func solveMVTest(t *testing.T, A, X0 *matrix.FloatMatrix, flags Flags, bN, bNB int) {
X1 := X0.Copy()
uplo := linalg.OptUpper
diag := linalg.OptNonUnit
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
blas.TrsvFloat(A, X0, uplo, diag)
Ar := A.FloatArray()
Xr := X1.FloatArray()
if bN == bNB {
DSolveUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN)
} else {
DSolveBlkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN, bNB)
}
ok := X1.AllClose(X0)
t.Logf("X1 == X0: %v\n", ok)
if !ok && bN < 8 {
t.Logf("A=\n%v\n", A)
t.Logf("X0=\n%v\n", X0)
t.Logf("blas: X0\n%v\n", X0)
t.Logf("X1:\n%v\n", X1)
}
}
func trmvTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
N := A.Cols()
//S := 0
//E := A.Cols()
X0 := matrix.FloatWithValue(A.Rows(), 1, 2.0)
X1 := X0.Copy()
trans := linalg.OptNoTrans
if flags&TRANS != 0 {
trans = linalg.OptTrans
}
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.TrmvFloat(A, X0, uplo, diag, trans)
Ar := A.FloatArray()
Xr := X1.FloatArray()
if nb == 0 {
DTrimvUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), N)
}
result := X0.AllClose(X1)
t.Logf(" X0 == X1: %v\n", result)
if !result && A.Rows() < 8 {
t.Logf(" BLAS TRMV X0:\n%v\n", X0)
t.Logf(" DTrmv X1:\n%v\n", X1)
}
return result
}
// Y := alpha * X + Y
func Axpy(Y, X *matrix.FloatMatrix, alpha float64) {
if X == nil || Y == nil {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
calgo.DAxpy(Xr, Yr, alpha, incX, incY, X.NumElements())
return
}
func syrkTest(t *testing.T, C, A *matrix.FloatMatrix, flags Flags, vlen, nb int) bool {
//var B0 *matrix.FloatMatrix
P := A.Cols()
S := 0
E := C.Rows()
C0 := C.Copy()
trans := linalg.OptNoTrans
if flags&TRANSA != 0 {
trans = linalg.OptTrans
P = A.Rows()
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.SyrkFloat(A, C0, 1.0, 1.0, uplo, trans)
if A.Rows() < 8 {
//t.Logf("..A\n%v\n", A)
t.Logf(" BLAS C0:\n%v\n", C0)
}
Ar := A.FloatArray()
Cr := C.FloatArray()
DSymmRankBlk(Cr, Ar, 1.0, 1.0, flags, C.LeadingIndex(), A.LeadingIndex(),
P, S, E, vlen, nb)
result := C0.AllClose(C)
t.Logf(" C0 == C: %v\n", result)
if A.Rows() < 8 {
t.Logf(" DMRank C:\n%v\n", C)
}
return result
}
// Swap X and Y.
func Swap(X, Y *matrix.FloatMatrix) {
if X == nil || Y == nil {
return
}
if X.NumElements() == 0 || Y.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
calgo.DSwap(Xr, Yr, incX, incY, X.NumElements())
}
// Solve multiple right sides. If flags&UNIT then A diagonal is assumed to
// to unit and is not referenced. (blas.TRSM)
// alpha*B = A.-1*B if flags&LEFT
// alpha*B = A.-T*B if flags&(LEFT|TRANS)
// alpha*B = B*A.-1 if flags&RIGHT
// alpha*B = B*A.-T if flags&(RIGHT|TRANS)
//
// Matrix A is N*N triangular matrix defined with flags bits as follow
// LOWER non-unit lower triangular
// LOWER|UNIT unit lower triangular
// UPPER non-unit upper triangular
// UPPER|UNIT unit upper triangular
//
// Matrix B is N*P if flags&LEFT or P*N if flags&RIGHT.
