    double normQ;
    int info_ortho;
    int i;
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    int minMN = chameleon_min(M, N);
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    double eps;
    double *work = (double *)malloc(minMN*sizeof(double));

    eps = LAPACKE_dlamch_work('e');
    alpha = 1.0;
    beta  = -1.0;

    /* Build the idendity matrix USE DLASET?*/
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    CHAMELEON_Complex64_t *Id = (CHAMELEON_Complex64_t *) malloc(minMN*minMN*sizeof(CHAMELEON_Complex64_t));
    memset((void*)Id, 0, minMN*minMN*sizeof(CHAMELEON_Complex64_t));
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    for (i = 0; i < minMN; i++)
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        Id[i*minMN+i] = (CHAMELEON_Complex64_t)1.0;
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    /* Perform Id - Q'Q */
    if (M >= N)
        cblas_zherk(CblasColMajor, CblasUpper, CblasConjTrans, N, M, alpha, Q, LDQ, beta, Id, N);
    else
        cblas_zherk(CblasColMajor, CblasUpper, CblasNoTrans, M, N, alpha, Q, LDQ, beta, Id, M);

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    normQ = LAPACKE_zlansy_work(LAPACK_COL_MAJOR, 'I', 'u', minMN, Id, minMN, work);
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    printf("============\n");
    printf("Checking the orthogonality of Q \n");
    printf("||Id-Q'*Q||_oo / (N*eps) = %e \n",normQ/(minMN*eps));

    if ( isnan(normQ / (minMN * eps)) || (normQ / (minMN * eps) > 10.0) ) {
        printf("-- Orthogonality is suspicious ! \n");
        info_ortho=1;
    }
    else {
        printf("-- Orthogonality is CORRECT ! \n");
        info_ortho=0;
    }

    free(work); free(Id);

    return info_ortho;
}

/*------------------------------------------------------------
 *  Check the factorization QR
 */

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int z_check_QRfactorization(int M, int N, CHAMELEON_Complex64_t *A1, CHAMELEON_Complex64_t *A2, int LDA, CHAMELEON_Complex64_t *Q)
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{
    double Anorm, Rnorm;
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    CHAMELEON_Complex64_t alpha, beta;
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    int info_factorization;
    int i,j;
    double eps;

    eps = LAPACKE_dlamch_work('e');

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    CHAMELEON_Complex64_t *Ql       = (CHAMELEON_Complex64_t *)malloc(M*N*sizeof(CHAMELEON_Complex64_t));
    CHAMELEON_Complex64_t *Residual = (CHAMELEON_Complex64_t *)malloc(M*N*sizeof(CHAMELEON_Complex64_t));
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    double *work              = (double *)malloc(chameleon_max(M,N)*sizeof(double));
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    alpha=1.0;
    beta=0.0;

    if (M >= N) {
        /* Extract the R */
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        CHAMELEON_Complex64_t *R = (CHAMELEON_Complex64_t *)malloc(N*N*sizeof(CHAMELEON_Complex64_t));
        memset((void*)R, 0, N*N*sizeof(CHAMELEON_Complex64_t));
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        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'u', M, N, A2, LDA, R, N);

        /* Perform Ql=Q*R */
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        memset((void*)Ql, 0, M*N*sizeof(CHAMELEON_Complex64_t));
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        cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, N, CBLAS_SADDR(alpha), Q, LDA, R, N, CBLAS_SADDR(beta), Ql, M);
        free(R);
    }
    else {
        /* Extract the L */
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        CHAMELEON_Complex64_t *L = (CHAMELEON_Complex64_t *)malloc(M*M*sizeof(CHAMELEON_Complex64_t));
        memset((void*)L, 0, M*M*sizeof(CHAMELEON_Complex64_t));
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        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'l', M, N, A2, LDA, L, M);

    /* Perform Ql=LQ */
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        memset((void*)Ql, 0, M*N*sizeof(CHAMELEON_Complex64_t));
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        cblas_zgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, M, CBLAS_SADDR(alpha), L, M, Q, LDA, CBLAS_SADDR(beta), Ql, M);
        free(L);
    }

    /* Compute the Residual */
    for (i = 0; i < M; i++)
        for (j = 0 ; j < N; j++)
            Residual[j*M+i] = A1[j*LDA+i]-Ql[j*M+i];

