github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/testlapack/dlasq2.go (about) 1 // Copyright ©2015 The gonum Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package testlapack 6 7 import ( 8 "fmt" 9 "math" 10 "math/rand" 11 "testing" 12 13 "github.com/gonum/floats" 14 ) 15 16 func printDlasq2FortranInput(z []float64, n int) { 17 printFortranArray(z, "z") 18 fmt.Println("n = ", n) 19 fmt.Println("info = 0") 20 } 21 22 type Dlasq2er interface { 23 Dgetrfer 24 Dlasq2(n int, z []float64) (info int) 25 } 26 27 func Dlasq2Test(t *testing.T, impl Dlasq2er) { 28 dTol := 1e-6 29 // Answers from calling the netlib Dlasq2 function directly. 30 for c, test := range []struct { 31 n int 32 z []float64 33 info int 34 zOut []float64 35 }{ 36 { 37 z: []float64{0.9975595900926172E+00, 0.5668247076112733E+00, 0.9659153754961249E+00, 0.7479276854714322E+00, 0.3673908973747557E+00, 0.4806368987547315E+00, 0.7375426363398452E-01, 0.5355229277727247E-02, 0.3470812885180155E+00, 0.3422438160728350E+00, 0.2179517263384726E+00, 0.1331604100136593E+00, 0.9005245144218924E+00, 0.3867660104574036E+00, 0.4454822893878481E+00, 0.6619321808958428E+00, 0.1610830043055933E-01, 0.6508548361039168E+00, 0.6464088254838254E+00, 0.3229872909405558E+00, 0.8556924028853313E+00, 0.4012869193638139E+00, 0.2068743292187569E+00, 0.9685394642165999E+00, 0.5983995343181346E+00, 0.6729807327762632E+00, 0.4568823106729620E+00, 0.3300151235733747E+00, 0.1003829265021773E+00, 0.7554533047597268E+00, 0.6056932669802318E+00, 0.7190479134084530E+00, 0.8973346038865299E+00, 0.6582291204811077E+00, 0.1507168371301046E+00, 0.6123149049967000E+00, 0.9786602381321465E+00, 0.9991422694268032E+00, 0.2567979861831603E+00, 0.5508654031552206E+00, 0.6590475178936379E+00, 0.5540051353968156E+00, 0.9777600986094505E+00, 0.9019233044604550E+00, 0.6579246844202109E+00, 0.7288585083995637E+00, 0.4024552650632751E+00, 0.9286276631540373E+00, 0.1478351900438915E+00, 0.6745292990637881E+00, 0.7696143092758962E+00, 0.3393225521457851E+00, 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0.4789189736721279E-06, 0.5466231772857101E-06, 0.5669018352800101E+00, 0.1893266172530428E-27, 0.9952011217509916E-06, 0.1128113648538554E-05, 0.3641671875118937E+00, 0.1993230626440035E-24, 0.2427606592544749E-05, 0.2156829827516489E-05, 0.2699135892930649E+00, 0.2761013168273541E-29, 0.3900010091178873E-05, 0.3393761026267541E-05, 0.1446269090001342E+00, 0.2150416673893778E-15, 0.8242388755752233E-05, 0.1105863902029246E-04, 0.8937359624216266E-01, 0.2934562567422164E-27, 0.3455780897358792E-04, 0.2250328346305790E-04, 0.5860931848549461E-01, 0.8147325136863849E-21, 0.2346512312055719E-04, 0.8962661529405173E-05, 0.3094108728329079E-01, 0.2460979885389816E-17, 0.5238375287742530E-03, 0.1080192509223090E-02, 0.6182329613034853E-03, 0.8383483586160605E-23, 0.7400552677463828E-02, 0.1581674273722876E-01}, 622 info: 0, 623 }, 624 { 625 z: []float64{0.7940281584071446E+00, 0.8540600349699839E+00, 0.8158431165852809E-01, 0.5431841788581357E+00, 0.3696613346727944E+00, 0.2343742079469738E+00, 0.4891909888056500E-01, 0.6769876984160987E+00, 0.4777767465052760E+00, 