Documentation
Resource
Rate This Document
Findability
Accuracy
Completeness
Readability
SubmitClose

?bdsqr

Solve singular values or left and right singular vectors using SVD of the QR algorithm for a bidiagonal matrix.

Interface Definition

C interface:

void sbdsqr_(const char *uplo, const int *n, const int *ncvt, const int *nru, const int *ncc, float *d, float *e, float *vt, const int *ldvt, float *u, const int *ldu,

float *c, const int *ldc, float *work, int *info)

void dbdsqr_(const char *uplo, const int *n, const int *ncvt, const int *nru, const int *ncc, double *d, double *e, double *vt, const int *ldvt, double *u, const int *ldu,

double *c, const int *ldc, double *work, int *info)

void cbdsqr_(const char *uplo, const int *n, const int *ncvt, const int *nru, const int *ncc, float *d, float *e, float _Complex *vt, const int *ldvt, float _Complex *u, const int *ldu,

float _Complex *c, const int *ldc, float *work, int *info)

void zbdsqr_(const char *uplo, const int *n, const int *ncvt, const int *nru, const int *ncc, double *d, double *e, double _Complex *vt, const int *ldvt, double _Complex *u,

const int *ldu, double _Complex *c, const int *ldc, double *work, int *info)

Fortran interface:

SBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)

DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)

CBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)

ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)

Parameters

Parameter

Type

Description

Input/Output

uplo

Character
  • 'U': B is an upper bidiagonal matrix.
  • 'L': B is a lower bidiagonal matrix.

Input

n

Integer

Order of matrix B. n ≥ 0.

Input

nru

Integer

Number of rows in matrix U. nru ≥ 0.

Input

ncvt

Integer

Number of columns in matrix VT. ncvt ≥ 0.

Input

ncc

Integer

Number of columns in matrix C. ncc ≥ 0.

Input

d
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision floating-point array for cbdsqr
  • A double-precision floating-point array for zbdsqr

The dimension is n.

  • On entry: n diagonal elements of the bidiagonal matrix B.
  • On exit:
    • If info = 0, the singular values of matrix B are sorted in descending order.

Input/Output

e
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision floating-point array for cbdsqr
  • A double-precision floating-point array for zbdsqr

The dimension is n–1.

  • On entry: n–1 off-diagonal elements of the bidiagonal matrix B.
  • On exit:
    • If info = 0, e is destroyed.
    • If info > 0, d and e store the diagonal and superdiagonal elements, respectively, of the bidiagonal matrix resulting from the orthogonalization of the input.

Input

Output

vt
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision complex array for cbdsqr
  • A double-precision complex array for zbdsqr

The dimension is ldvt*ncvt. This parameter is meaningless if nvct = 0.

  • On entry: a matrix VT of size n*ncvt.
  • On exit: overwritten by P^H*VT.

Input/Output

ldvt

Integer

Leading dimension of vt.

  • If ncvt > 0, ldvt ≥ max (1, N).
  • If ncvt = 0, ldvt > -1.

Input

u
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision complex array for cbdsqr
  • A double-precision complex array for zbdsqr

The dimension is LDU*N. This parameter is meaningless if NRU = 0.

  • On entry: a matrix of size NRU*N.
  • On exit: U is overwritten by U*Q.

Input/Output

ldu

Integer

Leading dimension of matrix U; ldu ≥ max(1, NRU).

Input

c
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision complex array for cbdsqr
  • A double-precision complex array for zbdsqr

The dimension is LDC*NCC. This parameter is meaningless if NCC = 0.

  • On entry: matrix C in size N*NCC.
  • On exit: overwritten by Q^H*C.

Input/Output

ldc

Integer

Leading dimension of C.

  • If NCC > 0, LDC ≥ max(1, N).
  • If NCC = 0, LDC ≥ 1.

Input

work
  • A single-precision floating-point array for sbdsqr
  • A double-precision floating-point array for dbdsqr
  • A single-precision floating-point array for cbdsqr
  • A double-precision floating-point array for zbdsqr

The dimension is 4*N.

Output

info

Integer
  • 0: success.
  • Smaller than 0: If info = -i, the i-th parameter has an illegal value.
  • Greater than 0: An error occurs during calculation.

Output

Dependencies

#include "klapack.h"

Examples

C Interface

const char uplo = 'l';
const int n = 5;
const int ncvt = 5;
const int nru = 5;
const int ncc = 5;
const int ldu = 5;
const int ldvt = 5;
const int ldc = 5;

double d[] = {-151.409804,-96.158378,30.604367,-49.958984,-65.000480};
double e[] = {187.838419,-61.829661,47.241856,4.133032};
double u[] = {0.562230,-0.822915,-0.081874,-0.001979,0.000007,
              0.504441,0.270668,0.734742,0.363253,-0.021916,
              -0.297298,-0.191539,-0.135822,0.802484,-0.460975,
              -0.148954,-0.098365,-0.044364,0.423397,0.887076,
              -0.564680,-0.450761,0.658054,-0.211655,-0.010871};
double c[] = {72.1673, 66.1857, 64.7644, 28.0199, 91.4151,
              6.5180,  62.8483, 72.4323, 46.5760, 8.6928,
              28.9821, 42.1828, 18.6437, 99.8612, 35.6972,
              67.9812, 5.0880,  85.5035, 79.2945, 54.5920,
              28.6869, 49.7512, 7.5186,  28.6929, 84.6041};
double vt[] = {-0.943444,-0.291675,0.133196,0.063327,0.055560,
               0.331373,-0.816196,0.395311,0.189552,0.178367,
               -0.010230,0.452864,0.497591,0.289640,0.680678,
               0.000389,-0.208325,-0.619098,-0.271648,0.706772,
               -0.000002,0.016272,0.441712,-0.895754,0.047431};
double *work = (double*)malloc(4 * (n-1) * sizeof(double));

int info = 0;

dbdsqr_(&uplo, &n, &ncvt, &nru, &ncc, d, e, vt, &ldvt, u, &ldu, c, &ldc, work, &info);
if (info != 0) {
    printf("Error, info = %d\n", info);
    return info;
}

