?latm5

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?latm5

Generates matrices involved in the Generalized Sylvester equation.

Syntax

void slatm5 (*prtype, lapack_int *m, lapack_int *n, float *a, lapack_int *lda, float *b, lapack_int *ldb, float *c, lapack_int *ldc, float *d, lapack_int *ldd, float *e, lapack_int *lde, float *f, lapack_int *ldf, float *r, lapack_int *ldr, float *l, lapack_int *ldl, float *alpha, lapack_int *qblcka, lapack_int *qblckb);

void dlatm5 (*prtype, lapack_int *m, lapack_int *n, double *a, lapack_int *lda, double *b, lapack_int *ldb, double *c, lapack_int *ldc, double *d, lapack_int *ldd, double *e, lapack_int *lde, double *f, lapack_int *ldf, double *r, lapack_int *ldr, double *l, lapack_int *ldl, double *alpha, lapack_int *qblcka, lapack_int *qblckb);

void clatm5 (*prtype, lapack_int *m, lapack_int *n, lapack_complex_float *a, lapack_int *lda, lapack_complex_float *b, lapack_int *ldb, lapack_complex_float *c, lapack_int *ldc, lapack_complex_float *d, lapack_int *ldd, lapack_complex_float *e, lapack_int *lde, lapack_complex_float *f, lapack_int *ldf, lapack_complex_float *r, lapack_int *ldr, lapack_complex_float *l, lapack_int *ldl, float *alpha, lapack_int *qblcka, lapack_int *qblckb);

void zlatm5 (*prtype, lapack_int *m, lapack_int *n, lapack_complex_double *a, lapack_int *lda, lapack_complex_double *b, lapack_int *ldb, lapack_complex_double *c, lapack_int *ldc, lapack_complex_double *d, lapack_int *ldd, lapack_complex_double *e, lapack_int *lde, lapack_complex_double *f, lapack_int *ldf, lapack_complex_double *r, lapack_int *ldr, lapack_complex_double *l, lapack_int *ldl, float *alpha, lapack_int *qblcka, lapack_int *qblckb);

Include Files

mkl.h

Description

The ?latm5 routine generates matrices involved in the Generalized Sylvester equation:

A * R - L * B = C

D * R - L * E = F

They also satisfy the diagonalization condition:

Input Parameters

prtype

Specifies the type of matrices to generate.

If prtype = 1, A and B are Jordan blocks, D and E are identity matrices.

A:

If (i == j) then A_{i, j} = 1.0.

If (j == i + 1) then A_{i, j} = -1.0.

Otherwise A_{i, j} = 0.0, i, j = 1...m

B:

If (i == j) then B_{i, j} = 1.0 - alpha.

If (j == i + 1) then B_{i, j} = 1.0 .

Otherwise B_{i, j} = 0.0, i, j = 1...n.

D:

If (i == j) then D_{i, j} = 1.0.

Otherwise D_{i, j} = 0.0, i, j = 1...m.

E:

If (i == j) then E_{i, j} = 1.0

Otherwise E_{i, j} = 0.0, i, j = 1...n.

L = R are chosen from [-10...10], which specifies the right hand sides (C, F).
If prtype = 2 or 3: Triangular and/or quasi- triangular.

A:

If (i ≤ j) then A_{i, j} = [-1...1].

Otherwise A_{i, j} = 0.0, i, j = 1...M.

If (prtype = 3) then A_{k + 1, k + 1} = A_{k, k};

A_{k + 1, k} = [-1...1];

sign(A_{k, k + 1}) = -(sign(A_{k + 1, k}).

k = 1, m- 1, qblcka

B :

If (i ≤ j) then B_{i, j} = [-1...1].

Otherwise B_{i, j} = 0.0, i, j = 1...n.

If (prtype = 3) thenB_{k + 1, k + 1} = B_{k, k}

B_{k + 1, k} = [-1...1]

sign(B_{k, k + 1})= -(sign(B_{k + 1, k})

k = 1, n - 1, qblckb.

D:

If (i ≤ j) then D_{i, j} = [-1...1].

Otherwise D_{i, j} = 0.0, i, j = 1...m.

E:

If (i <= j) then E_{i, j} = [-1...1].

Otherwise E_{i, j} = 0.0, i, j = 1...N.

L, R are chosen from [-10...10], which specifies the right hand sides (C, F).
If prtype = 4 Full

   A_{i, j} = [-10...10]

   D_{i, j} = [-1...1] i,j = 1...m

   B_{i, j} = [-10...10]

   E_{i, j} = [-1...1] i,j = 1...n

   R_{i, j} = [-10...10]

   L_{i, j} = [-1...1] i = 1..m ,j = 1...n

L and R specifies the right hand sides (C, F).
If prtype = 5 special case common and/or close eigs.

m

Specifies the order of A and D and the number of rows in C, F, R and L.

n

Specifies the order of B and E and the number of columns in C, F, R and L.

lda

The leading dimension of a.

ldb

The leading dimension of b.

ldc

The leading dimension of c.

ldd

The leading dimension of d.

lde

The leading dimension of e.

ldf

The leading dimension of f.

ldr

The leading dimension of r.

ldl

The leading dimension of l.

alpha

Parameter used in generating prtype = 1 and 5 matrices.

qblcka

When prtype = 3, specifies the distance between 2-by-2 blocks on the diagonal in A. Otherwise, qblcka is not referenced. qblcka > 1.

qblckb

When prtype = 3, specifies the distance between 2-by-2 blocks on the diagonal in B. Otherwise, qblckb is not referenced. qblckb > 1.

Output Parameters

a: Array, size lda*m. On exit a contains them-by-m array A initialized according to prtype.
b: Array, size ldb*n. On exit b contains the n-by-n array B initialized according to prtype.
c: Array, size ldc*n. On exit c contains the m-by-n array C initialized according to prtype.
d: Array, size ldd*m. On exit d contains the m-by-m array D initialized according to prtype.
e: Array, size lde*n. On exit e contains the n-by-n array E initialized according to prtype.
f: Array, size ldf*n. On exit f contains the m-by-n array F initialized according to prtype.
r: Array, size ldr*n. On exit R contains the m-by-n array R initialized according to prtype.
l: Array, size ldl*n. On exit l contains the m-by-narray L initialized according to prtype.

Parent topic: LAPACK Auxiliary Routines

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?latm5