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    Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, Residual, M, work);
    Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, A2, LDA, work);
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    if (M >= N) {
        printf("============\n");
        printf("Checking the QR Factorization \n");
        printf("-- ||A-QR||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
    }
    else {
        printf("============\n");
        printf("Checking the LQ Factorization \n");
        printf("-- ||A-LQ||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));
    }

    if (isnan(Rnorm / (Anorm * N *eps)) || (Rnorm / (Anorm * N * eps) > 10.0) ) {
        printf("-- Factorization is suspicious ! \n");
        info_factorization = 1;
    }
    else {
        printf("-- Factorization is CORRECT ! \n");
        info_factorization = 0;
    }

    free(work); free(Ql); free(Residual);

    return info_factorization;
}

/*------------------------------------------------------------------------
 *  Check the factorization of the matrix A2
 */

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int z_check_LLTfactorization(int N, CHAMELEON_Complex64_t *A1, CHAMELEON_Complex64_t *A2, int LDA, cham_uplo_t uplo)
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{
    double Anorm, Rnorm;
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    CHAMELEON_Complex64_t alpha;
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    int info_factorization;
    int i,j;
    double eps;

    eps = LAPACKE_dlamch_work('e');

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    CHAMELEON_Complex64_t *Residual = (CHAMELEON_Complex64_t *)malloc(N*N*sizeof(CHAMELEON_Complex64_t));
    CHAMELEON_Complex64_t *L1       = (CHAMELEON_Complex64_t *)malloc(N*N*sizeof(CHAMELEON_Complex64_t));
    CHAMELEON_Complex64_t *L2       = (CHAMELEON_Complex64_t *)malloc(N*N*sizeof(CHAMELEON_Complex64_t));
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    double *work              = (double *)malloc(N*sizeof(double));

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    memset((void*)L1, 0, N*N*sizeof(CHAMELEON_Complex64_t));
    memset((void*)L2, 0, N*N*sizeof(CHAMELEON_Complex64_t));
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    alpha= 1.0;

    LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,' ', N, N, A1, LDA, Residual, N);

    /* Dealing with L'L or U'U  */
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    if (uplo == ChamUpper){
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        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'u', N, N, A2, LDA, L1, N);
        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'u', N, N, A2, LDA, L2, N);
        cblas_ztrmm(CblasColMajor, CblasLeft, CblasUpper, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
    }
    else{
        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'l', N, N, A2, LDA, L1, N);
        LAPACKE_zlacpy_work(LAPACK_COL_MAJOR,'l', N, N, A2, LDA, L2, N);
        cblas_ztrmm(CblasColMajor, CblasRight, CblasLower, CblasConjTrans, CblasNonUnit, N, N, CBLAS_SADDR(alpha), L1, N, L2, N);
    }

    /* Compute the Residual || A -L'L|| */
    for (i = 0; i < N; i++)
        for (j = 0; j < N; j++)
           Residual[j*N+i] = L2[j*N+i] - Residual[j*N+i];

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    Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', N, N, Residual, N, work);
    Anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', N, N, A1, LDA, work);
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    printf("============\n");
    printf("Checking the Cholesky Factorization \n");
    printf("-- ||L'L-A||_oo/(||A||_oo.N.eps) = %e \n",Rnorm/(Anorm*N*eps));

    if ( isnan(Rnorm/(Anorm*N*eps)) || (Rnorm/(Anorm*N*eps) > 10.0) ){
        printf("-- Factorization is suspicious ! \n");
        info_factorization = 1;
    }
    else{
        printf("-- Factorization is CORRECT ! \n");
        info_factorization = 0;
    }

    free(Residual); free(L1); free(L2); free(work);

    return info_factorization;
}

/*--------------------------------------------------------------
 * Check the gemm
 */
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double z_check_gemm(cham_trans_t transA, cham_trans_t transB, int M, int N, int K,
                   CHAMELEON_Complex64_t alpha, CHAMELEON_Complex64_t *A, int LDA,
                   CHAMELEON_Complex64_t *B, int LDB,
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                   CHAMELEON_Complex64_t beta, CHAMELEON_Complex64_t *Ccham,
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                   CHAMELEON_Complex64_t *Cref, int LDC,
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                   double *Cinitnorm, double *Cchamnorm, double *Clapacknorm )
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{
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    CHAMELEON_Complex64_t beta_const = -1.0;
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    double Rnorm;
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    double *work = (double *)malloc(chameleon_max(K,chameleon_max(M, N))* sizeof(double));
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    *Cinitnorm   = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, Cref,    LDC, work);
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    *Cchamnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, Ccham, LDC, work);
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    cblas_zgemm(CblasColMajor, (CBLAS_TRANSPOSE)transA, (CBLAS_TRANSPOSE)transB, M, N, K,
                CBLAS_SADDR(alpha), A, LDA, B, LDB, CBLAS_SADDR(beta), Cref, LDC);