0.1867381312399053E+00, 0.2018744873845245E+00, 0.5511201479607295E+00, 0.6938788283912793E+00, 0.8167542438070282E+00, 0.7904606414789531E+00, 0.9443564310071292E+00, 0.7287247677237652E-01, 0.8645122013586991E+00, 0.1884651475116826E+00, 0.3844755283611681E+00, 0.9959264361467982E+00, 0.6424370932833342E+00, 0.1972122925077952E+00, 0.2842024247377670E+00, 0.9819646913482807E+00, 0.9118347224008859E+00, 0.8184691845197246E+00, 0.7051587281589254E+00, 0.7604703230109544E+00, 0.6312964755149379E+00, 0.5240863862347888E+00, 0.3442050916384676E-01, 0.2415614308212055E+00, 0.2814868323669945E+00, 0.6529284673126197E+00, 0.3727305084153835E+00, 0.5033733868757848E+00, 0.2317122058804952E+00, 0.7555584130128312E+00, 0.5854566742645219E+00, 0.5481204696337160E+00, 0.8479425268049923E+00, 0.2310874615764000E+00, 0.1250993726775007E-01, 0.6243285982203539E-01, 0.8533587246073391E+00, 0.9203815588639257E+00, 0.9256849509751471E+00, 0.6691405057262187E+00, 0.8847091531299658E+00, 0.6783572983386376E+00, 0.4701257141291857E+00, 0.8976078424378102E+00, 0.8575018884445876E+00, 0.4119363561363949E+00, 0.2824477027676924E+00, 0.2787507690368071E+00, 0.7994878185780909E+00, 0.6141832897278305E+00, 0.6772728066124333E+00, 0.1568652581579784E+00, 0.8025492691231176E+00, 0.2609459151100056E+00, 0.4956700691019098E+00, 0.1008839464621498E+00, 0.6129709499983976E+00, 0.4551038858718992E-02, 0.8382785474023564E+00, 0.9327452694814308E+00, 0.9710431593941808E+00, 0.3785578217695214E+00, 0.9620839159000718E+00, 0.3183561960196257E-01, 0.9167635157854341E+00, 0.8989971039988554E+00, 0.2723769512210017E-01, 0.4176537489735596E+00, 0.9619881273217982E+00, 0.8761769579995293E+00, 0.6385245520487358E+00, 0.6821739872929905E+00, 0.3927943300877799E+00, 0.3299501391296433E-01, 0.6026481165267817E+00}, 626 n: 21, 627 zOut: []float64{0.2841529467847260E+01, 0.2556740368064117E+01, 0.2029069210305357E+01, 0.1816492749229813E+01, 0.1807397947918166E+01, 0.1724050761249482E+01, 0.1394683696862690E+01, 0.1363282300837870E+01, 0.1235317529564993E+01, 0.1007821728138393E+01, 0.9728972767837659E+00, 0.8110838192609224E+00, 0.6190683239156912E+00, 0.3314348466978195E+00, 0.2969816495631171E+00, 0.2506421226611442E+00, 0.1551624233480766E+00, 0.1141049603637759E+00, 0.6806098279643324E-01, 0.4065442795375918E-01, 0.1509783792061944E-04, 0.2745446733802996E-19, 0.2334033424405603E-14, 0.7232047343832039E-15, 0.1394683696862690E+01, 0.7652022750203868E-17, 0.1502464319787860E-09, 0.5990324067027169E-10, 0.1363282300837870E+01, 0.5511008105786353E-19, 0.1215529748555577E-07, 0.3576186028975079E-08, 0.1235317529564993E+01, 0.6271335389136957E-17, 0.2589527811059762E-05, 0.3563684464760320E-05, 0.1007821728138393E+01, 0.6928731028484552E-15, 0.2286607739649456E-04, 0.2916328836696281E-04, 0.9728972767837659E+00, 0.4013724285764508E-25, 0.2143649169120057E+02, 0.2143649169120056E+02, 0.1080000000000000E+03, 0.3174603174603174E+01, 0.5555555555555555E+01, 0.5006788488237952E-04, 0.6190683239156912E+00, 0.1272779738919789E-24, 0.5392273695714327E-05, 0.6586751690782050E-05, 0.3314348466978195E+00, 0.9952016744778614E-24, 0.4588114650322476E-05, 