* output:
* d:
* 254.071515      87.547400       67.835074       64.370735       14.897476
* e:
* 0.000000        0.000000        0.000000        0.000000
* u:
* -0.074378       -0.669531       -0.639450       -0.366581       0.054025        0.159978        -0.508435       0.027239        0.845380        -0.022155       * -0.082621       0.347676        -0.436891       0.259353        0.783682        -0.684158       -0.337057       0.510908        -0.079527       0.388547        * -0.702835       0.242353        -0.372103       0.278142        -0.481107

* vt:
* 0.792096        0.561274        -0.189353       -0.143425       0.033614        -0.587068       0.711959        -0.120375       -0.230494       0.284338        * 0.154739        -0.190565       0.546605        -0.459085       0.655902        -0.063174       -0.042355       0.090008        -0.778081       -0.617013       * 0.000527        0.374135        0.801734        0.331865        -0.327278
* c:
* -19.247910      110.078454      -62.583336      72.822482       -34.891161      -54.076617      90.246359       9.555710        17.064964       5.701693        * -20.142043      75.228107       44.453325     64.653600        -44.635543      26.877086       126.100144      5.668549        67.580452       -1.791622       * -25.484162      42.029730       -35.053810      77.698370       -40.669875

Fortran Interface

CHARACTER :: uplo = "L"
PARAMETER (n = 5)  
PARAMETER (ncvt = 5)  
PARAMETER (nru = 5)  
PARAMETER (ncc = 5)  
PARAMETER (ldu = 5)
PARAMETER (ldc = 5)
PARAMETER (ldvt = 5)
INTEGER :: info = 0 
REAL(8) :: d(n)
REAL(8) :: e(n-1) 
REAL(8) :: u(ldu, n)
REAL(8) :: c(ldc, ncc)
REAL(8) :: vt(ldvt, ncvt)
REAL(8) :: work(4*(n-1))

DATA d / -151.409804,-96.158378,30.604367,-49.958984,-65.000480 /
DATA e / 187.838419,-61.829661,47.241856,4.133032 /
DATA u / 0.562230,-0.822915,-0.081874,-0.001979,0.000007,
         0.504441,0.270668,0.734742,0.363253,-0.021916,
         -0.297298,-0.191539,-0.135822,0.802484,-0.460975,
         -0.148954,-0.098365,-0.044364,0.423397,0.887076,
         -0.564680,-0.450761,0.658054,-0.211655,-0.010871 /
DATA c / 72.1673, 66.1857, 64.7644, 28.0199, 91.4151,
          6.5180,  62.8483, 72.4323, 46.5760, 8.6928,
          28.9821, 42.1828, 18.6437, 99.8612, 35.6972,
          67.9812, 5.0880,  85.5035, 79.2945, 54.5920,
          28.6869, 49.7512, 7.5186,  28.6929, 84.6041 /
DATA vt / -0.943444,-0.291675,0.133196,0.063327,0.055560,
           0.331373,-0.816196,0.395311,0.189552,0.178367,
           -0.010230,0.452864,0.497591,0.289640,0.680678,
           0.000389,-0.208325,-0.619098,-0.271648,0.706772,
           -0.000002,0.016272,0.441712,-0.895754,0.047431 /
EXTERNAL DBDSQR
CALL DBDSQR(uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info);

* output:
* d:
* 254.071515      87.547400       67.835074       64.370735       14.897476
* e:
* 0.000000        0.000000        0.000000        0.000000
* u:
* -0.074378       -0.669531       -0.639450       -0.366581       0.054025        0.159978        -0.508435       0.027239        0.845380        -0.022155       * -0.082621       0.347676        -0.436891       0.259353        0.783682        -0.684158       -0.337057       0.510908        -0.079527       0.388547        * -0.702835       0.242353        -0.372103       0.278142        -0.481107

* vt:
* 0.792096        0.561274        -0.189353       -0.143425       0.033614        -0.587068       0.711959        -0.120375       -0.230494       0.284338        * 0.154739        -0.190565       0.546605        -0.459085       0.655902        -0.063174       -0.042355       0.090008        -0.778081       -0.617013       * 0.000527        0.374135        0.801734        0.331865        -0.327278
* c:
* -19.247910      110.078454      -62.583336      72.822482       -34.891161      -54.076617      90.246359       9.555710        17.064964       5.701693        * -20.142043      75.228107       44.453325     64.653600        -44.635543      26.877086       126.100144      5.668549        67.580452       -1.791622       * -25.484162      42.029730       -35.053810      77.698370       -40.669875
Parent topic: SVD Functions
This site uses cookies to improve your browsing experience. By continuing to browse this site, you agree to our use of cookies.View Details