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// Copyright ©2020 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
// Dtbtrs solves a triangular system of the form
//
// A * X = B if trans == blas.NoTrans
// Aᵀ * X = B if trans == blas.Trans or blas.ConjTrans
//
// where A is an n×n triangular band matrix with kd super- or subdiagonals, and
// B is an n×nrhs matrix.
//
// Dtbtrs returns whether A is non-singular. If A is singular, no solution X is
// computed.
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) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case trans != blas.NoTrans && trans != blas.Trans && trans != blas.ConjTrans:
panic(badTrans)
case diag != blas.NonUnit && diag != blas.Unit:
panic(badDiag)
case n < 0:
panic(nLT0)
case kd < 0:
panic(kdLT0)
case nrhs < 0:
panic(nrhsLT0)
case lda < kd+1:
panic(badLdA)
case ldb < max(1, nrhs):
panic(badLdB)
}
// Quick return if possible.
if n == 0 {
return true
}
switch {
case len(a) < (n-1)*lda+kd+1:
panic(shortA)
case len(b) < (n-1)*ldb+nrhs:
panic(shortB)
}
// Check for singularity.
if diag == blas.NonUnit {
if uplo == blas.Upper {
for i := 0; i < n; i++ {
if a[i*lda] == 0 {
return false
}
}
} else {
for i := 0; i < n; i++ {
if a[i*lda+kd] == 0 {
return false
}
}
}
}
// Solve A * X = B or Aᵀ * X = B.
bi := blas64.Implementation()
for j := 0; j < nrhs; j++ {
bi.Dtbsv(uplo, trans, diag, n, kd, a, lda, b[j:], ldb)
}
return true
}
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