blob: f3d9559db7b28a0f87dbd4f35ce270d85e5f653f [file] [log] [blame]
// Copyright ©2019 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"
)
// Dpbtrs solves a system of linear equations A*X = B with an n×n symmetric
// positive definite band matrix A using the Cholesky factorization
// A = Uᵀ * U if uplo == blas.Upper
// A = L * Lᵀ if uplo == blas.Lower
// computed by Dpbtrf. kd is the number of super- or sub-diagonals of A. See the
// documentation for Dpbtrf for a description of the band storage format of A.
//
// On entry, b contains the n×nrhs right hand side matrix B. On return, it is
// overwritten with the solution matrix X.
func (Implementation) Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case kd < 0:
panic(kdLT0)
case nrhs < 0:
panic(nrhsLT0)
case ldab < kd+1:
panic(badLdA)
case ldb < max(1, nrhs):
panic(badLdB)
}
// Quick return if possible.
if n == 0 || nrhs == 0 {
return
}
if len(ab) < (n-1)*ldab+kd+1 {
panic(shortAB)
}
if len(b) < (n-1)*ldb+nrhs {
panic(shortB)
}
bi := blas64.Implementation()
if uplo == blas.Upper {
// Solve A*X = B where A = Uᵀ*U.
for j := 0; j < nrhs; j++ {
// Solve Uᵀ*Y = B, overwriting B with Y.
bi.Dtbsv(blas.Upper, blas.Trans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
// Solve U*X = Y, overwriting Y with X.
bi.Dtbsv(blas.Upper, blas.NoTrans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
}
} else {
// Solve A*X = B where A = L*Lᵀ.
for j := 0; j < nrhs; j++ {
// Solve L*Y = B, overwriting B with Y.
bi.Dtbsv(blas.Lower, blas.NoTrans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
// Solve Lᵀ*X = Y, overwriting Y with X.
bi.Dtbsv(blas.Lower, blas.Trans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
}
}
}