tpmlqt#

Functions

void stpmlqt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const INT            mb,
    const f32*  restrict V,
    const INT            ldv,
    const f32*  restrict T,
    const INT            ldt,
          f32*  restrict A,
    const INT            lda,
          f32*  restrict B,
    const INT            ldb,
          f32*  restrict work,
          INT*           info
);
void stpmlqt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const INT mb, const f32 *restrict V, const INT ldv, const f32 *restrict T, const INT ldt, f32 *restrict A, const INT lda, f32 *restrict B, const INT ldb, f32 *restrict work, INT *info)#

STPMLQT applies a real orthogonal matrix Q obtained from a “triangular-pentagonal” real block reflector H to a general real matrix C, which consists of two blocks A and B.

Parameters

in
side

‘L’: apply Q or Q**T from the Left; ‘R’: apply Q or Q**T from the Right.

in
trans

‘N’: No transpose, apply Q; ‘T’: Transpose, apply Q**T.

in
m

The number of rows of the matrix B. m >= 0.

in
n

The number of columns of the matrix B. n >= 0.

in
k

The number of elementary reflectors whose product defines the matrix Q.

in
l

The order of the trapezoidal part of V. k >= l >= 0. See Further Details.

in
mb

The block size used for the storage of T. k >= mb >= 1. This must be the same value of mb used to generate T in STPLQT.

in
V

Double precision array, dimension (ldv,k). The i-th row must contain the vector which defines the elementary reflector H(i), as returned by STPLQT in B.

in
ldv

The leading dimension of V. ldv >= k.

in
T

Double precision array, dimension (ldt,k). The upper triangular factors of the block reflectors as returned by STPLQT, stored as a mb-by-k matrix.

in
ldt

The leading dimension of T. ldt >= mb.

inout
A

Double precision array, dimension (lda,n) if side=’L’ or (lda,k) if side=’R’. On entry, the k-by-n or m-by-k matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T.

in
lda

The leading dimension of A. If side = ‘L’, lda >= max(1,k); if side = ‘R’, lda >= max(1,m).

inout
B

Double precision array, dimension (ldb,n). On entry, the m-by-n matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T.

in
ldb

The leading dimension of B. ldb >= max(1,m).

out
work

Double precision array. Dimension is n*mb if side=’L’, or m*mb if side=’R’.

out
info

  • = 0: successful exit.

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

Functions

void dtpmlqt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const INT            mb,
    const f64*  restrict V,
    const INT            ldv,
    const f64*  restrict T,
    const INT            ldt,
          f64*  restrict A,
    const INT            lda,
          f64*  restrict B,
    const INT            ldb,
          f64*  restrict work,
          INT*           info
);
void dtpmlqt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const INT mb, const f64 *restrict V, const INT ldv, const f64 *restrict T, const INT ldt, f64 *restrict A, const INT lda, f64 *restrict B, const INT ldb, f64 *restrict work, INT *info)#

DTPMLQT applies a real orthogonal matrix Q obtained from a “triangular-pentagonal” real block reflector H to a general real matrix C, which consists of two blocks A and B.

Parameters

in
side

‘L’: apply Q or Q**T from the Left; ‘R’: apply Q or Q**T from the Right.

in
trans

‘N’: No transpose, apply Q; ‘T’: Transpose, apply Q**T.

in
m

The number of rows of the matrix B. m >= 0.

in
n

The number of columns of the matrix B. n >= 0.

in
k

The number of elementary reflectors whose product defines the matrix Q.

in
l

The order of the trapezoidal part of V. k >= l >= 0. See Further Details.

in
mb

The block size used for the storage of T. k >= mb >= 1. This must be the same value of mb used to generate T in DTPLQT.

in
V

Double precision array, dimension (ldv,k). The i-th row must contain the vector which defines the elementary reflector H(i), as returned by DTPLQT in B.

in
ldv

The leading dimension of V. ldv >= k.

in
T

Double precision array, dimension (ldt,k). The upper triangular factors of the block reflectors as returned by DTPLQT, stored as a mb-by-k matrix.

in
ldt

The leading dimension of T. ldt >= mb.

inout
A

Double precision array, dimension (lda,n) if side=’L’ or (lda,k) if side=’R’. On entry, the k-by-n or m-by-k matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T.

in
lda

The leading dimension of A. If side = ‘L’, lda >= max(1,k); if side = ‘R’, lda >= max(1,m).

inout
B

Double precision array, dimension (ldb,n). On entry, the m-by-n matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T.

in
ldb

The leading dimension of B. ldb >= max(1,m).

out
work

Double precision array. Dimension is n*mb if side=’L’, or m*mb if side=’R’.

out
info

  • = 0: successful exit.

