QRBackSubst

Solves least squares problem for QR-decomposed matrix.

Syntax

Case 1: Matrix - vector operation

IppStatus ippmQRBackSubst_mv_32f(const Ipp32f* pSrc1, int src1Stride1, int src1Stride2, Ipp32f* pBuffer, const Ipp32f* pSrc2, int src2Stride2, Ipp32f* pDst, int dstStride2, int width, int height);

IppStatus ippmQRBackSubst_mv_64f(const Ipp64f* pSrc1, int src1Stride1, int src1Stride2, Ipp64f* pBuffer, const Ipp64f* pSrc2, int src2Stride2, Ipp64f* pDst, int dstStride2, int width, int height);

IppStatus ippmQRBackSubst_mv_32f_P(const Ipp32f** ppSrc1, int src1RoiShift, Ipp32f* pBuffer, const Ipp32f** ppSrc2, int src2RoiShift, Ipp32f** ppDst, int dstRoiShift, int width, int height);

IppStatus ippmQRBackSubst_mv_64f_P(const Ipp64f** ppSrc1, int src1RoiShift, Ipp64f* pBuffer, const Ipp64f** ppSrc2, int src2RoiShift, Ipp64f** ppDst, int dstRoiShift, int width, int height);

Case 2: Matrix - vector array operation

IppStatus ippmQRBackSubst_mva_32f(const Ipp32f* pSrc1, int src1Stride0, int src1Stride1, int src1Stride2, Ipp32f* pBuffer, const Ipp32f* pSrc2, int src2Stride0, int src2Stride2, Ipp32f* pDst, int dstStride0, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mva_64f(const Ipp64f* pSrc1, int src1Stride0, int src1Stride1, int src1Stride2, Ipp64f* pBuffer, const Ipp64f* pSrc2, int src2Stride0, int src2Stride2, Ipp64f* pDst, int dstStride0, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mva_32f_P(const Ipp32f** ppSrc1, int src1RoiShift, Ipp32f* pBuffer, const Ipp32f** ppSrc2, int src2RoiShift, int src2Stride0, Ipp32f** ppDst, int dstRoiShift, int dstStride0, int width, int height, int count);

IppStatus ippmQRBackSubst_mva_64f_P(const Ipp64f** ppSrc1, int src1RoiShift, Ipp64f* pBuffer, const Ipp64f** ppSrc2, int src2RoiShift, int src2Stride0, Ipp64f** ppDst, int dstRoiShift, int dstStride0, int width, int height, int count);

IppStatus ippmQRBackSubst_mva_32f_L(const Ipp32f** ppSrc1, int src1RoiShift, int src1Stride1, int src1Stride2, Ipp32f* pBuffer, const Ipp32f** ppSrc2, int src2RoiShift, int src2Stride2, Ipp32f** ppDst, int dstRoiShift, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mva_64f_L(const Ipp64f** ppSrc1, int src1RoiShift, int src1Stride1, int src1Stride2, Ipp64f* pBuffer, const Ipp64f** ppSrc2, int src2RoiShift, int src2Stride2, Ipp64f** ppDst, int dstRoiShift, int dstStride2, int width, int height, int count);

Case 3: Matrix array - vector array operation

IppStatus ippmQRBackSubst_mava_32f(const Ipp32f* pSrc1, int src1Stride0, int src1Stride1, int src1Stride2, Ipp32f* pBuffer, const Ipp32f* pSrc2, int src2Stride0, int src2Stride2, Ipp32f* pDst, int dstStride0, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mava_64f(const Ipp64f* pSrc1, int src1Stride0, int src1Stride1, int src1Stride2, Ipp64f* pBuffer, const Ipp64f* pSrc2, int src2Stride0, int src2Stride2, Ipp64f* pDst, int dstStride0, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mava_32f_P(const Ipp32f** ppSrc1, int src1RoiShift, int src1Stride0, Ipp32f* pBuffer, const Ipp32f** ppSrc2, int src2RoiShift, int src2Stride0, Ipp32f** ppDst, int dstRoiShift, int dstStride0, int width, int height, int count);

IppStatus ippmQRBackSubst_mava_64f_P(const Ipp64f** ppSrc1, int src1RoiShift, int src1Stride0, Ipp64f* pBuffer, const Ipp64f** ppSrc2, int src2RoiShift, int src2Stride0, Ipp64f** ppDst, int dstRoiShift, int dstStride0, int width, int height, int count);

IppStatus ippmQRBackSubst_mava_32f_L(const Ipp32f** ppSrc1, int src1RoiShift, int src1Stride1, int src1Stride2, Ipp32f* pBuffer, const Ipp32f** ppSrc2, int src2RoiShift, int src2Stride2, Ipp32f** ppDst, int dstRoiShift, int dstStride2, int width, int height, int count);

IppStatus ippmQRBackSubst_mava_64f_L(const Ipp64f** ppSrc1, int src1RoiShift, int src1Stride1, int src1Stride2, Ipp64f* pBuffer, const Ipp64f** ppSrc2, int src2RoiShift, int src2Stride2, Ipp64f** ppDst, int dstRoiShift, int dstStride2, int width, int height, int count);