//
func SolveTrm(B, A *matrix.FloatMatrix, alpha float64, flags Flags) error {
ok := true
empty := false
br, bc := B.Size()
ar, ac := A.Size()
switch flags & (LEFT | RIGHT) {
case LEFT:
empty = br == 0
ok = br == ac && ac == ar
case RIGHT:
empty = bc == 0
ok = bc == ar && ac == ar
}
if empty {
return nil
}
if !ok {
return onError("A, B size mismatch")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
E := bc
if flags&RIGHT != 0 {
E = br
}
// if more workers available can divide to tasks by B columns if flags&LEFT or by
// B rows if flags&RIGHT.
calgo.DSolveBlk(Br, Ar, alpha, calgo.Flags(flags), ldB, ldA, ac, 0, E, nB)
return nil
}
// A = alpha*A + beta*B
// A = alpha*A + beta*B.T if flags&TRANSB
func ScalePlus(A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
S := 0
L := A.Cols()
R := 0
E := A.Rows()
calgo.DScalePlus(Ar, Br, alpha, beta, calgo.Flags(flags), ldA, ldB, S, L, R, E)
return nil
}
func trmmTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
var B0 *matrix.FloatMatrix
N := A.Cols()
S := 0
E := A.Cols()
side := linalg.OptLeft
if flags&RIGHT != 0 {
B0 = matrix.FloatWithValue(2, A.Rows(), 2.0)
side = linalg.OptRight
E = B0.Rows()
} else {
B0 = matrix.FloatWithValue(A.Rows(), 2, 2.0)
E = B0.Cols()
}
B1 := B0.Copy()
trans := linalg.OptNoTrans
if flags&TRANSA != 0 {
trans = linalg.OptTransA
}
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
blas.TrmmFloat(A, B0, 1.0, uplo, diag, trans, side)
if A.Rows() < 8 {
//t.Logf("..A\n%v\n", A)
t.Logf(" BLAS B0:\n%v\n", B0)
}
Ar := A.FloatArray()
Br := B1.FloatArray()
if nb != 0 {
DTrmmBlk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
N, S, E, nb)
} else {
DTrmmUnblk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
N, S, E, 0)
}
result := B0.AllClose(B1)
t.Logf(" B0 == B1: %v\n", result)
if A.Rows() < 8 {
t.Logf(" DTrmm B1:\n%v\n", B1)
}
return result
}
// index of max |x|
func IAMax(X *matrix.FloatMatrix) int {
if X == nil {
return -1
}
if !isVector(X) {
return -1
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
return calgo.DIAMax(Xr, incX, X.NumElements())
}
// Scaling with scalar: X = alpha * X
func Scale(X *matrix.FloatMatrix, alpha float64) {
if X == nil || X.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
calgo.DScal(Xr, alpha, incX, X.NumElements())
}
// sum(|x|)
func ASum(X *matrix.FloatMatrix) float64 {
if X == nil {
return math.NaN()
}
if !isVector(X) {
return math.NaN()
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
return calgo.DAsum(Xr, incX, X.NumElements())
}
/*
* Compute
* C = C*diag(D) flags & RIGHT == true
* C = diag(D)*C flags & LEFT == true
*
* Arguments
* C M-by-N matrix if flags&RIGHT == true or N-by-M matrix if flags&LEFT == true
*
* D N element column or row vector or N-by-N matrix
*
* flags Indicator bits, LEFT or RIGHT
*/
func MultDiag(C, D *matrix.FloatMatrix, flags Flags) {
var c, d0 matrix.FloatMatrix
if D.Cols() == 1 {
// diagonal is column vector
switch flags & (LEFT | RIGHT) {
case LEFT:
// scale rows; for each column element-wise multiply with D-vector
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
c.Mul(D)
}
case RIGHT:
// scale columns
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
// scale the column
c.Scale(D.GetAt(k, 0))
}
}
} else {
// diagonal is row vector
var d *matrix.FloatMatrix
if D.Rows() == 1 {
d = D
} else {
D.SubMatrix(&d0, 0, 0, 1, D.Cols(), D.LeadingIndex()+1)
d = &d0
}
switch flags & (LEFT | RIGHT) {
case LEFT:
for k := 0; k < C.Rows(); k++ {
C.SubMatrix(&c, k, 0, 1, C.Cols())
// scale the row
c.Scale(d.GetAt(0, k))
}
case RIGHT:
// scale columns
for k := 0; k < C.Cols(); k++ {
C.SubMatrix(&c, 0, k, C.Rows(), 1)
// scale the column
c.Scale(d.GetAt(0, k))
}
}
}
}
// A = A + alpha*X*Y.T; A is N*N symmetric, X is row or column vector of length N.
