使用英特尔 MKL 计算“trans(a)*inv(b)*a”的正确方法

我在用英特尔的 MKL LAPACKE 和 CBLAS https://software.intel.com/en-us/mkl-developer-reference-c-cblas-gemm计算

yn = trans(a)*inv(zt)*a + trans(b)*inv(zl)*b

Where a and b是 m×n 实数矩阵，zt and zl是 m×m 的复数矩阵。由此产生的复杂矩阵yn是n×n。

我是这样做的：

zt <- inv(zt)
zl <- inv(zl)
c <- zt*a
yn <- trans(a)*c
c <- zl*b
yn <- trans(b)*c + yn

实际代码：

#include <math.h>
#include <complex.h>
#include <stdlib.h>
#include <mkl_types.h>
#define MKL_Complex16 _Complex double //overwrite type
#include <mkl.h>
#include <mkl_lapacke.h>

int calc_yn(
    _Complex double* yn, double* a, double *b, _Complex double* zl,
    _Complex double* zt, int m, int n)
{
    lapack_int* ipiv = (MKL_INT*) malloc(sizeof(lapack_int)*m);
    LAPACKE_zgetrf(LAPACK_ROW_MAJOR, m, m, zt, m, ipiv);
    LAPACKE_zgetri(LAPACK_ROW_MAJOR, m, zt, m, ipiv);
    LAPACKE_zgetrf(LAPACK_ROW_MAJOR, m, m, zl, m, ipiv);
    LAPACKE_zgetri(LAPACK_ROW_MAJOR, m, zl, m, ipiv);
    free(ipiv);
    const double alpha = 1.0;
    const double beta = 0.0;
    lapack_complex_double* c = (lapack_complex_double*) malloc(
        sizeof(lapack_complex_double)*(m*n));
    // c <- zt*a
    cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
                m, n, m,
                &alpha, zt, m, a, n,
                &beta, c, n);
    // yn <- aT*c
    cblas_zgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
                n, n, m,
                &alpha, a, n, c, n,
                &beta, yn, n);
    // c <- zl*b
    cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
                m, n, m,
                &alpha, zl, m, b, n,
                &beta, c, n);
    // yn <- bT*c + yn
    cblas_zgemm(CblasRowMajor, CblasTrans, CblasNoTrans,
                n, n, m,
                &alpha, b, n, c, n,
                &alpha, yn, n);
    free(c);
    return 0;
}

int main()
{
    int m = 2;
    int n = 3;
    _Complex double* yn = (_Complex double*) malloc(sizeof(_Complex double*)*(n*n));
    double a[] = {
        0.5, 0.0, 0.5,
        0.5, 0.5, 0.0
    };
    double b[] = {
        1.0, 0.0, -1.0,
        1.0, -1.0, 0.0
    };
    _Complex double zt[] = {
        (0.004 + 0.09*I), (-0.004 - 0.12*I),
        (-0.004 - 0.12*I), (0.005 + 0.11*I)
    };
    _Complex double zl[] = {
        (0.1 + 2.13*I), (-124.004 - 800.12*I),
        (-124.004 - 800.12*I), (0.4 + 4.08*I)
    };
    calc_yn(yn, a, b, zl, zt, m, n);
    free(yn);
    return 0;
}
// compile command (MKLROOT is defined by a bash script that is shipped together with intel's MKL):
//gcc -std=c11 -DMKL_ILP64 -m64 -g -o test.a test.c -L${MKLROOT}/lib/intel64 -Wl,--no-as-needed -lmkl_intel_ilp64 -lmkl_intel_thread -lmkl_core -liomp5 -lpthread -lm -ldl