Parameters

pSrc1, ppSrc1	Pointer to the source matrix or array of matrices. The matrix(ces) must be a result of calling ippmQRDecomp .
src1Stride0	Stride between the matrices in the source matrix array.
src1Stride1	Stride between the rows in the source matrix(ces).
src1Stride2	Stride between the elements in the source matrix(ces).
src1RoiShift	ROI shift in the source matrix(ces).
pSrc2, ppSrc2	Pointer to the source vector or array of vectors.
src2Stride0	Stride between the vectors in the source vector array.
src2Stride2	Stride between the elements in the source vector(s).
src2RoiShift	ROI shift in the source vector(s).
pBuffer	Pointer to a pre-allocated auxiliary array to be used for internal computations. The number of elements in the array must be at least height.
pDst, ppDst	Pointer to the destination matrix or array of matrices.
dstStride0	Stride between the vectors in the destination array.
dstStride2	Stride between the elements of the destination vector(s).
dstRoiShift	ROI shift in the destination vector(s).
width	Matrix width and destination vector length.
height	Matrix height and source vector length.
count	Number of matrices and right-hand part vectors in the array.

Description

The function ippmQRBackSubst is declared in the ippm.h header file. The function solves the least squares problem for an overdetermined system of linear equations

Ax = b,

where

A is the matrix of linear equations system, stored in pSrc1 or ppSrc1,

b is the vector of the right-hand side, stored in pSrc2 or ppSrc2,

x is the unknown vector, stored in pDst or ppDst.

The number of equations in the system height is equal to or greater than the number of unknown variables width, rank (A) = width.

A typical least squares problem is as follows: given a matrix A and a vector b, find the vector x that minimizes the L2-norm

You should call the function ippmQRDecomp to compute the QR decomposition of A before calling the ippmQRBackSubst function (Please see description for the function ippmQRDecomp.)

The following example demonstrates how to use the functions ippmQRDecomp_m_32f and ippmQRBackSubst_mva_32f. For more information, see also examples in Getting Started.

ippmQRFactorization_32f

IppStatus QRFactorization_32f(void) {

    /* Source matrix with width=4 and height=5 */

    Ipp32f pSrc[5*4] = {1, 1, 1, 1,

                        1, 3, 1, 1,

                        1,-1, 3, 1,

                        1, 1, 1, 3,

                        1, 1, 1, -1 };

    int srcStride2 = sizeof(Ipp32f);

    int srcStride1 = 4*sizeof(Ipp32f);

 
        /* Solver right-part is 2 vectors with length=5 */

    Ipp32f pSrc2[2*5] = { 2, 1, 6, 3, 1,

                          3, 4, 5, 6, 1 };

    int src2Stride2 = sizeof(Ipp32f);

    int src2Stride0 = 5*sizeof(Ipp32f);

    Ipp32f pDecomp[5*4]; /* Decomposed matrix location */

    int decompStride2 = sizeof(Ipp32f);

    int decompStride1 = 4*sizeof(Ipp32f);

    Ipp32f pDst[2*4]; /* Solver destination location */

    int dstStride2 = sizeof(Ipp32f);

    int dstStride0 = 4*sizeof(Ipp32f);

 
    int width  = 4;

    int height = 5;

    int count  = 2;

    Ipp32f pBuffer[5];  /* Buffer location */

    IppStatus status = ippmQRDecomp_m_32f((const Ipp32f*)pSrc,

        srcStride1, srcStride2, pBuffer,

        pDecomp, decompStride1, decompStride2, width, height);

    status = ippmQRBackSubst_mva_32f((const Ipp32f*)pDecomp,

       decompStride1, decompStride2, pBuffer, pSrc2, src2Stride0,

       src2Stride2, pDst, dstStride0, dstStride2, width, height, count);

/*

    // It is required for QR decomposition function to check return status

    // for catching wrong result in case of invalid input data

*/

    if (status == ippStsNoErr) {

       status = ippmQRBackSubst_mva_32f((const Ipp32f*)pDecomp,

           decompStride1, decompStride2, pBuffer, pSrc2, src2Stride0,

           src2Stride2, pDst, dstStride0, dstStride2, width, height, count);

        printf_m_Ipp32f("QRDecomp result:", pDecomp, 4, 5, status);

        printf_va_Ipp32f("2 destination vectors:", pDst, 4, 2, status);

    } else {

        printf("Function returns status: %s \n", ippGetStatusString(status));

    return status;

The program above produces the following output:

QRDecomp result:

-2.236068 -2.236068 -3.130495 -2.236068

0.309017 -2.828427 1.414214 -0.000000

0.309017 -0.414214 -1.095445 0.000000

0.309017 -0.000000 -0.130449 -2.828427

0.309017 -0.000000 -0.130449 -0.414214

2 destination vectors:

0.500000 -0.500000 1.500000 0.500000

0.583333 0.333333 1.166667 1.250000

Return Values

ippStsOk	Returns no error.
ippStsNullPtrErr	Returns an error when one of the input pointers is NULL.
ippStsSizeErr	Returns an error when the size of the source matrix is equal to 0.
ippStsStrideMatrixErr	Returns an error when the stride value is not positive or not divisible by size of data type.
ippStsRoiShiftMatrixErr	RoiShift value is negative or not divisible by size of data type.
ippStsCountMatrixErr	Returns an error when the count value is less or equal to zero.
ippStsSizeMatchMatrixErr	Returns an error when the sizes of the source matrices are unsuitable.