func MVSymmUpdateUpper(A, X *matrix.FloatMatrix, alpha float64) error {
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Xr := X.FloatArray()
incX := 1
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
}
// NOTE: This could diveded to parallel tasks per column.
calgo.DSymmRankMV(Ar, Xr, alpha, calgo.UPPER, ldA, incX, 0, A.Cols(), 0)
return nil
}
// Rank update for symmetric lower or upper matrix (blas.SYRK)
// C = beta*C + alpha*A*A.T + alpha*A.T*A
func RankUpdateSym(C, A *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
if C.Rows() != C.Cols() {
return onError("C not a square matrix")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
S := 0
E := C.Rows()
P := A.Cols()
if flags&TRANSA != 0 {
P = A.Rows()
}
// if more workers available C can be divided to blocks [S:E, S:E] along diagonal
// and updated in separate tasks.
calgo.DSymmRankBlk(Cr, Ar, alpha, beta, calgo.Flags(flags), ldC, ldA, P, S, E,
vpLen, nB)
return nil
}
// Tridiagonal multiplication; X = A*X
func MVMultTrm(X, A *matrix.FloatMatrix, flags Flags) error {
if A.Rows() == 0 || A.Cols() == 0 {
return nil
}
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Xr := X.FloatArray()
incX := 1
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
}
calgo.DTrimvUnblkMV(Xr, Ar, calgo.Flags(flags), incX, ldA, A.Cols())
return nil
}
// Calculate C = alpha*A*B.T + beta*C, C is M*N, A is M*P and B is N*P
func MMMultTransB(C, A, B *matrix.FloatMatrix, alpha, beta float64) error {
psize := int64(C.NumElements() * A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.TRANSB, ldC, ldA, ldB,
B.Rows(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.TRANSB, ldC, ldA, ldB, B.Rows(),
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
//scheduleWork(colworks, rowworks, worker)
return nil
}
// Calculate C = alpha*A*B + beta*C, C is M*N, A is M*M and B is M*N
func MMSymmUpper(C, A, B *matrix.FloatMatrix, alpha, beta float64) error {
if A.Rows() != A.Cols() {
return errors.New("A matrix not square matrix.")
}
psize := int64(C.NumElements() * A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.LEFT|calgo.UPPER, ldC, ldA, ldB,
A.Cols(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.LEFT|calgo.UPPER, ldC, ldA, ldB,
A.Cols(), cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
// Y = alpha*A.T*X + beta*Y
func MVMultTransA(Y, A, X *matrix.FloatMatrix, alpha, beta float64) error {
if Y.Rows() != 1 && Y.Cols() != 1 {
return errors.New("Y not a vector.")
