70 lines
2.0 KiB
Go
70 lines
2.0 KiB
Go
// Copyright ©2019 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package gonum
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dpbtrs solves a system of linear equations A*X = B with an n×n symmetric
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// positive definite band matrix A using the Cholesky factorization
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//
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// A = Uᵀ * U if uplo == blas.Upper
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// A = L * Lᵀ if uplo == blas.Lower
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//
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// computed by Dpbtrf. kd is the number of super- or sub-diagonals of A. See the
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// documentation for Dpbtrf for a description of the band storage format of A.
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//
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// On entry, b contains the n×nrhs right hand side matrix B. On return, it is
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// overwritten with the solution matrix X.
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func (Implementation) Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int) {
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switch {
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case uplo != blas.Upper && uplo != blas.Lower:
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panic(badUplo)
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case n < 0:
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panic(nLT0)
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case kd < 0:
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panic(kdLT0)
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case nrhs < 0:
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panic(nrhsLT0)
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case ldab < kd+1:
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panic(badLdA)
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case ldb < max(1, nrhs):
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panic(badLdB)
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}
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// Quick return if possible.
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if n == 0 || nrhs == 0 {
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return
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}
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if len(ab) < (n-1)*ldab+kd+1 {
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panic(shortAB)
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}
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if len(b) < (n-1)*ldb+nrhs {
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panic(shortB)
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}
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bi := blas64.Implementation()
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if uplo == blas.Upper {
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// Solve A*X = B where A = Uᵀ*U.
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for j := 0; j < nrhs; j++ {
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// Solve Uᵀ*Y = B, overwriting B with Y.
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bi.Dtbsv(blas.Upper, blas.Trans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
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// Solve U*X = Y, overwriting Y with X.
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bi.Dtbsv(blas.Upper, blas.NoTrans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
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}
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} else {
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// Solve A*X = B where A = L*Lᵀ.
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for j := 0; j < nrhs; j++ {
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// Solve L*Y = B, overwriting B with Y.
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bi.Dtbsv(blas.Lower, blas.NoTrans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
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// Solve Lᵀ*X = Y, overwriting Y with X.
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bi.Dtbsv(blas.Lower, blas.Trans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
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}
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}
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}
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