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

Functions

void ctpmlqt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const INT            mb,
    const c64*  restrict V,
    const INT            ldv,
    const c64*  restrict T,
    const INT            ldt,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict B,
    const INT            ldb,
          c64*  restrict work,
          INT*           info
);
void ctpmlqt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const INT mb, const c64 *restrict V, const INT ldv, const c64 *restrict T, const INT ldt, c64 *restrict A, const INT lda, c64 *restrict B, const INT ldb, c64 *restrict work, INT *info)#

CTPMLQT applies a complex unitary matrix Q obtained from a “triangular-pentagonal” complex block reflector H to a general complex matrix C, which consists of two blocks A and B.

Parameters

in
side

‘L’: apply Q or Q**H from the Left; ‘R’: apply Q or Q**H from the Right.

in
trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q**H.

in
m

The number of rows of the matrix B. m >= 0.

in
n

The number of columns of the matrix B. n >= 0.

in
k

The number of elementary reflectors whose product defines the matrix Q.

in
l

The order of the trapezoidal part of V. k >= l >= 0. See Further Details.

in
mb

The block size used for the storage of T. k >= mb >= 1. This must be the same value of mb used to generate T in CTPLQT.

in
V

Complex*16 array, dimension (ldv,k). The i-th row must contain the vector which defines the elementary reflector H(i), as returned by CTPLQT in B.

in
ldv

The leading dimension of V. ldv >= k.

in
T

Complex*16 array, dimension (ldt,k). The upper triangular factors of the block reflectors as returned by CTPLQT, stored as a mb-by-k matrix.

in
ldt

The leading dimension of T. ldt >= mb.

inout
A

Complex*16 array, dimension (lda,n) if side=’L’ or (lda,k) if side=’R’. On entry, the k-by-n or m-by-k matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H.

in
lda

The leading dimension of A. If side = ‘L’, lda >= max(1,k); if side = ‘R’, lda >= max(1,m).

inout
B

Complex*16 array, dimension (ldb,n). On entry, the m-by-n matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H.

in
ldb

The leading dimension of B. ldb >= max(1,m).

out
work

Complex*16 array. Dimension is n*mb if side=’L’, or m*mb if side=’R’.

out
info

  • = 0: successful exit.

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

Functions

void ztpmlqt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const INT            mb,
    const c128* restrict V,
    const INT            ldv,
    const c128* restrict T,
    const INT            ldt,
          c128* restrict A,
    const INT            lda,
          c128* restrict B,
    const INT            ldb,
          c128* restrict work,
          INT*           info
);
void ztpmlqt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const INT mb, const c128 *restrict V, const INT ldv, const c128 *restrict T, const INT ldt, c128 *restrict A, const INT lda, c128 *restrict B, const INT ldb, c128 *restrict work, INT *info)#

ZTPMLQT applies a complex unitary matrix Q obtained from a “triangular-pentagonal” complex block reflector H to a general complex matrix C, which consists of two blocks A and B.

Parameters

in
side

‘L’: apply Q or Q**H from the Left; ‘R’: apply Q or Q**H from the Right.

in
trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q**H.

in
m

The number of rows of the matrix B. m >= 0.

in
n

The number of columns of the matrix B. n >= 0.

in
k

The number of elementary reflectors whose product defines the matrix Q.

in
l

The order of the trapezoidal part of V. k >= l >= 0. See Further Details.

in
mb

The block size used for the storage of T. k >= mb >= 1. This must be the same value of mb used to generate T in ZTPLQT.

in
V

Complex*16 array, dimension (ldv,k). The i-th row must contain the vector which defines the elementary reflector H(i), as returned by ZTPLQT in B.

in
ldv

The leading dimension of V. ldv >= k.

in
T

Complex*16 array, dimension (ldt,k). The upper triangular factors of the block reflectors as returned by ZTPLQT, stored as a mb-by-k matrix.

in
ldt

The leading dimension of T. ldt >= mb.

inout
A

Complex*16 array, dimension (lda,n) if side=’L’ or (lda,k) if side=’R’. On entry, the k-by-n or m-by-k matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H.

in
lda

The leading dimension of A. If side = ‘L’, lda >= max(1,k); if side = ‘R’, lda >= max(1,m).

inout
B

Complex*16 array, dimension (ldb,n). On entry, the m-by-n matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H.

in
ldb

The leading dimension of B. ldb >= max(1,m).

out
work

Complex*16 array. Dimension is n*mb if side=’L’, or m*mb if side=’R’.

out
info

  • = 0: successful exit.

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