}
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Yr := Y.FloatArray()
incY := 1
lenY := Y.Rows()
if Y.Rows() == 1 {
// row vector
incY = Y.LeadingIndex()
lenY = Y.Cols()
}
Xr := X.FloatArray()
incX := 1
lenX := X.Rows()
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
lenX = X.Cols()
}
calgo.DMultMV(Yr, Ar, Xr, alpha, beta, calgo.TRANSA, incY, ldA, incX,
0, lenX, 0, lenY, vpLen, mB)
return nil
}
// Add inner product: Z[index] = beta*Z[index] + alpha * X * Y
func AddDot(Z, X, Y *matrix.FloatMatrix, alpha, beta float64, index int) {
if X == nil || Y == nil {
return
}
if X.NumElements() == 0 || Y.NumElements() == 0 {
return
}
if !isVector(X) {
return
}
if !isVector(Y) {
return
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
Zr := Z.FloatArray()
incZ := 1
if Z.Cols() != 1 {
// Row vector
incZ = Z.LeadingIndex()
}
calgo.DDotSum(Zr[incZ*index:], Xr, Yr, alpha, beta, incZ, incX, incY, X.NumElements())
}
func Mult0(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
if A.Cols() != B.Rows() {
return errors.New("A.cols != B.rows: size mismatch")
}
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMult0(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, B.Rows(),
0, C.Cols(), 0, C.Rows(),
vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult0(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, B.Rows(),
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
// Compute
// Y = alpha*A*X + beta*Y
// Y = alpha*A.T*X + beta*Y ; flags = TRANSA
//
// A is M*N or N*M generic matrix,
// X is row or column vector of length N
// Y is row or column vector of legth M.
//
// MVMult is vector orientation agnostic. It does not matter if Y, X are row or
// column vectors, they are always handled as if they were column vectors.
func MVMult(Y, A, X *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
if A.Rows() == 0 || A.Cols() == 0 {
return nil
}
if Y.Rows() != 1 && Y.Cols() != 1 {
return errors.New("Y not a vector.")
}
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Yr := Y.FloatArray()
incY := 1
lenY := Y.NumElements()
if Y.Rows() == 1 {
// row vector
incY = Y.LeadingIndex()
}
Xr := X.FloatArray()
incX := 1
lenX := X.NumElements()
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
}
// NOTE: This could diveded to parallel tasks by rows.
calgo.DMultMV(Yr, Ar, Xr, alpha, beta, calgo.Flags(flags), incY, ldA, incX,
0, lenX, 0, lenY, vpLen, mB)
return nil
}
// Matrix-vector rank update A = A + alpha*X*Y.T
// A is M*N generic matrix,
// X is row or column vector of length M
// Y is row or column vector of legth N.
func MVRankUpdate(A, X, Y *matrix.FloatMatrix, alpha float64) error {
if A.Rows() == 0 || A.Cols() == 0 {
return nil
}
if Y.Rows() != 1 && Y.Cols() != 1 {
return errors.New("Y not a vector.")
}
if X.Rows() != 1 && X.Cols() != 1 {
return errors.New("X not a vector.")
}
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Yr := Y.FloatArray()
incY := 1
if Y.Rows() == 1 {
// row vector
incY = Y.LeadingIndex()
}
Xr := X.FloatArray()
incX := 1
if X.Rows() == 1 {
// row vector
incX = X.LeadingIndex()
}
// NOTE: This could diveded to parallel tasks like matrix-matrix multiplication
calgo.DRankMV(Ar, Xr, Yr, alpha, ldA, incX, incY, 0, A.Cols(), 0, A.Rows(), 0, 0)
return nil
}
// Generic matrix-matrix multpily. (blas.GEMM). Calculates
// C = beta*C + alpha*A*B (default)
// C = beta*C + alpha*A.T*B flags&TRANSA
// C = beta*C + alpha*A*B.T flags&TRANSB
// C = beta*C + alpha*A.T*B.T flags&(TRANSA|TRANSB)
//
// C is M*N, A is M*P or P*M if flags&TRANSA. B is P*N or N*P if flags&TRANSB.