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    *Clapacknorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work);
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    cblas_zaxpy(LDC * N, CBLAS_SADDR(beta_const), Ccham, 1, Cref, 1);
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    Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work);
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    free(work);

    return Rnorm;
}

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#if defined(PRECISION_z) || defined(PRECISION_c)
/*--------------------------------------------------------------
 * Check the hemm
 */
double z_check_hemm( cham_side_t side, cham_uplo_t uplo, int M, int N,
                     CHAMELEON_Complex64_t alpha, const CHAMELEON_Complex64_t *A, int LDA,
                                                  const CHAMELEON_Complex64_t *B, int LDB,
                     CHAMELEON_Complex64_t beta,  const CHAMELEON_Complex64_t *Ccham,
                                                        CHAMELEON_Complex64_t *Cref, int LDC,
                     double *Cinitnorm, double *Cchamnorm, double *Clapacknorm )
{
    CHAMELEON_Complex64_t beta_const = -1.0;
    double Rnorm;
    double *work = (double *)malloc( chameleon_max(M, N)* sizeof(double) );

    *Cinitnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref,  LDC, work );
    *Cchamnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Ccham, LDC, work );

    cblas_zhemm( CblasColMajor, (CBLAS_SIDE)side, (CBLAS_UPLO)uplo, M, N,
                 CBLAS_SADDR(alpha), A, LDA, B, LDB, CBLAS_SADDR(beta), Cref, LDC );

    *Clapacknorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work );

    cblas_zaxpy( LDC * N, CBLAS_SADDR(beta_const), Ccham, 1, Cref, 1 );

    Rnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work );

    free(work);

    return Rnorm;
}
#endif /* defined(PRECISION_z) || defined(PRECISION_c) */

/*--------------------------------------------------------------
 * Check the symm
 */
double z_check_symm( cham_side_t side, cham_uplo_t uplo, int M, int N,
                     CHAMELEON_Complex64_t alpha, const CHAMELEON_Complex64_t *A, int LDA,
                                                  const CHAMELEON_Complex64_t *B, int LDB,
                     CHAMELEON_Complex64_t beta,  const CHAMELEON_Complex64_t *Ccham,
                                                        CHAMELEON_Complex64_t *Cref, int LDC,
                     double *Cinitnorm, double *Cchamnorm, double *Clapacknorm )
{
    CHAMELEON_Complex64_t beta_const = -1.0;
    double Rnorm;
    double *work = (double *)malloc( chameleon_max(M, N)* sizeof(double) );

    *Cinitnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref,  LDC, work );
    *Cchamnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Ccham, LDC, work );

    cblas_zsymm( CblasColMajor, (CBLAS_SIDE)side, (CBLAS_UPLO)uplo, M, N,
                 CBLAS_SADDR(alpha), A, LDA, B, LDB, CBLAS_SADDR(beta), Cref, LDC );

    *Clapacknorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work );

    cblas_zaxpy( LDC * N, CBLAS_SADDR(beta_const), Ccham, 1, Cref, 1 );

    Rnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'I', M, N, Cref, LDC, work );

    free(work);

    return Rnorm;
}

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/*--------------------------------------------------------------
 * Check the trsm
 */
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double z_check_trsm(cham_side_t side, cham_uplo_t uplo, cham_trans_t trans, cham_diag_t diag,
                   int M, int NRHS, CHAMELEON_Complex64_t alpha,
                   CHAMELEON_Complex64_t *A, int LDA,
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                   CHAMELEON_Complex64_t *Bcham, CHAMELEON_Complex64_t *Bref, int LDB,
                   double *Binitnorm, double *Bchamnorm, double *Blapacknorm )
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{
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    CHAMELEON_Complex64_t beta_const = -1.0;
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    double Rnorm;
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    double *work = (double *)malloc(chameleon_max(M, NRHS)* sizeof(double));
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    /*double eps = LAPACKE_dlamch_work('e');*/