0.4104030919118472E-05, 0.2969816495631171E+00, 0.1254277227268884E-20, 0.1579210272170037E-05, 0.2523508055026877E-05, 0.2506421226611442E+00, 0.1514835081255253E-22, 0.9117975197333799E-05, 0.1415311657319248E-04, 0.1551624233480766E+00, 0.3272195034856757E-26, 0.3128414626489953E-04, 0.4770966856082524E-04, 0.1141049603637759E+00, 0.7575261888623807E-20, 0.6277758538102519E-05, 0.4644422903178713E-05, 0.6806098279643324E-01, 0.3715389965619895E-21, 0.5956965112658162E-05, 0.4447744978930882E-05, 0.4065442795375918E-01, 0.1972152263052530E-30, 0.2965586553650948E-04, 0.1900611263569203E-04, 0.1509783792061944E-04, 0.1009741958682895E-26, 0.1608958133772104E-02, 0.9583670521235791E-03}, 628 info: 0, 629 }, 630 } { 631 z := make([]float64, len(test.z)) 632 copy(z, test.z) 633 634 info := impl.Dlasq2(test.n, z) 635 if !floats.EqualApprox(test.zOut, z, dTol) { 636 diff := make([]float64, len(z)) 637 floats.SubTo(diff, z, test.zOut) 638 for i := range diff { 639 diff[i] = math.Abs(diff[i]) 640 } 641 t.Errorf("Case %v, Z Mismatch", c) 642 } 643 if test.info != info { 644 t.Errorf("Info mismatch. Want %v, got %v", test.info, info) 645 } 646 } 647 648 rnd := rand.New(rand.NewSource(1)) 649 // Perform a bunch of random tests to check for access out of bounds or 650 // infinite loops. 651 // TODO(btracey): Implement direct tests. 652 // bi := blas64.Implementation() 653 for _, n := range []int{5, 8, 20, 25} { 654 for k := 0; k < 10; k++ { 655 z := make([]float64, 4*n) 656 for i := range z { 657 z[i] = rnd.Float64() 658 } 659 zCopy := make([]float64, len(z)) 660 copy(zCopy, z) 661 662 // Compute the eigenvalues 663 impl.Dlasq2(n, z) 664 665 // Below is the code to test the eigenvalues. Eventually implement 666 // real tests. 667 // The code below is missing the transformation from L and U into 668 // the symmetric tridiagonal matrix. 669 // See discussion http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=4839 670 // for format. 671 672 /* 673 ldl := n 674 ldu := n 675 u := make([]float64, n*n) 676 for i := 0; i < n; i++ { 677 u[i*ldu+i] = zCopy[2*i] 678 if i != n-1 { 679 u[i*ldu+i+1] = 1 680 } 681 } 682 l := make([]float64, n*n) 683 for i := 0; i < n; i++ { 684 l[i*ldl+i] = 1 685 if i != n-1 { 686 l[(i+1)*ldl+i] = zCopy[2*i+1] 687 } 688 } 689 690 ldTriDi := n 691 triDi := make([]float64, n*n) 692 bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, l, ldl, u, ldu, 0, triDi, ldTriDi) 693 694 tridi2 := make([]float64, n*n) 695 bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, triDi, n, triDi, n, 0, tridi2, n) 696 697 // Eigenvalues have the property that det(A - lambda I ) = 0 698 triDiCopy := make([]float64, len(triDi)) 699 copy(triDiCopy, triDi) 700 for _, lambda := range z[1:n] { 701 copy(triDi, triDiCopy) 702 for i := 0; i < n; i++ { 703 triDi[i*n+i] -= lambda 704 } 705 706 // Compute LU 707 //ipiv := make([]int, n) 708 //impl.Dgetrf(n, n, triDi, n, ipiv) 709 ok := impl.Dpotrf(blas.Upper, n, triDi, n) 710 fmt.Println(ok) 711 712 var det float64 713 for i := 0; i < n; i++ { 714 det += math.Log(math.Abs(triDi[i*n+i])) 715 } 716 fmt.Println("det = ", math.Exp(det)) 717 } 718 */ 719 } 720 } 721 }