//
func Mult(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
var ok, empty bool
// error checking must take in account flag values!
ar, ac := A.Size()
br, bc := B.Size()
cr, cc := C.Size()
switch flags & (TRANSA | TRANSB) {
case TRANSA | TRANSB:
empty = ac == 0 || br == 0
ok = cr == ac && cc == br && ar == bc
case TRANSA:
empty = ac == 0 || bc == 0
ok = cr == ac && cc == bc && ar == br
case TRANSB:
empty = ar == 0 || br == 0
ok = cr == ar && cc == br && ac == bc
default:
empty = ar == 0 || bc == 0
ok = cr == ar && cc == bc && ac == br
}
if empty {
return nil
}
if !ok {
return errors.New("Mult: size mismatch")
}
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
// matrix A, B common dimension
P := A.Cols()
if flags&TRANSA != 0 {
P = A.Rows()
}
if nWorker <= 1 || psize <= limitOne {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, P,
0, C.Cols(), 0, C.Rows(),
vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMult(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB, P,
cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
func update(t *testing.T, Y1, Y2, C1, C2, T, W *matrix.FloatMatrix) {
if W.Rows() != C1.Cols() {
panic("W.Rows != C1.Cols")
}
// W = C1.T
ScalePlus(W, C1, 0.0, 1.0, TRANSB)
//fmt.Printf("W = C1.T:\n%v\n", W)
// W = C1.T*Y1
//MultTrm(W, Y1, 1.0, LOWER|UNIT|RIGHT)
Wr := W.FloatArray()
Y1r := Y1.FloatArray()
ldW := W.LeadingIndex()
ldY := Y1.LeadingIndex()
calgo.DTrmmUnblk(Wr, Y1r, 1.0, calgo.Flags(LOWER|UNIT|RIGHT),
ldW, ldY, Y1.Cols(), 0, W.Rows(), 0)
t.Logf("W = C1.T*Y1:\n%v\n", W)
// W = W + C2.T*Y2
Mult(W, C2, Y2, 1.0, 1.0, TRANSA)
t.Logf("W = W + C2.T*Y2:\n%v\n", W)
// --- here: W == C.T*Y ---
// W = W*T
MultTrm(W, T, 1.0, UPPER|RIGHT)
t.Logf("W = C.T*Y*T:\n%v\n", W)
// --- here: W == C.T*Y*T ---
// C2 = C2 - Y2*W.T
Mult(C2, Y2, W, -1.0, 1.0, TRANSB)
t.Logf("C2 = C2 - Y2*W.T:\n%v\n", C2)
// W = Y1*W.T ==> W.T = W*Y1.T
MultTrm(W, Y1, 1.0, LOWER|UNIT|TRANSA|RIGHT)
t.Logf("W.T = W*Y1.T:\n%v\n", W)
// C1 = C1 - W.T
ScalePlus(C1, W, 1.0, -1.0, TRANSB)
//fmt.Printf("C1 = C1 - W.T:\n%v\n", C1)
// --- here: C = (I - Y*T*Y.T).T * C ---
}
// Symmetric matrix multiply. (blas.SYMM)
// C = beta*C + alpha*A*B (default)
// C = beta*C + alpha*A.T*B flags&TRANSA
// C = beta*C + alpha*A*B.T flags&TRANSB
// C = beta*C + alpha*A.T*B.T flags&(TRANSA|TRANSB)
//
// C is N*P, A is N*N symmetric matrix. B is N*P or P*N if flags&TRANSB.
