mirror of
https://github.com/gonum/gonum.git
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136 lines
3.1 KiB
Go
136 lines
3.1 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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"math"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/lapack"
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)
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// Dlansb returns the given norm of an n×n symmetric band matrix with kd
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// super-diagonals.
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//
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// When norm is lapack.MaxColumnSum or lapack.MaxRowSum, the length of work must
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// be at least n.
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func (impl Implementation) Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64 {
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switch {
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case norm != lapack.MaxAbs && norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius:
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panic(badNorm)
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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 ldab < kd+1:
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panic(badLdA)
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}
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// Quick return if possible.
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if n == 0 {
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return 0
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}
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switch {
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case len(ab) < (n-1)*ldab+kd+1:
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panic(shortAB)
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case len(work) < n && (norm == lapack.MaxColumnSum || norm == lapack.MaxRowSum):
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panic(shortWork)
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}
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var value float64
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switch norm {
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case lapack.MaxAbs:
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if uplo == blas.Upper {
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for i := 0; i < n; i++ {
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for j := 0; j < min(n-i, kd+1); j++ {
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aij := math.Abs(ab[i*ldab+j])
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if aij > value || math.IsNaN(aij) {
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value = aij
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}
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}
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}
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} else {
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for i := 0; i < n; i++ {
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for j := max(0, kd-i); j < kd+1; j++ {
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aij := math.Abs(ab[i*ldab+j])
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if aij > value || math.IsNaN(aij) {
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value = aij
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}
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}
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}
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}
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case lapack.MaxColumnSum, lapack.MaxRowSum:
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work = work[:n]
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var sum float64
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if uplo == blas.Upper {
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for i := range work {
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work[i] = 0
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}
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for i := 0; i < n; i++ {
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sum := work[i] + math.Abs(ab[i*ldab])
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for j := i + 1; j < min(i+kd+1, n); j++ {
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aij := math.Abs(ab[i*ldab+j-i])
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sum += aij
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work[j] += aij
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}
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if sum > value || math.IsNaN(sum) {
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value = sum
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}
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}
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} else {
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for i := 0; i < n; i++ {
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sum = 0
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for j := max(0, i-kd); j < i; j++ {
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aij := math.Abs(ab[i*ldab+kd+j-i])
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sum += aij
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work[j] += aij
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}
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work[i] = sum + math.Abs(ab[i*ldab+kd])
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}
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for _, sum := range work {
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if sum > value || math.IsNaN(sum) {
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value = sum
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}
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}
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}
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case lapack.Frobenius:
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scale := 0.0
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ssq := 1.0
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if uplo == blas.Upper {
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if kd > 0 {
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// Sum off-diagonals.
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for i := 0; i < n-1; i++ {
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ilen := min(n-i-1, kd)
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rowscale, rowssq := impl.Dlassq(ilen, ab[i*ldab+1:], 1, 0, 1)
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scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
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}
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ssq *= 2
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}
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// Sum diagonal.
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dscale, dssq := impl.Dlassq(n, ab, ldab, 0, 1)
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scale, ssq = impl.Dcombssq(scale, ssq, dscale, dssq)
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} else {
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if kd > 0 {
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// Sum off-diagonals.
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for i := 1; i < n; i++ {
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ilen := min(i, kd)
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rowscale, rowssq := impl.Dlassq(ilen, ab[i*ldab+kd-ilen:], 1, 0, 1)
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scale, ssq = impl.Dcombssq(scale, ssq, rowscale, rowssq)
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}
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ssq *= 2
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}
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// Sum diagonal.
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dscale, dssq := impl.Dlassq(n, ab[kd:], ldab, 0, 1)
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scale, ssq = impl.Dcombssq(scale, ssq, dscale, dssq)
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}
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value = scale * math.Sqrt(ssq)
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}
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return value
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}
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