.TH "lasv2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lasv2 \- lasv2: 2x2 triangular SVD
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlasv2\fP (f, g, h, ssmin, ssmax, snr, csr, snl, csl)"
.br
.RI "\fBDLASV2\fP computes the singular value decomposition of a 2-by-2 triangular matrix\&. "
.ti -1c
.RI "subroutine \fBslasv2\fP (f, g, h, ssmin, ssmax, snr, csr, snl, csl)"
.br
.RI "\fBSLASV2\fP computes the singular value decomposition of a 2-by-2 triangular matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlasv2 (double precision f, double precision g, double precision h, double precision ssmin, double precision ssmax, double precision snr, double precision csr, double precision snl, double precision csl)"

.PP
\fBDLASV2\fP computes the singular value decomposition of a 2-by-2 triangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLASV2 computes the singular value decomposition of a 2-by-2
 triangular matrix
    [  F   G  ]
    [  0   H  ]\&.
 On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the
 smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
 right singular vectors for abs(SSMAX), giving the decomposition

    [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
    [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ]\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is DOUBLE PRECISION
          The (1,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is DOUBLE PRECISION
          abs(SSMIN) is the smaller singular value\&.
.fi
.PP
.br
\fISSMAX\fP 
.PP
.nf
          SSMAX is DOUBLE PRECISION
          abs(SSMAX) is the larger singular value\&.
.fi
.PP
.br
\fISNL\fP 
.PP
.nf
          SNL is DOUBLE PRECISION
.fi
.PP
.br
\fICSL\fP 
.PP
.nf
          CSL is DOUBLE PRECISION
          The vector (CSL, SNL) is a unit left singular vector for the
          singular value abs(SSMAX)\&.
.fi
.PP
.br
\fISNR\fP 
.PP
.nf
          SNR is DOUBLE PRECISION
.fi
.PP
.br
\fICSR\fP 
.PP
.nf
          CSR is DOUBLE PRECISION
          The vector (CSR, SNR) is a unit right singular vector for the
          singular value abs(SSMAX)\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  Any input parameter may be aliased with any output parameter\&.

  Barring over/underflow and assuming a guard digit in subtraction, all
  output quantities are correct to within a few units in the last
  place (ulps)\&.

  In IEEE arithmetic, the code works correctly if one matrix element is
  infinite\&.

  Overflow will not occur unless the largest singular value itself
  overflows or is within a few ulps of overflow\&.

  Underflow is harmless if underflow is gradual\&. Otherwise, results
  may correspond to a matrix modified by perturbations of size near
  the underflow threshold\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine slasv2 (real f, real g, real h, real ssmin, real ssmax, real snr, real csr, real snl, real csl)"

.PP
\fBSLASV2\fP computes the singular value decomposition of a 2-by-2 triangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLASV2 computes the singular value decomposition of a 2-by-2
 triangular matrix
    [  F   G  ]
    [  0   H  ]\&.
 On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the
 smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and
 right singular vectors for abs(SSMAX), giving the decomposition

    [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
    [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ]\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIF\fP 
.PP
.nf
          F is REAL
          The (1,1) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIG\fP 
.PP
.nf
          G is REAL
          The (1,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIH\fP 
.PP
.nf
          H is REAL
          The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fISSMIN\fP 
.PP
.nf
          SSMIN is REAL
          abs(SSMIN) is the smaller singular value\&.
.fi
.PP
.br
\fISSMAX\fP 
.PP
.nf
          SSMAX is REAL
          abs(SSMAX) is the larger singular value\&.
.fi
.PP
.br
\fISNL\fP 
.PP
.nf
          SNL is REAL
.fi
.PP
.br
\fICSL\fP 
.PP
.nf
          CSL is REAL
          The vector (CSL, SNL) is a unit left singular vector for the
          singular value abs(SSMAX)\&.
.fi
.PP
.br
\fISNR\fP 
.PP
.nf
          SNR is REAL
.fi
.PP
.br
\fICSR\fP 
.PP
.nf
          CSR is REAL
          The vector (CSR, SNR) is a unit right singular vector for the
          singular value abs(SSMAX)\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  Any input parameter may be aliased with any output parameter\&.

  Barring over/underflow and assuming a guard digit in subtraction, all
  output quantities are correct to within a few units in the last
  place (ulps)\&.

  In IEEE arithmetic, the code works correctly if one matrix element is
  infinite\&.

  Overflow will not occur unless the largest singular value itself
  overflows or is within a few ulps of overflow\&.

  Underflow is harmless if underflow is gradual\&. Otherwise, results
  may correspond to a matrix modified by perturbations of size near
  the underflow threshold\&.
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.