gonum.org/v1/gonum@v0.14.0/lapack/gonum/dtbtrs.go (about)

     1  // Copyright ©2020 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package gonum
     6  
     7  import (
     8  	"gonum.org/v1/gonum/blas"
     9  	"gonum.org/v1/gonum/blas/blas64"
    10  )
    11  
    12  // Dtbtrs solves a triangular system of the form
    13  //
    14  //	A * X = B   if trans == blas.NoTrans
    15  //	Aᵀ * X = B  if trans == blas.Trans or blas.ConjTrans
    16  //
    17  // where A is an n×n triangular band matrix with kd super- or subdiagonals, and
    18  // B is an n×nrhs matrix.
    19  //
    20  // Dtbtrs returns whether A is non-singular. If A is singular, no solution X is
    21  // computed.
    22  func (impl Implementation) Dtbtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, kd, nrhs int, a []float64, lda int, b []float64, ldb int) (ok bool) {
    23  	switch {
    24  	case uplo != blas.Upper && uplo != blas.Lower:
    25  		panic(badUplo)
    26  	case trans != blas.NoTrans && trans != blas.Trans && trans != blas.ConjTrans:
    27  		panic(badTrans)
    28  	case diag != blas.NonUnit && diag != blas.Unit:
    29  		panic(badDiag)
    30  	case n < 0:
    31  		panic(nLT0)
    32  	case kd < 0:
    33  		panic(kdLT0)
    34  	case nrhs < 0:
    35  		panic(nrhsLT0)
    36  	case lda < kd+1:
    37  		panic(badLdA)
    38  	case ldb < max(1, nrhs):
    39  		panic(badLdB)
    40  	}
    41  
    42  	// Quick return if possible.
    43  	if n == 0 {
    44  		return true
    45  	}
    46  
    47  	switch {
    48  	case len(a) < (n-1)*lda+kd+1:
    49  		panic(shortA)
    50  	case len(b) < (n-1)*ldb+nrhs:
    51  		panic(shortB)
    52  	}
    53  
    54  	// Check for singularity.
    55  	if diag == blas.NonUnit {
    56  		if uplo == blas.Upper {
    57  			for i := 0; i < n; i++ {
    58  				if a[i*lda] == 0 {
    59  					return false
    60  				}
    61  			}
    62  		} else {
    63  			for i := 0; i < n; i++ {
    64  				if a[i*lda+kd] == 0 {
    65  					return false
    66  				}
    67  			}
    68  		}
    69  	}
    70  
    71  	// Solve A * X = B  or Aᵀ * X = B.
    72  	bi := blas64.Implementation()
    73  	for j := 0; j < nrhs; j++ {
    74  		bi.Dtbsv(uplo, trans, diag, n, kd, a, lda, b[j:], ldb)
    75  	}
    76  	return true
    77  }