当我运行该测试时出现错误

*** Error in `./test.a': free(): invalid next size (fast): 0x0000000001f72010 ***
======= Backtrace: =========
/lib/x86_64-linux-gnu/libc.so.6(+0x777e5)[0x7f8dee29c7e5]
/lib/x86_64-linux-gnu/libc.so.6(+0x8037a)[0x7f8dee2a537a]
/lib/x86_64-linux-gnu/libc.so.6(cfree+0x4c)[0x7f8dee2a953c]
./test.a[0x400d49]
/lib/x86_64-linux-gnu/libc.so.6(__libc_start_main+0xf0)[0x7f8dee245830]
./test.a[0x4007b9]
======= Memory map: ========
00400000-00401000 r-xp 00000000 08:06 2883692                            /home/pedro/codigos/HP_HEM/test.a
00601000-00602000 r--p 00001000 08:06 2883692                            /home/pedro/codigos/HP_HEM/test.a
00602000-00603000 rw-p 00002000 08:06 2883692                            /home/pedro/codigos/HP_HEM/test.a
01f72000-01f93000 rw-p 00000000 00:00 0                                  [heap]
7f8de4000000-7f8de4021000 rw-p 00000000 00:00 0 
7f8de4021000-7f8de8000000 ---p 00000000 00:00 0 
7f8de9d2f000-7f8dea73e000 rw-p 00000000 00:00 0 
7f8dea73e000-7f8deddf9000 r-xp 00000000 08:06 2505573                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_avx2.so
7f8deddf9000-7f8dedff8000 ---p 036bb000 08:06 2505573                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_avx2.so
7f8dedff8000-7f8dedfff000 r--p 036ba000 08:06 2505573                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_avx2.so
7f8dedfff000-7f8dee00a000 rw-p 036c1000 08:06 2505573                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_avx2.so
7f8dee00a000-7f8dee00f000 rw-p 00000000 00:00 0 
7f8dee00f000-7f8dee025000 r-xp 00000000 08:06 1184923                    /lib/x86_64-linux-gnu/libgcc_s.so.1
7f8dee025000-7f8dee224000 ---p 00016000 08:06 1184923                    /lib/x86_64-linux-gnu/libgcc_s.so.1
7f8dee224000-7f8dee225000 rw-p 00015000 08:06 1184923                    /lib/x86_64-linux-gnu/libgcc_s.so.1
7f8dee225000-7f8dee3e5000 r-xp 00000000 08:06 1184885                    /lib/x86_64-linux-gnu/libc-2.23.so
7f8dee3e5000-7f8dee5e5000 ---p 001c0000 08:06 1184885                    /lib/x86_64-linux-gnu/libc-2.23.so
7f8dee5e5000-7f8dee5e9000 r--p 001c0000 08:06 1184885                    /lib/x86_64-linux-gnu/libc-2.23.so
7f8dee5e9000-7f8dee5eb000 rw-p 001c4000 08:06 1184885                    /lib/x86_64-linux-gnu/libc-2.23.so
7f8dee5eb000-7f8dee5ef000 rw-p 00000000 00:00 0 
7f8dee5ef000-7f8dee5f2000 r-xp 00000000 08:06 1184909                    /lib/x86_64-linux-gnu/libdl-2.23.so
7f8dee5f2000-7f8dee7f1000 ---p 00003000 08:06 1184909                    /lib/x86_64-linux-gnu/libdl-2.23.so
7f8dee7f1000-7f8dee7f2000 r--p 00002000 08:06 1184909                    /lib/x86_64-linux-gnu/libdl-2.23.so
7f8dee7f2000-7f8dee7f3000 rw-p 00003000 08:06 1184909                    /lib/x86_64-linux-gnu/libdl-2.23.so
7f8dee7f3000-7f8dee8fb000 r-xp 00000000 08:06 1184955                    /lib/x86_64-linux-gnu/libm-2.23.so
7f8dee8fb000-7f8deeafa000 ---p 00108000 08:06 1184955                    /lib/x86_64-linux-gnu/libm-2.23.so
7f8deeafa000-7f8deeafb000 r--p 00107000 08:06 1184955                    /lib/x86_64-linux-gnu/libm-2.23.so
7f8deeafb000-7f8deeafc000 rw-p 00108000 08:06 1184955                    /lib/x86_64-linux-gnu/libm-2.23.so
7f8deeafc000-7f8deeb14000 r-xp 00000000 08:06 1185031                    /lib/x86_64-linux-gnu/libpthread-2.23.so
7f8deeb14000-7f8deed13000 ---p 00018000 08:06 1185031                    /lib/x86_64-linux-gnu/libpthread-2.23.so
7f8deed13000-7f8deed14000 r--p 00017000 08:06 1185031                    /lib/x86_64-linux-gnu/libpthread-2.23.so
7f8deed14000-7f8deed15000 rw-p 00018000 08:06 1185031                    /lib/x86_64-linux-gnu/libpthread-2.23.so
7f8deed15000-7f8deed19000 rw-p 00000000 00:00 0 
