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---
:name: sormbr
:md5sum: 30eacbb06a36a13208c27693866dce81
:category: :subroutine
:arguments:
- vect:
:type: char
:intent: input
- side:
:type: char
:intent: input
- trans:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- k:
:type: integer
:intent: input
- a:
:type: real
:intent: input
:dims:
- lda
- MIN(nq,k)
- lda:
:type: integer
:intent: input
- tau:
:type: real
:intent: input
:dims:
- MIN(nq,k)
- c:
:type: real
:intent: input/output
:dims:
- ldc
- n
- ldc:
:type: integer
:intent: input
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "lsame_(&side,\"L\") ? n : lsame_(&side,\"R\") ? m : 0"
- info:
:type: integer
:intent: output
:substitutions:
nq: "lsame_(&side,\"L\") ? m : lsame_(&side,\"R\") ? n : 0"
:fortran_help: " SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C\n\
* with\n\
* SIDE = 'L' SIDE = 'R'\n\
* TRANS = 'N': Q * C C * Q\n\
* TRANS = 'T': Q**T * C C * Q**T\n\
*\n\
* If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C\n\
* with\n\
* SIDE = 'L' SIDE = 'R'\n\
* TRANS = 'N': P * C C * P\n\
* TRANS = 'T': P**T * C C * P**T\n\
*\n\
* Here Q and P**T are the orthogonal matrices determined by SGEBRD when\n\
* reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and\n\
* P**T are defined as products of elementary reflectors H(i) and G(i)\n\
* respectively.\n\
*\n\
* Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the\n\
* order of the orthogonal matrix Q or P**T that is applied.\n\
*\n\
* If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:\n\
* if nq >= k, Q = H(1) H(2) . . . H(k);\n\
* if nq < k, Q = H(1) H(2) . . . H(nq-1).\n\
*\n\
* If VECT = 'P', A is assumed to have been a K-by-NQ matrix:\n\
* if k < nq, P = G(1) G(2) . . . G(k);\n\
* if k >= nq, P = G(1) G(2) . . . G(nq-1).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* = 'Q': apply Q or Q**T;\n\
* = 'P': apply P or P**T.\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* = 'L': apply Q, Q**T, P or P**T from the Left;\n\
* = 'R': apply Q, Q**T, P or P**T from the Right.\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* = 'N': No transpose, apply Q or P;\n\
* = 'T': Transpose, apply Q**T or P**T.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix C. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix C. N >= 0.\n\
*\n\
* K (input) INTEGER\n\
* If VECT = 'Q', the number of columns in the original\n\
* matrix reduced by SGEBRD.\n\
* If VECT = 'P', the number of rows in the original\n\
* matrix reduced by SGEBRD.\n\
* K >= 0.\n\
*\n\
* A (input) REAL array, dimension\n\
* (LDA,min(nq,K)) if VECT = 'Q'\n\
* (LDA,nq) if VECT = 'P'\n\
* The vectors which define the elementary reflectors H(i) and\n\
* G(i), whose products determine the matrices Q and P, as\n\
* returned by SGEBRD.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A.\n\
* If VECT = 'Q', LDA >= max(1,nq);\n\
* if VECT = 'P', LDA >= max(1,min(nq,K)).\n\
*\n\
* TAU (input) REAL array, dimension (min(nq,K))\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i) or G(i) which determines Q or P, as returned\n\
* by SGEBRD in the array argument TAUQ or TAUP.\n\
*\n\
* C (input/output) REAL array, dimension (LDC,N)\n\
* On entry, the M-by-N matrix C.\n\
* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q\n\
* or P*C or P**T*C or C*P or C*P**T.\n\
*\n\
* LDC (input) INTEGER\n\
* The leading dimension of the array C. LDC >= max(1,M).\n\
*\n\
* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK.\n\
* If SIDE = 'L', LWORK >= max(1,N);\n\
* if SIDE = 'R', LWORK >= max(1,M).\n\
* For optimum performance LWORK >= N*NB if SIDE = 'L', and\n\
* LWORK >= M*NB if SIDE = 'R', where NB is the optimal\n\
* blocksize.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN\n CHARACTER TRANST\n INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n INTEGER ILAENV\n EXTERNAL ILAENV, LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SORMLQ, SORMQR, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, MIN\n\
* ..\n"
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