lapack/gonum: add Dpbtrs

lapack/gonum/dpbtrs.go

@@ -0,0 +1,62 @@
+// 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 a symmetric positive
+// definite band matrix A using the Cholesky factorization A = U^T * U or
+// A = L * L^T  computed by Dpbtrf.
+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 {
+		panic(shortAB)
+	}
+	if len(b) < (n-1)*ldb+nrhs {
+		panic(shortB)
+	}
+
+	bi := blas64.Implementation()
+	if uplo == blas.Upper {
+		// Solve A*X = B where A = U^T*U.
+		for j := 0; j < nrhs; j++ {
+			// Solve U^T*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*L^T.
+		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 L^T*X = Y, overwriting Y with X.
+			bi.Dtbsv(blas.Lower, blas.Trans, blas.NonUnit, n, kd, ab, ldab, b[j:], ldb)
+		}
+	}
+	return
+}