7f8deed19000-7f8deeeb6000 r-xp 00000000 08:06 2505566                    /opt/intel/compilers_and_libraries_2018.2.199/linux/compiler/lib/intel64_lin/libiomp5.so
7f8deeeb6000-7f8def0b6000 ---p 0019d000 08:06 2505566                    /opt/intel/compilers_and_libraries_2018.2.199/linux/compiler/lib/intel64_lin/libiomp5.so
7f8def0b6000-7f8def0b8000 r--p 0019d000 08:06 2505566                    /opt/intel/compilers_and_libraries_2018.2.199/linux/compiler/lib/intel64_lin/libiomp5.so
7f8def0b8000-7f8def0c2000 rw-p 0019f000 08:06 2505566                    /opt/intel/compilers_and_libraries_2018.2.199/linux/compiler/lib/intel64_lin/libiomp5.so
7f8def0c2000-7f8def0f1000 rw-p 00000000 00:00 0 
7f8def0f1000-7f8df2eb3000 r-xp 00000000 08:06 2505576                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_core.so
7f8df2eb3000-7f8df30b2000 ---p 03dc2000 08:06 2505576                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_core.so
7f8df30b2000-7f8df30b9000 r--p 03dc1000 08:06 2505576                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_core.so
7f8df30b9000-7f8df30e6000 rw-p 03dc8000 08:06 2505576                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_core.so
7f8df30e6000-7f8df30fa000 rw-p 00000000 00:00 0 
7f8df30fa000-7f8df4fd7000 r-xp 00000000 08:06 2505580                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_thread.so
7f8df4fd7000-7f8df51d6000 ---p 01edd000 08:06 2505580                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_thread.so
7f8df51d6000-7f8df51da000 r--p 01edc000 08:06 2505580                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_thread.so
7f8df51da000-7f8df543e000 rw-p 01ee0000 08:06 2505580                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_thread.so
7f8df543e000-7f8df5446000 rw-p 00000000 00:00 0 
7f8df5446000-7f8df5c5b000 r-xp 00000000 08:06 2505578                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_ilp64.so
7f8df5c5b000-7f8df5e5a000 ---p 00815000 08:06 2505578                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_ilp64.so
7f8df5e5a000-7f8df5e5c000 r--p 00814000 08:06 2505578                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_ilp64.so
7f8df5e5c000-7f8df5e6e000 rw-p 00816000 08:06 2505578                    /opt/intel/compilers_and_libraries_2018.2.199/linux/mkl/lib/intel64_lin/libmkl_intel_ilp64.so
7f8df5e6e000-7f8df5e74000 rw-p 00000000 00:00 0 
7f8df5e74000-7f8df5e9a000 r-xp 00000000 08:06 1184857                    /lib/x86_64-linux-gnu/ld-2.23.so
7f8df6028000-7f8df607d000 rw-p 00000000 00:00 0 
7f8df6096000-7f8df6099000 rw-p 00000000 00:00 0 
7f8df6099000-7f8df609a000 r--p 00025000 08:06 1184857                    /lib/x86_64-linux-gnu/ld-2.23.so
7f8df609a000-7f8df609b000 rw-p 00026000 08:06 1184857                    /lib/x86_64-linux-gnu/ld-2.23.so
7f8df609b000-7f8df609c000 rw-p 00000000 00:00 0 
7ffc998d2000-7ffc998f4000 rw-p 00000000 00:00 0                          [stack]
7ffc99987000-7ffc9998a000 r--p 00000000 00:00 0                          [vvar]
7ffc9998a000-7ffc9998c000 r-xp 00000000 00:00 0                          [vdso]
ffffffffff600000-ffffffffff601000 r-xp 00000000 00:00 0                  [vsyscall]
Aborted (core dumped)

它不显示我是否评论第二次和第四次调用zgemm。从我读到的docs https://software.intel.com/en-us/mkl-developer-reference-c-cblas-gemm，参数正确。我尝试更改它们，但错误仍然存​​在，或者出现参数不正确的错误，例如：

Intel MKL ERROR: Parameter 9 was incorrect on entry to cblas_zgemm.

那么，我的代码有什么问题吗？

变量yn被声明为一个指向_Complex double，即它可以看作是一个数组_Complex double元素。但是你分配内存n*n类型元素_Complex double*.

如果尺寸为_Complex double大于_Complex double*（很有可能，可能两次（甚至four倍）大小），那么您分配的内存就很少，并且在使用数组时会超出范围。

出界会导致未定义的行为 https://en.wikipedia.org/wiki/Undefined_behavior.