6.5.1 vsip_dqrd_create_p - Create QR Decomposition Object

typedef enum _vsip_qrd_qopt { 
  VSIP_QRD_NOSAVEQ = 0, // Do not save Q 
  VSIP_QRD_SAVEQ   = 1, // Save full Q 
  VSIP_QRD_SAVEQ1  = 2 // Save skinny Q 
} vsip_qrd_qopt; 
 
vsip_qr_f* vsip_qrd_create_f(vsip_length m, vsip_length n, vsip_qrd_qopt qopt); 
vsip_cqr_f* vsip_cqrd_create_f(vsip_length m, vsip_length n, vsip_qrd_qopt qopt);

Description

This function creates a QR decomposition object that can be used to compute the QR factorization of an matrix. The QR decomposition expresses a matrix as the product of an orthogonal matrix and an upper triangular matrix , such that .

The vsip_qrd_qopt parameter allows you to specify how the orthogonal matrix should be stored.

Parameters

• vsip_length m: Number of rows in the matrix to be decomposed.

• vsip_length n: Number of columns in the matrix to be decomposed.

• vsip_qrd_qopt qopt: Option specifying how the matrix should be saved:

  • VSIP_QRD_NOSAVEQ: Don’t save (only compute )

  • VSIP_QRD_SAVEQ1: Save essential parts of (more memory efficient)

  • VSIP_QRD_SAVEQ: Save full matrix

Return Value

• On success, returns a pointer to the newly created QR decomposition object.

• On error (e.g., if memory allocation fails), returns NULL.

Example

vsip_qr_f *qrd; 
vsip_length m = 100, n = 50; 
 
// Create a QR decomposition object 
// Using SAVEQ2 as a good compromise between memory and functionality 
qrd = vsip_qrd_create_f(m, n, VSIP_QRD_SAVEQ2); 
 
if (qrd == NULL) { 
    fprintf(stderr, "Failed to create QR decomposition object\n"); 
    return; 
}

Notes

• The QR decomposition object must be destroyed with vsip_dqrd_destroy_p when no longer needed.

• The choice of qopt affects both memory usage and the operations that can be performed with the decomposition:

  • VSIP_QRD_SAVEQ allows full access to but uses more memory

  • VSIP_QRD_SAVEQ1 is a good compromise for most applications

  • VSIP_QRD_NOSAVEQ is most memory efficient but only allows operations with

• For square matrices (), the QR decomposition can be used to compute determinants and inverses.

• For tall matrices (), the decomposition is useful for least squares problems.

• This function allocates internal storage for the decomposition, which is freed when the QR object is destroyed.

• For repeated decompositions of matrices with the same dimensions, you can reuse the QR object by calling vsip_dqrd_p multiple times with the same object.