hptrd#

chptrd

Functions

void chptrd(
    const char* uplo,
    const INT   n,
          c64*  AP,
          f32*  d,
          f32*  e,
          c64*  tau,
          INT*  info
);

void chptrd(const char *uplo, const INT n, c64 *AP, f32 *d, f32 *e, c64 *tau, INT *info)#

CHPTRD reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.

If UPLO = ‘U’, the matrix Q is represented as a product of elementary reflectors

Q = H(n-1) … H(2) H(1).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, overwriting A(1:i-1,i+1), and tau is stored in TAU(i).

If UPLO = ‘L’, the matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) … H(n-1).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, overwriting A(i+2:n,i), and tau is stored in TAU(i).

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The order of the matrix A. N >= 0.

inout

AP

Complex*16 array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = ‘U’, AP(i + (j-1)*j/2) = A(i,j) for 0<=i<=j; if UPLO = ‘L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n-1. On exit, if UPLO = ‘U’, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = ‘L’, the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details.

out

d

Single precision array, dimension (N). The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).

out

e

Single precision array, dimension (N-1). The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = ‘U’, E(i) = A(i+1,i) if UPLO = ‘L’.

out

tau

Complex*16 array, dimension (N-1). The scalar factors of the elementary reflectors (see Further Details).

out

info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value.

zhptrd

Functions

void zhptrd(
    const char* uplo,
    const INT   n,
          c128* AP,
          f64*  d,
          f64*  e,
          c128* tau,
          INT*  info
);

void zhptrd(const char *uplo, const INT n, c128 *AP, f64 *d, f64 *e, c128 *tau, INT *info)#

ZHPTRD reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.

If UPLO = ‘U’, the matrix Q is represented as a product of elementary reflectors

Q = H(n-1) … H(2) H(1).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, overwriting A(1:i-1,i+1), and tau is stored in TAU(i).

If UPLO = ‘L’, the matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) … H(n-1).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, overwriting A(i+2:n,i), and tau is stored in TAU(i).

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The order of the matrix A. N >= 0.

inout

AP

Complex*16 array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = ‘U’, AP(i + (j-1)*j/2) = A(i,j) for 0<=i<=j; if UPLO = ‘L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n-1. On exit, if UPLO = ‘U’, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = ‘L’, the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details.

out

d

Double precision array, dimension (N). The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).

out

e

Double precision array, dimension (N-1). The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = ‘U’, E(i) = A(i+1,i) if UPLO = ‘L’.

out

tau

Complex*16 array, dimension (N-1). The scalar factors of the elementary reflectors (see Further Details).

out

info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value.

hptrd#

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