stpmqrt - pentagonal" real block reflector H to a general real matrix C, which consists of two blocks
SUBROUTINE STPMQRT(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) CHARACTER*1 SIDE, TRANS INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT REAL V(LDV,*), A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) SUBROUTINE STPMQRT_64(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) CHARACTER*1 SIDE, TRANS INTEGER*8 INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT REAL V(LDV,*), A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE TPMQRT(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) REAL, DIMENSION(:,:) :: V, T, A, B INTEGER :: M, N, K, L, NB, LDV, LDT, LDA, LDB, INFO CHARACTER(LEN=1) :: SIDE, TRANS REAL, DIMENSION(:) :: WORK SUBROUTINE TPMQRT_64(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) REAL, DIMENSION(:,:) :: V, T, A, B INTEGER(8) :: M, N, K, L, NB, LDV, LDT, LDA, LDB, INFO CHARACTER(LEN=1) :: SIDE, TRANS REAL, DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void stpmqrt (char side, char trans, int m, int n, int k, int l, int nb, float *v, int ldv, float *t, int ldt, float *a, int lda, float *b, int ldb, int *info); void stpmqrt_64 (char side, char trans, long m, long n, long k, long l, long nb, float *v, long ldv, float *t, long ldt, float *a, long lda, float *b, long ldb, long *info);
Oracle Solaris Studio Performance Library stpmqrt(3P) NAME stpmqrt - apply 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 SYNOPSIS SUBROUTINE STPMQRT(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) CHARACTER*1 SIDE, TRANS INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT REAL V(LDV,*), A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) SUBROUTINE STPMQRT_64(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) CHARACTER*1 SIDE, TRANS INTEGER*8 INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT REAL V(LDV,*), A(LDA,*), B(LDB,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE TPMQRT(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) REAL, DIMENSION(:,:) :: V, T, A, B INTEGER :: M, N, K, L, NB, LDV, LDT, LDA, LDB, INFO CHARACTER(LEN=1) :: SIDE, TRANS REAL, DIMENSION(:) :: WORK SUBROUTINE TPMQRT_64(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) REAL, DIMENSION(:,:) :: V, T, A, B INTEGER(8) :: M, N, K, L, NB, LDV, LDT, LDA, LDB, INFO CHARACTER(LEN=1) :: SIDE, TRANS REAL, DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void stpmqrt (char side, char trans, int m, int n, int k, int l, int nb, float *v, int ldv, float *t, int ldt, float *a, int lda, float *b, int ldb, int *info); void stpmqrt_64 (char side, char trans, long m, long n, long k, long l, long nb, float *v, long ldv, float *t, long ldt, float *a, long lda, float *b, long ldb, long *info); PURPOSE stpmqrt 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. ARGUMENTS SIDE (input) SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS (input) TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. M (input) M is INTEGER The number of rows of the matrix B. M >= 0. N (input) N is INTEGER The number of columns of the matrix B. N >= 0. K (input) K is INTEGER The number of elementary reflectors whose product defines the matrix Q. L (input) L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. NB (input) NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in STPQRT. V (input) V is REAL array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STPQRT in B. See Further Details. LDV (input) LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N). T (input) T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by STPQRT, stored as a NB-by-K matrix. LDT (input) LDT is INTEGER The leading dimension of the array T. LDT >= NB. A (input/output) A is REAL 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. See Further Details. LDA (input) LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M). B (input/output) B is REAL 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. See Further Details. LDB (input) LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). WORK (output) WORK is REAL array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS The columns of the pentagonal matrix V contain the elementary reflec- tors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangu- lar; if L=0, there is no trapezoidal block, hence V = V1 is rectangu- lar. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by- K. The real orthogonal matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q*C. If TRANS='T' and SIDE='L', C is on exit replaced with Q**T*C. If TRANS='N' and SIDE='R', C is on exit replaced with C*Q. If TRANS='T' and SIDE='R', C is on exit replaced with C*Q**T. 7 Nov 2015 stpmqrt(3P)