//
func MultSym(C, A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {
var ok, empty bool
ar, ac := A.Size()
br, bc := B.Size()
cr, cc := C.Size()
switch flags & (TRANSA | TRANSB) {
case TRANSA | TRANSB:
empty = ac == 0 || br == 0
ok = ar == ac && cr == ac && cc == br && ar == bc
case TRANSA:
empty = ac == 0 || bc == 0
ok = ar == ac && cr == ac && cc == bc && ar == br
case TRANSB:
empty = ar == 0 || br == 0
ok = ar == ac && cr == ar && cc == br && ac == bc
default:
empty = ar == 0 || bc == 0
ok = ar == ac && cr == ar && cc == bc && ac == br
}
if empty {
return nil
}
if !ok {
return errors.New("MultSym: size mismatch")
}
/*
if A.Rows() != A.Cols() {
return errors.New("A matrix not square matrix.");
}
if A.Cols() != B.Rows() {
return errors.New("A.cols != B.rows: size mismatch")
}
*/
psize := int64(C.NumElements()) * int64(A.Cols())
Ar := A.FloatArray()
ldA := A.LeadingIndex()
Br := B.FloatArray()
ldB := B.LeadingIndex()
Cr := C.FloatArray()
ldC := C.LeadingIndex()
if nWorker <= 1 || psize <= limitOne {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB,
A.Cols(), 0, C.Cols(), 0, C.Rows(), vpLen, nB, mB)
return nil
}
// here we have more than one worker available
worker := func(cstart, cend, rstart, rend int, ready chan int) {
calgo.DMultSymm(Cr, Ar, Br, alpha, beta, calgo.Flags(flags), ldC, ldA, ldB,
A.Cols(), cstart, cend, rstart, rend, vpLen, nB, mB)
ready <- 1
}
colworks, rowworks := divideWork(C.Rows(), C.Cols(), nWorker)
scheduleWork(colworks, rowworks, C.Cols(), C.Rows(), worker)
return nil
}
// Inner product: alpha * X * Y
func Dot(X, Y *matrix.FloatMatrix, alpha float64) float64 {
if X == nil || Y == nil {
return math.NaN()
}
if !isVector(X) {
return math.NaN()
}
if !isVector(Y) {
return math.NaN()
}
Xr := X.FloatArray()
incX := 1
if X.Cols() != 1 {
// Row vector
incX = X.LeadingIndex()
}
Yr := Y.FloatArray()
incY := 1
if Y.Cols() != 1 {
// Row vector
incY = Y.LeadingIndex()
}
return calgo.DDot(Xr, Yr, alpha, incX, incY, X.NumElements())
}
func trsmSolve(t *testing.T, A *matrix.FloatMatrix, flags Flags, rand bool, nrhs, nb int) bool {
var B0 *matrix.FloatMatrix
side := linalg.OptLeft
trans := linalg.OptNoTrans
N := A.Cols()
S := 0
E := A.Rows()
_ = S
_ = E
if flags&RIGHT != 0 {
if rand {
B0 = matrix.FloatNormal(nrhs, A.Rows())
} else {
B0 = matrix.FloatWithValue(nrhs, A.Rows(), 2.0)
}
side = linalg.OptRight
E = B0.Rows()
} else {
if rand {
B0 = matrix.FloatNormal(A.Rows(), nrhs)
} else {
B0 = matrix.FloatWithValue(A.Rows(), nrhs, 2.0)
}
E = B0.Cols()
}
B1 := B0.Copy()
diag := linalg.OptNonUnit
if flags&UNIT != 0 {
diag = linalg.OptUnit
}
uplo := linalg.OptUpper
if flags&LOWER != 0 {
uplo = linalg.OptLower
}
if flags&TRANSA != 0 {
trans = linalg.OptTransA
}
blas.TrsmFloat(A, B0, 1.0, uplo, diag, side, trans)
Ar := A.FloatArray()
Br := B1.FloatArray()
if nb == 0 || nb == N {