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    *Binitnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'i', M, NRHS, Bref,  LDB, work );
    *Bchamnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'i', M, NRHS, Bcham, LDB, work );
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    cblas_ztrsm( CblasColMajor, (CBLAS_SIDE)side, (CBLAS_UPLO)uplo,
                 (CBLAS_TRANSPOSE)trans, (CBLAS_DIAG)diag, M, NRHS,
                 CBLAS_SADDR(alpha), A, LDA, Bref, LDB );
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    *Blapacknorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'i', M, NRHS, Bref, LDB, work );
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    cblas_zaxpy( LDB * NRHS, CBLAS_SADDR(beta_const), Bcham, 1, Bref, 1 );
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    Rnorm = LAPACKE_zlange_work( LAPACK_COL_MAJOR, 'i', M, NRHS, Bref, LDB, work );
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    Rnorm = Rnorm / *Blapacknorm;
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    /* chameleon_max(M,NRHS) * eps);*/
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    free(work);

    return Rnorm;
}

/*--------------------------------------------------------------
 * Check the solution
 */

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double z_check_solution(int M, int N, int NRHS, CHAMELEON_Complex64_t *A, int LDA,
                      CHAMELEON_Complex64_t *B,  CHAMELEON_Complex64_t *X, int LDB,
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                      double *anorm, double *bnorm, double *xnorm )
{
/*     int info_solution; */
    double Rnorm = -1.00;
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    CHAMELEON_Complex64_t zone  =  1.0;
    CHAMELEON_Complex64_t mzone = -1.0;
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    double *work = (double *)malloc(chameleon_max(M, N)* sizeof(double));
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    *anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, N,    A, LDA, work);
    *xnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', M, NRHS, X, LDB, work);
    *bnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', N, NRHS, B, LDB, work);
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    cblas_zgemm( CblasColMajor, CblasNoTrans, CblasNoTrans, M, NRHS, N,
                 CBLAS_SADDR(zone),  A, LDA, X, LDB,
                 CBLAS_SADDR(mzone), B, LDB );
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    Rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'I', N, NRHS, B, LDB, work);
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    free(work);

    return Rnorm;
}

/*------------------------------------------------------------------------
 *  *  Check the accuracy of the computed inverse
 *   */

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int z_check_inverse( int N, CHAMELEON_Complex64_t *A1, CHAMELEON_Complex64_t *A2, int LDA,
                     cham_uplo_t uplo, double *rnorm, double *anorm, double *ainvnorm )
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{
    int info_inverse;
    int i, j;
    double result;
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    CHAMELEON_Complex64_t alpha, beta, zone;
    CHAMELEON_Complex64_t *workz = (CHAMELEON_Complex64_t *)malloc(N*N*sizeof(CHAMELEON_Complex64_t));
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    double *workd = (double *)malloc(N*sizeof(double));
    double eps;

    eps = LAPACKE_dlamch_work('e');

    alpha = -1.0;
    beta  = 0.0;
    zone = 1.0;

    /* Rebuild the other part of the inverse matrix */
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    if(uplo == ChamUpper){
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       for(j=0; j<N; j++)
          for(i=0; i<j; i++)
             *(A2+j+i*LDA) = *(A2+i+j*LDA);
       cblas_zhemm(CblasColMajor, CblasLeft, CblasUpper, N, N, CBLAS_SADDR(alpha), A2, LDA, A1, LDA, CBLAS_SADDR(beta), workz, N);

    }
    else {
       for(j=0; j<N; j++)
          for(i=j; i<N; i++)
             *(A2+j+i*LDA) = *(A2+i+j*LDA);
       cblas_zhemm(CblasColMajor, CblasLeft, CblasLower, N, N, CBLAS_SADDR(alpha), A2, LDA, A1, LDA, CBLAS_SADDR(beta), workz, N);
    }

    /* Add the identity matrix to workz */
     for(i=0; i<N; i++)
        *(workz+i+i*N) = *(workz+i+i*N) + zone;


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    *rnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'O', N, N,    workz, N, workd);
    *anorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'O', N, N, A1, LDA, workd);
    *ainvnorm = LAPACKE_zlange_work(LAPACK_COL_MAJOR, 'O', N, N, A2, LDA, workd);
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      result = *rnorm / ( ((*anorm) * (*ainvnorm))*N*eps ) ;

    if (  isnan(*ainvnorm) || isinf(*ainvnorm) || isnan(result) || isinf(result) || (result > 60.0) ) {
        info_inverse = 1;
     }
    else{
        info_inverse = 0;
    }

    free(workz);
    free(workd);

    return info_inverse;
}