DSolveUnblk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(), N, S, E)
} else {
DSolveBlk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(), N, S, E, nb)
}
result := B1.AllClose(B0)
t.Logf("B1 == B0: %v\n", result)
if !result {
if nrhs < 10 {
t.Logf("blas: B0\n%v\n", B0)
t.Logf("B1:\n%v\n", B1)
} else {
b0 := B0.FloatArray()
b1 := B1.FloatArray()
for k := 0; k < len(b0); k++ {
if !isClose(b0[k], b1[k]) {
t.Logf("first divergences at %d ... col %d, row %d\n", k, k/B0.Rows(), k%B0.Rows())
break
}
}
}
}
return result
}
func TestMultMVTransASmall(t *testing.T) {
data6 := [][]float64{
[]float64{-1.59e+00, 6.56e-02, 2.14e-01, 6.79e-01, 2.93e-01, 5.24e-01},
[]float64{4.28e-01, 1.57e-01, 3.81e-01, 2.19e-01, 2.97e-01, 2.83e-02},
[]float64{3.02e-01, 9.70e-02, 3.18e-01, 2.03e-01, 7.53e-01, 1.58e-01},
[]float64{1.99e-01, 3.01e-01, 4.69e-01, 3.61e-01, 2.07e-01, 6.07e-01},
[]float64{1.93e-01, 5.15e-01, 2.83e-01, 5.71e-01, 8.65e-01, 9.75e-01},
[]float64{3.13e-01, 8.14e-01, 2.93e-01, 8.62e-01, 6.97e-01, 7.95e-02}}
data5 := [][]float64{
[]float64{1.57e-01, 3.81e-01, 2.19e-01, 2.97e-01, 2.83e-02},
[]float64{9.70e-02, 3.18e-01, 2.03e-01, 7.53e-01, 1.58e-01},
[]float64{3.01e-01, 4.69e-01, 3.61e-01, 2.07e-01, 6.07e-01},
[]float64{5.15e-01, 2.83e-01, 5.71e-01, 8.65e-01, 9.75e-01},
[]float64{8.14e-01, 2.93e-01, 8.62e-01, 6.97e-01, 7.95e-02}}
data2 := []float64{4.28e-01, 3.02e-01, 1.99e-01, 1.93e-01, 3.13e-01}
bM := 5
bN := 4
nb := 2
//A := matrix.FloatNormal(bN, bM)
//X := matrix.FloatWithValue(bN, 1, 1.0)
A := matrix.FloatMatrixFromTable(data5, matrix.RowOrder)
X := matrix.FloatNew(5, 1, data2)
bM = A.Rows()
bN = A.Cols()
Ym := matrix.FloatZeros(3, bM)
Y1 := matrix.FloatZeros(bM, 1)
Y0 := matrix.FloatZeros(bM, 1)
Ar := A.FloatArray()
Xr := X.FloatArray()
Y1r := Y1.FloatArray()
blas.GemvFloat(A, X, Y0, 1.0, 1.0, linalg.OptTrans)
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok := Y0.AllClose(Y1)
t.Logf("Y0 == Y1: %v\n", ok)
if ok || !ok {
t.Logf("blas: Y=A.T*X\n%v\n", Y0)
t.Logf("Y1: Y1 = A*X\n%v\n", Y1)
}
// zero Y0, Y1
Y0.Scale(0.0)
Y1.Scale(0.0)
// test with matrix view; A is view
var A0 matrix.FloatMatrix
A6 := matrix.FloatMatrixFromTable(data6, matrix.RowOrder)
A0.SubMatrixOf(A6, 1, 1)
blas.GemvFloat(&A0, X, Y0, 1.0, 1.0, linalg.OptTrans)
Ar = A0.FloatArray()
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A0.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok = Y0.AllClose(Y1)
t.Logf("lda>rows: Y0 == Y1: %v\n", ok)
if ok || !ok {
t.Logf("blas: Y=A.T*X\n%v\n", Y0)
t.Logf("Y1: Y1 = A*X\n%v\n", Y1)
}
// Y is view too.
Y1.SubMatrixOf(Ym, 0, 0, 1, bM)
Y1r = Y1.FloatArray()
DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, Y1.LeadingIndex(), A0.LeadingIndex(), 1, 0, bN, 0, bM, nb, nb)
ok = Y0.AllClose(Y1.Transpose())
t.Logf("Y0 == Y1 row: %v\n", ok)
t.Logf("row Y1: %v\n", Y1)
}
